JP2009036669A - Welding residual stress analysis method and welding residual stress analysis system - Google Patents

Welding residual stress analysis method and welding residual stress analysis system Download PDF

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JP2009036669A
JP2009036669A JP2007201963A JP2007201963A JP2009036669A JP 2009036669 A JP2009036669 A JP 2009036669A JP 2007201963 A JP2007201963 A JP 2007201963A JP 2007201963 A JP2007201963 A JP 2007201963A JP 2009036669 A JP2009036669 A JP 2009036669A
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dimensional
deformation
residual stress
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welded structure
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Mitsuo Komuro
三男 小室
Tadashi Murofushi
正 室伏
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Toshiba Corp
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Abstract

<P>PROBLEM TO BE SOLVED: To provide an analysis method that can reduce a calculating time and calculating cost while having high analysis accuracy even in a welded structure under conditions where three-dimensional restriction occurs strongly. <P>SOLUTION: A welding residual stress analysis method comprises a three-dimensional thermal deformation quantity acquisition step of acquiring the three-dimensional thermal deformation quantity of the welded structure 26 in a residual stress analysis method by a finite element method of the three-dimensional welded structure 26; a deformation correction quantity computing step of computing the deformation correction quantity of a two-dimensional symmetrical model 30 of the welded structure 26 based on the three-dimensional thermal deformation quantity acquired in the three-dimensional thermal deformation quantity acquisition step; a deformation restricting condition setting step of setting deformation restricting conditions of the two-dimensional symmetrical model 30 based on the computed deformation correction quantity; and a two-dimensional thermal elastoplasticity analysis step of making a two-dimensional thermal elastoplasticity analysis of the two-dimensional symmetrical model 30 under the set deformation restricting conditions. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

本発明は、溶接残留応力を解析によって計算する方法およびそのシステムに係り、特に、３次元的な拘束が強く発生する条件の溶接構造物においても、解析精度が高くかつその計算時間を削減可能な溶接残留応力解析方法および溶接残留応力解析システムに関する。   The present invention relates to a method and system for calculating welding residual stress by analysis, and in particular, even in a welded structure under conditions where three-dimensional constraints are strongly generated, the analysis accuracy is high and the calculation time can be reduced. The present invention relates to a welding residual stress analysis method and a welding residual stress analysis system.

一般に、配管などの溶接構造物は、溶接時の熱源によって引き起こされる急激、且つ局所的な温度変化により残留応力が発生する。この発生する残留応力の値によっては、応力腐食割れ（ＳＣＣ：Ｓｔｒｅｓｓ Ｃｏｒｒｏｓｉｏｎ Ｃｒａｃｋｉｎｇ）などの問題を起こすことがあるために、溶接時の残留応力を予測することは溶接構造物の健全性を評価する上で重要である。このような溶接時の残留応力を予測する方法、すなわち、大型計算機などによって残留応力を数値解析によって予測する方法がある。   Generally, in a welded structure such as a pipe, a residual stress is generated due to a rapid and local temperature change caused by a heat source during welding. Depending on the value of the generated residual stress, problems such as stress corrosion cracking (SCC) may occur, so predicting the residual stress during welding evaluates the soundness of the welded structure. Is important above. There is a method of predicting the residual stress during welding, that is, a method of predicting the residual stress by numerical analysis using a large computer or the like.

従来の溶接構造物の残留応力を予測する方法およびシステムは、解析精度の向上や計算時間の短縮および計算費用の削減などを目的に以下のような種々の方法およびシステムが提案されており、その一例としては、例えば、特開２００４−５３３６６号公報(特許文献１）に開示されている。   Conventional methods and systems for predicting residual stress in welded structures have been proposed for the purpose of improving analysis accuracy, reducing calculation time, and reducing calculation costs. As an example, it is disclosed by Unexamined-Japanese-Patent No. 2004-53366 (patent document 1), for example.

また、溶接時の残留応力を解析する際に、溶接構造物を模擬した３次元解析モデルを用いて伝熱計算（伝熱解析）を行い、溶接構造物の温度分布と温度時刻歴変化を求めるシステムおよび方法がある。このようなシステムおよび方法は、例えば、特開２００５−８３８１０号公報（特許文献２）に開示されている。
特開２００４−５３３６６号公報 特開２００５−８３８１０号公報 Also, when analyzing the residual stress during welding, heat transfer calculation (heat transfer analysis) is performed using a three-dimensional analysis model simulating the welded structure, and the temperature distribution and temperature time history change of the welded structure are obtained. There are systems and methods. Such a system and method are disclosed in, for example, Japanese Patent Laid-Open No. 2005-83810 (Patent Document 2).
JP 2004-53366 A JP 2005-83810 A

上述した従来技術では、２次元解析モデルを用いて残留応力解析を行っている。これは、溶接パスごとに実際の入熱状況を模擬した３次元モデル解析を行うと、溶接パス数が多い部材または部品を対象とした場合、現在の大型計算機の性能をもってしても多大な計算時間と計算費用が必要となるためである。すなわち、残留応力を高精度に解析するための最も信頼性の高い解析手法である３次元モデル解析を行うためには、溶接パス数が少ない部材等に対象が限定されるという課題がある。   In the prior art described above, residual stress analysis is performed using a two-dimensional analysis model. This is because if a three-dimensional model analysis that simulates the actual heat input situation for each welding pass is performed, if a member or part with a large number of welding passes is targeted, even if it has the performance of the current large-scale computer, This is because time and calculation costs are required. That is, in order to perform a three-dimensional model analysis which is the most reliable analysis method for analyzing the residual stress with high accuracy, there is a problem that the target is limited to a member having a small number of welding passes.

一方、計算時間と計算費用を削減する観点から上述した従来の２次元解析モデルを用いた残留応力解析の場合、溶接構造物の幾何形状（例えば、配管径や板厚等）により、溶接構造物内部で３次元的な拘束が強く発生する条件下では、解析精度が悪くなるという課題がある。例えば、小口径の配管などは、上記の３次元的な拘束が強く発生する条件下にあり、従来の解析方法では残留応力を高精度で予測することが困難である。   On the other hand, in the case of residual stress analysis using the above-described conventional two-dimensional analysis model from the viewpoint of reducing calculation time and calculation cost, the welded structure depends on the geometry of the welded structure (for example, pipe diameter, plate thickness, etc.). There is a problem that the analysis accuracy deteriorates under conditions in which three-dimensional constraints are strongly generated inside. For example, a small-diameter pipe or the like is under a condition in which the above three-dimensional constraint is strongly generated, and it is difficult to predict the residual stress with high accuracy by the conventional analysis method.

本発明の目的は、３次元的な拘束が強く発生する条件の溶接構造物においても、解析精度が高く、かつ、その計算時間および計算費用の低減可能な解析手法を提供することである。   An object of the present invention is to provide an analysis method that is high in analysis accuracy and capable of reducing the calculation time and calculation cost even in a welded structure under a condition in which three-dimensional constraints are strongly generated.

本発明に係る溶接残留応力解析方法は、上述した課題を解決するため、特許請求の範囲に記載したように、３次元溶接構造物の有限要素法による残留応力解析方法において、前記３次元溶接構造物の３次元熱変形量を取得する３次元熱変形量取得ステップと、前記３次元熱変形量取得ステップで取得した３次元熱変形量に基づき、前記溶接構造物の回転軸を対称軸として２次元にモデル化された２次元対称モデルの変形補正量を算出する変形補正量算出ステップと、前記変形補正量算出ステップで算出された変形補正量に基づき前記２次元対称モデルの変形拘束条件を設定する変形拘束条件設定ステップと、前記変形拘束条件設定ステップで設定された条件下で前記２次元対称モデルの２次元熱弾塑性解析を行い、前記溶接構造物の溶接残留応力を得る２次元熱弾塑性解析ステップと、を備えることを特徴とする。   In order to solve the above-described problem, the welding residual stress analysis method according to the present invention includes a three-dimensional welded structure according to the finite element method of a three-dimensional welded structure as described in the claims. Based on the three-dimensional thermal deformation amount acquisition step for acquiring the three-dimensional thermal deformation amount of the object and the three-dimensional thermal deformation amount acquired in the three-dimensional thermal deformation amount acquisition step, the rotational axis of the welded structure is 2 A deformation correction amount calculating step for calculating a deformation correction amount of the two-dimensional symmetric model modeled in two dimensions, and setting a deformation constraint condition of the two-dimensional symmetric model based on the deformation correction amount calculated in the deformation correction amount calculating step A deformation constraint condition setting step, and a two-dimensional thermoelastic-plastic analysis of the two-dimensional symmetric model under the conditions set in the deformation constraint condition setting step. Characterized in that it comprises a two-dimensional thermal elastic-plastic analysis to obtain the power, the.

本発明に係る溶接残留応力解析システムは、上述した課題を解決するため、特許請求の範囲に記載したように、溶接残留応力解析の対象となる溶接構造物の２次元対称モデルを用いて２次元熱弾塑性解析を行う際に設定する前記２次元対称モデルの変形拘束条件を決定する変形拘束条件設定手段と、前記変形拘束条件設定手段が決定した変形拘束条件を考慮して前記２次元対称モデルを用いた２次元熱弾塑性解析を行い前記溶接構造物の溶接残留応力解析結果を得る溶接残留応力解析手段とを具備することを特徴とする。   In order to solve the above-described problems, the welding residual stress analysis system according to the present invention uses a two-dimensional symmetry model of a welded structure to be subjected to welding residual stress analysis as described in the claims. Deformation constraint condition setting means for determining the deformation constraint condition of the two-dimensional symmetry model set when performing the thermoelastic-plastic analysis, and the two-dimensional symmetry model in consideration of the deformation constraint condition determined by the deformation constraint condition setting means And a welding residual stress analysis means for obtaining a welding residual stress analysis result of the welded structure by performing a two-dimensional thermoelastic-plastic analysis using a welding.

本発明によれば、比較的短時間で計算可能な３次元モデルを用いた熱弾性解析を行い得られた溶接構造物の熱変形の情報を変形拘束条件として、３次元モデルを用いた熱弾塑性解析に比べて計算時間がはるかに少ない２次元対称モデルを用いた熱弾塑性解析を行うので、３次元的な拘束が強く発生する条件の溶接構造物においても、解析精度が高く、かつ、その計算時間および計算費用の低減可能な溶接残留応力解析方法および溶接残留応力解析システムを提供することができる。   According to the present invention, information on the thermal deformation of a welded structure obtained by performing a thermoelastic analysis using a three-dimensional model that can be calculated in a relatively short time is used as a deformation constraint, and a thermal elastic using the three-dimensional model. Thermoelastic-plastic analysis using a two-dimensional symmetric model that requires much less calculation time than plastic analysis, so even in a welded structure where three-dimensional constraints occur strongly, the analysis accuracy is high, and A welding residual stress analysis method and a welding residual stress analysis system capable of reducing the calculation time and calculation cost can be provided.

以下、本発明に係る溶接残留応力解析方法および溶接残留応力解析システムについて、添付の図面を参照して説明する。   Hereinafter, a welding residual stress analysis method and a welding residual stress analysis system according to the present invention will be described with reference to the accompanying drawings.

尚、本発明に係る溶接残留応力解析システムは、ハードウェアであるコンピュータとソフトウェアである溶接残留応力解析用プログラムとが協働することで、すなわち、コンピュータが溶接残留応力解析用プログラムを実行することで実現されるシステムである。すなわち、以下に説明する各実施形態に係る溶接残留応力解析システムは、ユーザーが指令を入力する入力手段およびコンピュータがユーザーへ情報を提示する出力手段等のマン−マシンインターフェイスや電子情報を所定の記録媒体に記録する記録手段等、コンピュータとして標準的な手段を備えている。   In the welding residual stress analysis system according to the present invention, the hardware computer and the software welding residual stress analysis program cooperate, that is, the computer executes the welding residual stress analysis program. It is a system realized by. That is, the welding residual stress analysis system according to each embodiment described below has a predetermined record of man-machine interface and electronic information such as an input means for a user to input a command and an output means for a computer to present information to the user. Standard means are provided as a computer, such as recording means for recording on a medium.

［第１の実施形態］
図１は、本発明の第１の実施形態に係る溶接残留応力解析システムの一実施例である溶接残留応力解析システム１Ａの機能的構成要素を概略的に示した機能ブロック図である。 [First Embodiment]
FIG. 1 is a functional block diagram schematically showing functional components of a welding residual stress analysis system 1A which is an example of a welding residual stress analysis system according to the first embodiment of the present invention.

図１に示される溶接残留応力解析システム１Ａは、溶接残留応力解析の対象となる溶接構造物（以下、単に解析対象物とする。）の２次元対称モデル３０（後述する図５参照）を用いて２次元熱弾塑性解析を行う際に設定する２次元対称モデル３０の変形拘束条件を決定する変形拘束条件設定手段２Ａと、変形拘束条件設定手段２Ａが決定した変形拘束条件を考慮して解析対象物の２次元対称モデル３０を用いて溶接残留応力解析を得る溶接残留応力解析手段３とを具備する。溶接残留応力解析システム１Ａが求めた溶接残留応力解析結果は、例えば、表示手段４に画像出力される等してユーザーに提示される。   A welding residual stress analysis system 1A shown in FIG. 1 uses a two-dimensional symmetric model 30 (see FIG. 5 to be described later) of a welded structure (hereinafter simply referred to as an analysis target) that is a target of welding residual stress analysis. In consideration of the deformation constraint conditions determined by the deformation constraint condition setting means 2A and the deformation constraint condition setting means 2A for determining the deformation constraint conditions of the two-dimensional symmetry model 30 set when performing the two-dimensional thermoelastic-plastic analysis. Welding residual stress analysis means 3 for obtaining a welding residual stress analysis using a two-dimensional symmetrical model 30 of the object. The welding residual stress analysis result obtained by the welding residual stress analysis system 1A is presented to the user by, for example, outputting an image on the display means 4.

このように、溶接残留応力解析システム１Ａが、２次元対称モデル３０の変形拘束条件を考慮して解析対象物の溶接残留応力解析を行うように構成される理由は、溶接構造物２６（後述する図３参照）の形状によっては、溶接残留応力分布の解析精度が低下する場合があり、この解析精度の低下を抑制するためである。   As described above, the reason why the welding residual stress analysis system 1A is configured to perform the welding residual stress analysis of the analysis object in consideration of the deformation constraint condition of the two-dimensional symmetric model 30 is the welding structure 26 (described later). Depending on the shape of FIG. 3), the analysis accuracy of the welding residual stress distribution may decrease, and this is to suppress the decrease in the analysis accuracy.

溶接残留応力分布の解析精度の低下の要因の一つは、従来の溶接残留応力解析システムでは、２次元対称モデル３０の周方向（図５において、紙面に垂直な方向）の温度分布は一様となるため、溶接残留応力解析手段３で取り扱われる温度情報においても、周方向に一様な温度分布条件で計算される点にある。例えば、小口径配管の溶接や板に配管を溶接した溶接構造物２６などを解析対象とした場合、これらの３次元的な変形挙動が、溶接残留応力の解析結果に対して誤差を与えるものと考えられる。そこで、本発明に係る溶接残留応力解析システム１では、３次元的な変形挙動が顕著に現れる形状を持つ溶接構造物２６に対しては、２次元対称モデル３０を仮想的に変形拘束して計算することで誤差の低減化を図っている。   One of the causes of a decrease in the analysis accuracy of the welding residual stress distribution is that in the conventional welding residual stress analysis system, the temperature distribution in the circumferential direction (direction perpendicular to the paper surface in FIG. 5) of the two-dimensional symmetric model 30 is uniform. Therefore, the temperature information handled by the welding residual stress analysis means 3 is also calculated at a uniform temperature distribution condition in the circumferential direction. For example, when the analysis target is a welded small-diameter pipe or a welded structure 26 in which a pipe is welded to a plate, the three-dimensional deformation behavior gives an error to the analysis result of the welding residual stress. Conceivable. Therefore, in the welding residual stress analysis system 1 according to the present invention, for the welded structure 26 having a shape in which a three-dimensional deformation behavior appears remarkably, a calculation is performed by virtually deforming the two-dimensional symmetry model 30. By doing so, the error is reduced.

続いて、溶接残留応力解析システム１Ａが具備する変形拘束条件設定手段２Ａおよび溶接残留応力解析手段３について説明する。   Next, the deformation constraint condition setting unit 2A and the welding residual stress analysis unit 3 included in the welding residual stress analysis system 1A will be described.

変形拘束条件設定手段２Ａは、３次元伝熱解析を行い解析対象（溶接構造物）の３次元温度分布を示す情報（以下、溶接構造物温度分布とする）５を得る３次元伝熱解析部６と、溶接構造物温度分布５に基づき３次元熱弾性解析を行い解析対象の３次元熱変形量を得る３次元熱弾性解析部７と、解析対象の３次元熱変形量に基づき解析対象の３次元変形補正量を算出する変形補正量算出部８と、変形補正量算出部８が算出した変形補正量を考慮して２次元対称モデル３０の変形を仮想的に拘束する拘束条件を具現化した型枠モデル３１（後述する図５参照）を作成する型枠モデル作成部９とを備える。   The deformation constraint condition setting means 2A performs a three-dimensional heat transfer analysis and obtains information (hereinafter referred to as a welded structure temperature distribution) 5 indicating the three-dimensional temperature distribution of the analysis target (welded structure) 5D. 6, a three-dimensional thermoelastic analysis unit 7 for obtaining a three-dimensional thermal deformation amount to be analyzed by performing a three-dimensional thermoelastic analysis based on the weld structure temperature distribution 5, and an analysis target based on the three-dimensional thermal deformation amount of the analysis target A deformation correction amount calculation unit 8 for calculating a three-dimensional deformation correction amount and a constraint condition for virtually constraining the deformation of the two-dimensional symmetric model 30 in consideration of the deformation correction amount calculated by the deformation correction amount calculation unit 8 are realized. And a formwork model creation unit 9 for creating the formwork model 31 (see FIG. 5 described later).

３次元伝熱解析部６は、３次元モデル２１によってモデル化された溶接構造物２６の３次元伝熱解析を行う機能を有する（３次元伝熱解析機能）。当該機能を用いて、３次元伝熱解析部６は解析対象の溶接条件から伝熱解析を行う。３次元伝熱解析部６は、伝熱解析を行うことで、解析対象の３次元温度分布情報である溶接構造物温度分布５を得る。   The three-dimensional heat transfer analysis unit 6 has a function of performing a three-dimensional heat transfer analysis of the welded structure 26 modeled by the three-dimensional model 21 (three-dimensional heat transfer analysis function). Using this function, the three-dimensional heat transfer analysis unit 6 performs heat transfer analysis from the welding conditions to be analyzed. The three-dimensional heat transfer analysis unit 6 obtains a welded structure temperature distribution 5 which is three-dimensional temperature distribution information to be analyzed by performing heat transfer analysis.

３次元熱弾性解析部７は、３次元熱弾性解析を行う機能を有する（３次元熱弾性解析機能）。３次元熱弾性解析部７は、３次元伝熱解析部６から解析対象である溶接構造物の溶接構造物温度分布５を取得して、解析対象の３次元熱弾性解析を行う。３次元熱弾性解析部７は、３次元熱弾性解析を行うことで、解析対象の３次元熱変形量を得る。   The three-dimensional thermoelastic analysis unit 7 has a function of performing a three-dimensional thermoelastic analysis (three-dimensional thermoelastic analysis function). The three-dimensional thermoelastic analysis unit 7 acquires the welded structure temperature distribution 5 of the welded structure that is the analysis target from the three-dimensional heat transfer analysis unit 6 and performs the three-dimensional thermoelastic analysis of the analysis target. The three-dimensional thermoelastic analysis unit 7 obtains a three-dimensional thermal deformation amount to be analyzed by performing a three-dimensional thermoelastic analysis.

変形補正量算出部８は、例えば、４方位（０度，９０度，１８０度，２７０度）等の数箇所以上において解析対象の３次元熱変形量の情報を取得し、全方位（上記例では４ポイント）の平均熱変形量を算出する。また、変形補正量算出部８は、取得した全方位の解析対象の３次元熱変形量の情報に基づき最大の熱変形量を取得する。そして、最大の熱変形量と平均熱変形量との差分を算出し、算出結果を３次元変形補正量とする。この変形補正量が、２次元対称モデル３０の変形拘束条件となる。   The deformation correction amount calculation unit 8 acquires information on the three-dimensional thermal deformation amount to be analyzed in several locations such as four directions (0 degrees, 90 degrees, 180 degrees, and 270 degrees), for example. Then, an average thermal deformation amount of 4 points) is calculated. Further, the deformation correction amount calculation unit 8 acquires the maximum amount of thermal deformation based on the acquired information on the three-dimensional thermal deformation amount of the omnidirectional analysis target. Then, the difference between the maximum thermal deformation amount and the average thermal deformation amount is calculated, and the calculation result is set as a three-dimensional deformation correction amount. This deformation correction amount becomes a deformation constraint condition of the two-dimensional symmetric model 30.

型枠モデル作成部９は、変形補正量算出部８が算出した３次元変形補正量を考慮して、溶接残留応力解析手段３が熱弾塑性解析時に使用する３次元モデル２１に対応する２次元対称モデル３０の変形を仮想的に拘束する型枠モデル３１を作成する機能を有する（変形拘束モデル作成機能）。拘束条件決定部としての型枠モデル作成部９は、変形補正量算出部８から３次元変形補正量を取得し、取得した３次元変形補正量を考慮して、２次元対称モデル３０の変形を仮想的に拘束する型枠モデル３１を作成する。   The formwork model creation unit 9 takes into consideration the three-dimensional deformation correction amount calculated by the deformation correction amount calculation unit 8, and the two-dimensional model corresponding to the three-dimensional model 21 used by the welding residual stress analysis means 3 during the thermoelastic-plastic analysis. It has a function of creating a form model 31 that virtually constrains deformation of the symmetric model 30 (deformation constraint model creation function). The formwork model creation unit 9 as the constraint condition determination unit acquires the three-dimensional deformation correction amount from the deformation correction amount calculation unit 8, and considers the acquired three-dimensional deformation correction amount to deform the two-dimensional symmetric model 30. A form model 31 that is virtually constrained is created.

また、溶接残留応力解析手段３は、設定された所定の変形拘束条件下において、２次元対称モデル３０の２次元熱弾塑性解析を行うことで、溶接構造物２６の溶接残留応力解析結果を得る手段である。溶接残留応力解析手段３は、３次元伝熱解析部６が得た解析対象の溶接構造物温度分布５および溶接速度に基づいて解析対象の２次元対称モデル３０の温度推移（温度の時刻歴変化）を得る温度情報取得部１１と、２次元対称モデル３０を用いて、変形拘束条件を考慮した２次元の熱弾塑性解析を行う熱弾塑性解析部１２とを備える。   Further, the welding residual stress analysis means 3 obtains a welding residual stress analysis result of the welded structure 26 by performing a two-dimensional thermoelastic-plastic analysis of the two-dimensional symmetric model 30 under a set predetermined deformation constraint condition. Means. The welding residual stress analysis means 3 is a temperature transition (change in temperature history of temperature) of the two-dimensional symmetric model 30 to be analyzed based on the temperature distribution 5 and the welding speed of the analysis target welded structure obtained by the three-dimensional heat transfer analysis unit 6. ) And a thermoelastic-plastic analysis unit 12 that performs a two-dimensional thermoelastic-plastic analysis in consideration of deformation constraint conditions using a two-dimensional symmetric model 30.

温度情報取得部１１は、３次元伝熱解析部６が得た解析対象の溶接構造物温度分布５および溶接速度に基づいて得られる３次元モデル２１の３次元温度推移（温度の時刻歴変化）を、２次元対称モデル３０における２次元の温度分布情報および温度推移情報に変換して取得する機能を有する（２次元温度情報取得機能）。温度情報取得部１１は、２次元温度情報取得機能を用いて、２次元対称モデル３０の温度情報（２次元温度分布および当該温度分布の時刻歴）を取得し、取得した情報を熱弾塑性解析部１２へ送る。   The temperature information acquisition unit 11 is a three-dimensional temperature transition (temperature time history change) of the three-dimensional model 21 obtained based on the weld structure temperature distribution 5 and welding speed to be analyzed obtained by the three-dimensional heat transfer analysis unit 6. Is obtained by converting the two-dimensional temperature distribution information and temperature transition information in the two-dimensional symmetric model 30 (two-dimensional temperature information acquisition function). The temperature information acquisition unit 11 acquires temperature information (two-dimensional temperature distribution and time history of the temperature distribution) of the two-dimensional symmetry model 30 using a two-dimensional temperature information acquisition function, and the acquired information is subjected to thermal elastic-plastic analysis. Send to part 12.

熱弾塑性解析部１２は、２次元対称モデル３０等の２次元モデルについて２次元の熱弾塑性解析を行う機能を有する（２次元熱弾塑性解析機能）。熱弾塑性解析部１２は、２次元熱弾塑性解析機能を用いて、２次元対称モデル３０の熱弾塑性解析を行う。２次元対称モデル３０の熱弾塑性解析については、例えば、特開２００４−５３３６６号公報(特許文献１）に開示される公知技術等を採用することで実施する。   The thermoelastic-plastic analysis unit 12 has a function of performing a two-dimensional thermoelastic-plastic analysis on a two-dimensional model such as the two-dimensional symmetric model 30 (two-dimensional thermoelastic-plastic analysis function). The thermoelastic-plastic analysis unit 12 performs a thermoelastic-plastic analysis of the two-dimensional symmetric model 30 using a two-dimensional thermoelastic-plastic analysis function. The thermoelastic-plastic analysis of the two-dimensional symmetric model 30 is performed by adopting, for example, a known technique disclosed in Japanese Patent Application Laid-Open No. 2004-53366 (Patent Document 1).

尚、溶接残留応力解析システム１Ａにおいて使用するモデル（２次元対称モデル３０他）は、いわゆるソリッドモデルである。   A model (two-dimensional symmetric model 30 and the like) used in the welding residual stress analysis system 1A is a so-called solid model.

次に、図２乃至図５を引用して、変形拘束条件設定手段２Ａの各構成要素の機能および作用について説明する。   Next, the function and action of each component of the deformation constraint condition setting means 2A will be described with reference to FIGS.

図２は、３次元伝熱解析部６が行う３次元伝熱解析の概念を説明する模式図であり、解析対象物の一例として溶接部２０を有する構造物（以下、溶接構造物とする）の３次元モデル２１の一例を示したものである。   FIG. 2 is a schematic diagram for explaining the concept of the three-dimensional heat transfer analysis performed by the three-dimensional heat transfer analysis unit 6, and a structure having a welded portion 20 as an example of an analysis target (hereinafter referred to as a welded structure). An example of the three-dimensional model 21 is shown.

図２に示されるように、変形拘束条件設定手段２Ａの３次元伝熱解析部６では、溶接構造物に対して固定した溶接棒２２の先端を溶接の熱源２３として同じ速度で移動する移動座標系または熱源２３と同じ角速度で回転する回転座標系を用いて伝熱計算（伝熱解析）を実施する。尚、図２において、符号２０ａおよび２０ｂは溶接完了部および溶接未完了部、矢印は溶接棒２２に対する回転方向、符号Ｌは３次元モデル２１の対称軸、すなわち、回転座標系における回転軸である。   As shown in FIG. 2, in the three-dimensional heat transfer analysis unit 6 of the deformation constraint condition setting means 2 </ b> A, the movement coordinates that move at the same speed with the tip of the welding rod 22 fixed to the welded structure as the heat source 23 for welding. Heat transfer calculation (heat transfer analysis) is performed using a rotating coordinate system that rotates at the same angular velocity as the system or heat source 23. In FIG. 2, reference numerals 20a and 20b are welded and unwelded parts, arrows are directions of rotation with respect to the welding rod 22, and L is an axis of symmetry of the three-dimensional model 21, that is, a rotation axis in the rotational coordinate system. .

図３は、図２に示される３次元モデル２１としてモデル化された溶接構造物２６の溶接部２０およびその周辺を拡大して示した概略図である。   FIG. 3 is an enlarged schematic view showing the welded portion 20 and its periphery of the welded structure 26 modeled as the three-dimensional model 21 shown in FIG.

図３に示される溶接構造物２６は、二つの被溶接金属である母材２６ａ，２６ｂを長手方向（軸方向）に突き合わせ、溶接金属で形成される溶接パス２７を５層等の複数層形成（肉盛り）することによって接合された構成された構造物である。図３に示される溶接部２０では、溶接部２０が凹状の形状をしており、この凹状部分について図２に示される溶接棒２２を用いて周方向に５層５パスの溶接が実施されているため、最終的には、溶接部２０の近傍付近に溶接残留応力が発生していると考えられる。   The welded structure 26 shown in FIG. 3 has two base metals 26a and 26b, which are welded metals, butted in the longitudinal direction (axial direction) to form a plurality of weld paths 27 such as five layers formed of weld metal. It is a structured structure joined by (building up). In the welded portion 20 shown in FIG. 3, the welded portion 20 has a concave shape, and five layers and five passes are welded in the circumferential direction using the welding rod 22 shown in FIG. 2. Therefore, it is considered that the welding residual stress is finally generated in the vicinity of the welded portion 20.

３次元伝熱解析部６は、まず、伝熱解析として、溶接パス２７毎に用いる電流値、電圧値、溶接速度および溶接効率等の溶接条件から溶接部２０への入熱量を求める。そして、各溶接パス２７が盛られる順に、順次繰り返し各溶接パス２７に溶接部２０の溶接条件から得られた入熱量を与える。   First, as a heat transfer analysis, the three-dimensional heat transfer analysis unit 6 obtains the heat input to the weld 20 from welding conditions such as a current value, a voltage value, a welding speed, and welding efficiency used for each welding path 27. And the heat input obtained from the welding conditions of the welding part 20 is given to each welding path 27 repeatedly in order in which each welding path 27 is piled up.

続いて、母材２６ａ，２６ｂおよび溶接パス２７として使用する金属の熱伝導率および表面熱伝達率等の解析条件および与えられた熱量に基づき、溶接部２０の温度分布および温度変化等の温度情報の解析を行う。上記伝熱解析は、例えば、特開２００５−８３８１０号公報（特許文献２）に開示された公知技術等の一般的な手法を採用することで実施することができる。上記伝熱解析を行った結果、３次元伝熱解析部６は、３次元モデル（３次元解析メッシュ）２１でモデル化された溶接構造物２６において各溶接パス２７が盛られるときの３次元解析メッシュの温度分布を求めることができる。   Subsequently, based on analysis conditions such as the thermal conductivity and surface heat transfer coefficient of the metals used as the base materials 26a and 26b and the welding path 27 and the given amount of heat, temperature information such as the temperature distribution of the welded portion 20 and temperature changes. Perform analysis. The heat transfer analysis can be performed, for example, by adopting a general technique such as a known technique disclosed in Japanese Patent Laid-Open No. 2005-83810 (Patent Document 2). As a result of the heat transfer analysis, the three-dimensional heat transfer analysis unit 6 performs a three-dimensional analysis when each welding path 27 is formed in the welded structure 26 modeled by the three-dimensional model (three-dimensional analysis mesh) 21. The temperature distribution of the mesh can be obtained.

図４は、図２に示される３次元モデル２１を回転軸Ｌと平行な方向（高さ方向）から見た場合における平面図である。   FIG. 4 is a plan view when the three-dimensional model 21 shown in FIG. 2 is viewed from a direction parallel to the rotation axis L (height direction).

３次元熱弾性解析部７は、３次元解析メッシュの温度分布、すなわち、溶接構造物２６の溶接構造物温度分布５に基づき３次元熱変形量を得るが、３次元熱変形量の求め方は、例えば、図４に示されるように、ある高さの断面において４方位（０度，９０度，１８０度，２７０度）等の数箇所以上の解析箇所において解析対象（ここでは３次元モデル２１）の軸（図２に示される回転軸Ｌ）方向および径方向の外表面および内表面における熱変形量を算出する。軸方向および径方向の熱変形量の算出は、３次元モデル２１の高さ方向において解析に必要な長さ（全長または部分長）に亘り所定の間隔毎に算出される。この結果、溶接構造物の内表面および外表面の３次元熱変形量の情報が得られる。   The three-dimensional thermoelastic analysis unit 7 obtains a three-dimensional thermal deformation amount based on the temperature distribution of the three-dimensional analysis mesh, that is, the weld structure temperature distribution 5 of the welded structure 26. For example, as shown in FIG. 4, the analysis target (here, the three-dimensional model 21) at several or more analysis points such as four directions (0 degrees, 90 degrees, 180 degrees, 270 degrees) in a cross section at a certain height. ) (The rotational axis L shown in FIG. 2) and the amount of thermal deformation on the outer and inner surfaces in the radial direction. The amount of thermal deformation in the axial direction and the radial direction is calculated at predetermined intervals over the length (full length or partial length) required for analysis in the height direction of the three-dimensional model 21. As a result, information on the three-dimensional thermal deformation amounts of the inner surface and the outer surface of the welded structure can be obtained.

変形補正量算出部８は、例えば、４方位（０度，９０度，１８０度，２７０度）等の数箇所以上において解析対象の３次元熱変形量の情報を取得し、全方位（上記例では４ポイント）の平均熱変形量を算出する。また、変形補正量算出部８は、取得した全方位の解析対象の３次元熱変形量の情報に基づき最大の熱変形量を取得する。そして、最大の熱変形量と平均熱変形量との差分を算出し、算出結果を３次元変形補正量とする。   The deformation correction amount calculation unit 8 acquires information on the three-dimensional thermal deformation amount to be analyzed in several locations such as four directions (0 degrees, 90 degrees, 180 degrees, and 270 degrees), for example. Then, an average thermal deformation amount of 4 points) is calculated. Further, the deformation correction amount calculation unit 8 acquires the maximum amount of thermal deformation based on the acquired information on the three-dimensional thermal deformation amount of the omnidirectional analysis target. Then, the difference between the maximum thermal deformation amount and the average thermal deformation amount is calculated, and the calculation result is set as a three-dimensional deformation correction amount.

型枠モデル作成部９は、変形補正量算出部８が算出した３次元変形補正量を考慮して、溶接残留応力解析手段３が熱弾塑性解析時に使用する３次元モデル２１に対応する２次元対称モデル３０の変形を仮想的に拘束する型枠モデル３１を作成する機能を有する（変形拘束モデル作成機能）。型枠モデル作成部９は、変形補正量算出部８から３次元変形補正量を取得し、取得した３次元変形補正量を考慮して、２次元対称モデル３０の変形を拘束する型枠モデル３１を作成する。   The formwork model creation unit 9 takes into consideration the three-dimensional deformation correction amount calculated by the deformation correction amount calculation unit 8, and the two-dimensional model corresponding to the three-dimensional model 21 used by the welding residual stress analysis means 3 during the thermoelastic-plastic analysis. It has a function of creating a form model 31 that virtually constrains deformation of the symmetric model 30 (deformation constraint model creation function). The formwork model creation unit 9 acquires the three-dimensional deformation correction amount from the deformation correction amount calculation unit 8, and takes into consideration the acquired three-dimensional deformation correction amount, and the formwork model 31 that constrains the deformation of the two-dimensional symmetric model 30. Create

図５は、溶接残留応力解析手段３が熱弾塑性解析時に使用する２次元対称モデル３０および型枠モデル作成部９が作成する型枠モデル３１について概略的に表した概略図である。   FIG. 5 is a schematic diagram schematically showing a two-dimensional symmetric model 30 used by the welding residual stress analysis means 3 at the time of thermal elastic-plastic analysis and a mold model 31 created by the mold model creation unit 9.

図５に示される２次元対称モデル３０とは、図２に示される回転軸Ｌを含む平面で３次元モデル２１を切断した場合の断面示す２次元モデルであって溶接残留応力解析手段３が熱弾塑性解析時に使用する２次元モデルである。この２次元対称モデル３０の残留応力を周の全長に亘って解析すれば、３次元モデル２１で模擬される解析対象の残留応力を解析することができる。   The two-dimensional symmetric model 30 shown in FIG. 5 is a two-dimensional model showing a cross section when the three-dimensional model 21 is cut along a plane including the rotation axis L shown in FIG. It is a two-dimensional model used at the time of elastic-plastic analysis. If the residual stress of the two-dimensional symmetric model 30 is analyzed over the entire circumference, the residual stress to be analyzed simulated by the three-dimensional model 21 can be analyzed.

また、型枠モデル３１とは、従来、３次元熱弾塑性解析時の熱変形量の誤差に対して大きくなる２次元熱弾塑性解析時の熱変形量の誤差を抑制するため、２次元対称モデル３０の変形を拘束する変形拘束条件に基づき具体的に２次元対称モデル３０の変形を拘束する変形拘束用治具としてモデル化した２次元モデルである。   In addition, the form model 31 is a two-dimensional symmetry in order to suppress an error in the amount of thermal deformation at the time of two-dimensional thermoelastic-plastic analysis, which becomes larger than an error of the amount of thermal deformation at the time of three-dimensional thermoelastic-plastic analysis. This is a two-dimensional model that is modeled as a deformation restraining jig that specifically restrains deformation of the two-dimensional symmetric model 30 based on a deformation constraint condition that restrains deformation of the model 30.

型枠モデル３１は、解析を行う座標系に完全固定されており、いかなる外部負荷に対して変形しない物体として模擬される。また、型枠モデル３１と２次元対称モデル３０との接触条件として両者は熱的に絶縁されるという条件が与えられており、型枠モデル３１が接触面Ｓを介して熱の影響を受けることはない。   The formwork model 31 is completely fixed to a coordinate system for analysis, and is simulated as an object that does not deform with respect to any external load. Further, as a contact condition between the mold model 31 and the two-dimensional symmetric model 30, a condition that both are thermally insulated is given, and the mold model 31 is affected by heat through the contact surface S. There is no.

次に、本発明の第１の実施形態に係る溶接残留応力解析方法（以下、第１の溶接残留応力解析方法とする）について説明する。   Next, a welding residual stress analysis method according to the first embodiment of the present invention (hereinafter referred to as a first welding residual stress analysis method) will be described.

図６は、第１の溶接残留応力解析方法の一例として実行される溶接残留応力解析システム１Ａの処理ステップ（以下、第１の溶接残留応力解析手順とする）を示した処理フロー図である。   FIG. 6 is a process flow diagram showing processing steps of the welding residual stress analysis system 1A executed as an example of the first welding residual stress analysis method (hereinafter referred to as a first welding residual stress analysis procedure).

第１の溶接残留応力解析手順では、図６に示されるように、溶接残留応力解析手順の実行要求を受け付けて、処理ステップが開始されると（ＳＴＡＲＴ）、まず、ステップＳ１で３次元伝熱解析ステップが実行される。３次元伝熱解析ステップでは、３次元伝熱解析部６が溶接構造物２６の伝熱解析を行い、当該溶接構造物２６の溶接構造物温度分布５を得る。３次元伝熱解析部６が解析対象の溶接構造物温度分布５を得ると、ステップＳ２およびステップＳ５に進み、一方のステップＳ２では３次元熱弾性解析ステップが、他方のステップＳ５では温度情報取得ステップが実行される。   In the first welding residual stress analysis procedure, as shown in FIG. 6, when an execution request for the welding residual stress analysis procedure is received and a processing step is started (START), first, three-dimensional heat transfer is performed in step S1. An analysis step is performed. In the three-dimensional heat transfer analysis step, the three-dimensional heat transfer analysis unit 6 performs heat transfer analysis of the welded structure 26 to obtain a welded structure temperature distribution 5 of the welded structure 26. When the three-dimensional heat transfer analysis unit 6 obtains the temperature distribution 5 of the welded structure to be analyzed, the process proceeds to step S2 and step S5. In one step S2, the three-dimensional thermoelastic analysis step is performed, and in the other step S5, temperature information is acquired. A step is executed.

ステップＳ１に引き続き実行される３次元熱弾性解析ステップ（ステップＳ２）では、３次元熱弾性解析部７が、溶接構造物温度分布５に基づいて解析対象である溶接構造物２６の３次元熱弾性解析を実行し、解析対象の３次元熱変形量を得る。３次元熱弾性解析部７が、溶接構造物２６の３次元熱変形量を得ると、ステップＳ３に進み、変形補正量算出ステップが実行される。   In the three-dimensional thermoelasticity analysis step (step S2) executed subsequent to step S1, the three-dimensional thermoelasticity analysis unit 7 performs the three-dimensional thermoelasticity of the welded structure 26 to be analyzed based on the welded structure temperature distribution 5. The analysis is executed, and the three-dimensional thermal deformation amount to be analyzed is obtained. When the three-dimensional thermoelastic analysis unit 7 obtains the three-dimensional thermal deformation amount of the welded structure 26, the process proceeds to step S3, and a deformation correction amount calculating step is executed.

変形補正量算出ステップ（ステップＳ３）では、変形補正量算出部８が、溶接構造物２６の３次元熱変形量に基づき、２次元対称モデル３０の変形拘束条件となる３次元変形補正量を算出する。変形補正量算出部８が、３次元変形補正量を算出すると、続いて、ステップＳ４に進み、型枠モデル作成ステップが実行される。   In the deformation correction amount calculation step (step S3), the deformation correction amount calculation unit 8 calculates a three-dimensional deformation correction amount that is a deformation constraint condition of the two-dimensional symmetric model 30 based on the three-dimensional thermal deformation amount of the welded structure 26. To do. When the deformation correction amount calculation unit 8 calculates the three-dimensional deformation correction amount, the process proceeds to step S4, where a form model creation step is executed.

型枠モデル作成ステップ（ステップＳ４）では、変形補正量算出ステップ（ステップＳ３）で算出された３次元変形補正量を考慮して、型枠モデル作成部９が、２次元対称モデル３０の変形を仮想的に拘束する型枠モデル３１を作成する。型枠モデル作成部９が、２次元対称モデル３０の変形を仮想的に拘束する型枠モデル３１を作成すると、ステップＳ６に進み、２次元熱弾塑性解析ステップが実行される。   In the mold model creation step (step S4), the mold model creation unit 9 deforms the two-dimensional symmetry model 30 in consideration of the three-dimensional deformation correction amount calculated in the deformation correction amount calculation step (step S3). A form model 31 that is virtually constrained is created. When the formwork model creation unit 9 creates the formwork model 31 that virtually constrains the deformation of the two-dimensional symmetry model 30, the process proceeds to step S6, and a two-dimensional thermoelastic-plastic analysis step is executed.

他方、ステップＳ１に引き続き実行される温度情報取得ステップ（ステップＳ５）では、温度情報取得部１１が溶接構造物温度分布５および溶接速度に基づいて解析対象（溶接構造物２６）の温度情報、すなわち、２次元対称モデル３０の温度分布および温度推移情報（温度の時刻歴変化）を得る。温度情報取得部１１が２次元対称モデル３０の温度分布および当該温度の時刻歴変化の情報を得ると、ステップＳ６に進み、２次元熱弾塑性解析ステップが実行される。   On the other hand, in the temperature information acquisition step (step S5) executed subsequent to step S1, the temperature information acquisition unit 11 performs temperature information on the analysis target (welded structure 26) based on the weld structure temperature distribution 5 and the welding speed, that is, The temperature distribution and temperature transition information (temperature time history change) of the two-dimensional symmetric model 30 are obtained. When the temperature information acquisition unit 11 obtains information on the temperature distribution of the two-dimensional symmetry model 30 and the time history change of the temperature, the process proceeds to step S6, and a two-dimensional thermoelastic-plastic analysis step is executed.

２次元熱弾塑性解析ステップ（ステップＳ６）では、熱弾塑性解析部１２が、ステップＳ５で得られた２次元対称モデル３０の温度情報と、ステップＳ４で作成された型枠モデル３１に基づき、２次元対称モデル３０を型枠モデル３１で拘束した状態、すなわち、変形拘束条件を考慮した熱弾塑性解析を行う。熱弾塑性解析部１２が、２次元対称モデル３０を型枠モデル３１で拘束した状態下で熱弾塑性解析を行い、当該解析結果を得ると、２次元熱弾塑性解析ステップは完了し、第１の溶接残留応力解析手順の全処理ステップが完了する（ＥＮＤ）。２次元熱弾塑性解析ステップで得られた熱弾塑性解析の結果は、溶接構造物２６の溶接残留応力解析結果として、例えば、図１に示される表示手段４等の情報出力手段を通じてユーザーに提示される。   In the two-dimensional thermoelastic-plastic analysis step (step S6), the thermoelastic-plastic analysis unit 12 is based on the temperature information of the two-dimensional symmetry model 30 obtained in step S5 and the form model 31 created in step S4. A state in which the two-dimensional symmetric model 30 is constrained by the form model 31, that is, thermoelastic-plastic analysis is performed in consideration of deformation constraint conditions. When the thermo-elasto-plastic analysis unit 12 performs thermo-elasto-plastic analysis under the condition that the two-dimensional symmetry model 30 is constrained by the mold model 31 and obtains the analysis result, the two-dimensional thermo-elasto-plastic analysis step is completed, All the processing steps of the welding residual stress analysis procedure 1 are completed (END). The result of the thermo-elasto-plastic analysis obtained in the two-dimensional thermo-elasto-plastic analysis step is presented to the user through an information output means such as the display means 4 shown in FIG. Is done.

第１の溶接残留応力解析システム１Ａおよび第１の溶接残留応力解析方法によれば、従来、解析精度が低下していた小口径配管等の３次元的な変形挙動が顕著に現れる形状を持つ溶接構造物２６に対する溶接残留応力解析の際に、仮想的な変形拘束条件を溶接残留応力解析手段３に与えることにより、溶接残留応力解析の精度を向上させることができる。   According to the first welding residual stress analysis system 1A and the first welding residual stress analysis method, a weld having a shape in which three-dimensional deformation behavior such as small-diameter pipes, which has conventionally been reduced in analysis accuracy, remarkably appears. By giving a virtual deformation constraint condition to the welding residual stress analysis means 3 during the welding residual stress analysis for the structure 26, the accuracy of the welding residual stress analysis can be improved.

また、溶接時の電流、電圧、溶接速度等の溶接条件がわかれば当該溶接条件に基づいて溶接残留応力を計算（解析）することができるので、溶接構造物２６の温度、ひずみ、変位などを測定する必要がなく、簡便に溶接残留応力を解析することができる。   In addition, if the welding conditions such as the current, voltage, and welding speed during welding are known, the welding residual stress can be calculated (analyzed) based on the welding conditions. Therefore, the temperature, strain, displacement, etc. of the welded structure 26 can be calculated. There is no need to measure, and the welding residual stress can be easily analyzed.

さらに、比較的短時間で計算可能な３次元モデルを用いた熱弾性解析を行い得られた溶接構造物の熱変形の情報を変形拘束条件として、３次元モデル２１を用いた熱弾塑性解析に比べて計算時間がはるかに少ない２次元対称モデル３０を用いた熱弾塑性解析を行うので、３次元的な拘束が強く発生する条件の溶接構造物２６においても、解析精度が高く、かつ、その計算時間および計算費用を低減することができる。より具体的には、３次元モデル２１を用いた熱弾塑性解析を実施した場合に対して、計算時間は約１／３０〜１／２０に削減することができる。   Furthermore, thermal elastic-plastic analysis using the three-dimensional model 21 is performed using the information on the thermal deformation of the welded structure obtained by performing the thermoelastic analysis using a three-dimensional model that can be calculated in a relatively short time as a deformation constraint. Compared to the thermoelastic-plastic analysis using the two-dimensional symmetric model 30 which requires much less calculation time, the analysis accuracy is high even in the welded structure 26 under the condition that the three-dimensional constraint is strongly generated. Calculation time and calculation cost can be reduced. More specifically, the calculation time can be reduced to about 1/30 to 1/20 compared to the case where the thermoelastic-plastic analysis using the three-dimensional model 21 is performed.

解析の精度については、溶接残留応力解析結果についての評価を説明する説明図として添付した図７（Ａ）および図７（Ｂ）を参照して説明する。なお、図７（Ａ）および図７（Ｂ）において、横軸の応力は、正が引張応力、負が圧縮応力を示しており、縦軸の溶接部中央からの距離は、３次元モデル２１の軸方向の距離であり、正負は溶接部２０からの方向を示す。   The accuracy of the analysis will be described with reference to FIG. 7A and FIG. 7B attached as explanatory diagrams for explaining the evaluation of the welding residual stress analysis result. 7A and 7B, the stress on the horizontal axis indicates tensile stress on the horizontal axis and the compressive stress on the negative axis, and the distance from the center of the weld on the vertical axis is the three-dimensional model 21. The positive / negative sign indicates the direction from the weld 20.

図７（Ａ）および図７（Ｂ）に示されるように、本発明を適用した場合における残留応力分布３２、３次元熱弾塑性解析を行った場合における残留応力分布３３、および、従来の２次元熱弾塑性解析を行った場合における残留応力分布３４を比較すれば、本発明を適用した場合、従来の２次元熱弾塑性解析を行った場合よりも精度良く、かつ、３次元熱弾塑性解析を行う場合と大差ない解析精度を得られることがわかる。   As shown in FIGS. 7A and 7B, the residual stress distribution 32 when the present invention is applied, the residual stress distribution 33 when the three-dimensional thermal elastic-plastic analysis is performed, and the conventional 2 Comparing the residual stress distribution 34 in the case where the three-dimensional thermoelastic-plastic analysis is performed, when the present invention is applied, the three-dimensional thermoelastic-plasticity is more accurate than the conventional two-dimensional thermoelastic-plastic analysis. It can be seen that the analysis accuracy is not much different from the case of performing the analysis.

尚、第１の溶接残留応力解析システム１Ａおよび第１の溶接残留応力解析方法において、溶接残留応力解析時に与える変形拘束条件としての型枠モデル３１は、計算簡略化の観点から、配管外径側の型枠モデル３１を除いた配管内径側のみに型枠モデル３１を配置して行っても良い。これは、配管を溶接した溶接構造物２６の場合、溶接部２０の塑性変形により、溶接部２０の近傍では配管中心方向に変形することが一般的に知られており、このような事情を踏まえたものである。配管内面側のみの型枠モデル３１を配置した場合にも、配管外面側の型枠モデル３１を除かない場合と比べて同様の効果があることを確認している。   In the first welding residual stress analysis system 1A and the first welding residual stress analysis method, the form model 31 as a deformation constraint condition given at the time of welding residual stress analysis is the pipe outer diameter side from the viewpoint of simplifying the calculation. The mold model 31 may be arranged only on the inner diameter side of the pipe excluding the mold model 31. In general, it is known that in the case of a welded structure 26 in which piping is welded, the plastic deformation of the welded portion 20 causes deformation in the vicinity of the welded portion 20 toward the center of the pipe. It is a thing. It has been confirmed that even when the formwork model 31 only on the inner surface side of the pipe is arranged, the same effect is obtained as compared with the case where the formwork model 31 on the outer surface side of the pipe is not removed.

また、３次元熱弾性解析部７が３次元熱変形量を求める際に、３次元熱変形測定箇所は数箇所以上であれば任意で良いが、多くしすぎると測定データが増大してしまうため、必要最低限度の解析精度を維持しつつデータ量を抑制する観点から、図３に示されるように、中心角９０度の均等間隔で４箇所程度を抽出して行うことが好ましい。   In addition, when the three-dimensional thermoelastic analysis unit 7 determines the three-dimensional thermal deformation amount, the number of three-dimensional thermal deformation measurement points may be arbitrary as long as it is several or more, but measurement data increases if the number is too large. From the viewpoint of suppressing the amount of data while maintaining the necessary minimum analysis accuracy, it is preferable to extract about four locations at equal intervals of 90 degrees as shown in FIG.

［第２の実施形態］
図８は、本発明の第２の実施形態に係る溶接残留応力解析システムの一実施例である溶接残留応力解析システム１Ｂの機能的構成要素を概略的に示した機能ブロック図である。 [Second Embodiment]
FIG. 8 is a functional block diagram schematically showing functional components of a welding residual stress analysis system 1B which is an example of a welding residual stress analysis system according to the second embodiment of the present invention.

図８に示されるように、溶接残留応力解析システム１Ｂは、変形拘束条件設定手段２Ｂと、溶接残留応力解析手段３とを具備する。すなわち、図１に示される溶接残留応力解析システム１Ａに対して、変形拘束条件設定手段２Ａの代わりに変形拘束条件設定手段２Ｂを具備する点で相違するが、その他の点では実質的な相違は無い。そこで、本実施形態では、変形拘束条件設定手段２Ｂを中心に説明し、溶接残留応力解析システム１Ｂの構成要素と実質的に相違しない構成要素については同じ符号を付して説明を省略する。   As shown in FIG. 8, the welding residual stress analysis system 1 </ b> B includes a deformation constraint condition setting unit 2 </ b> B and a welding residual stress analysis unit 3. That is, the welding residual stress analysis system 1A shown in FIG. 1 is different from the welding residual stress analysis system 1A in that the deformation constraint condition setting unit 2B is provided instead of the deformation constraint condition setting unit 2A. No. Therefore, in the present embodiment, the deformation constraint condition setting unit 2B will be mainly described, and the constituent elements that are not substantially different from the constituent elements of the welding residual stress analysis system 1B are denoted by the same reference numerals and description thereof is omitted.

図８によれば、変形拘束条件設定手段２Ｂは、３次元伝熱解析部６と、３次元熱弾性解析部７と、変形補正量算出部８と、変形補正量算出部８が算出した変形補正量を考慮して２次元対称モデル３０の変形を仮想的に拘束するための圧力条件（拘束条件）を与える拘束条件決定部としての圧力条件設定部３６とを備える。圧力条件設定部３６が設定する圧力分布および圧力値は、補正すべき変位量と圧力による変位量が同等となる圧力条件である。   According to FIG. 8, the deformation constraint condition setting means 2B includes the deformation calculated by the three-dimensional heat transfer analysis unit 6, the three-dimensional thermoelastic analysis unit 7, the deformation correction amount calculation unit 8, and the deformation correction amount calculation unit 8. A pressure condition setting unit 36 as a constraint condition determining unit that gives a pressure condition (constraint condition) for virtually constraining deformation of the two-dimensional symmetric model 30 in consideration of the correction amount; The pressure distribution and the pressure value set by the pressure condition setting unit 36 are pressure conditions in which the amount of displacement to be corrected is equal to the amount of displacement due to pressure.

後述する図９を引用して、圧力条件設定部３６が設定する圧力分布および圧力値（圧力条件）について説明する。   With reference to FIG. 9 described later, the pressure distribution and pressure value (pressure condition) set by the pressure condition setting unit 36 will be described.

図９は、解析対象物としての２次元対称モデル３０と、圧力条件設定部３６が設定する圧力条件との関係を説明する説明図である。   FIG. 9 is an explanatory diagram for explaining the relationship between the two-dimensional symmetric model 30 as the analysis object and the pressure condition set by the pressure condition setting unit 36.

溶接構造物２６の時刻歴毎の径方向変形を考察すると、溶接パス２７に熱を与えた瞬間から最大温度に達するまでは径方向に対して外側方向に変形すると考えられる。また、最大温度から冷却までは径方向に対して内側方向に変形すると考えられる。そこで、このような温度推移および変形過程を考慮して圧力条件を決定する。   Considering radial deformation of the welded structure 26 for each time history, it is considered that the welded structure 27 is deformed outward from the radial direction until the maximum temperature is reached from the moment when heat is applied to the welding path 27. Further, it is considered that the deformation from the maximum temperature to the cooling is inward with respect to the radial direction. Therefore, the pressure condition is determined in consideration of such temperature transition and deformation process.

圧力条件設定部３６が設定する圧力条件、すなわち、圧力を与える場所とタイミングは、図９に示されるように、溶接パス２７に熱を与えた瞬間から最大温度までは、溶接構造物２６を模擬した２次元対称モデル３０の外壁面３９に圧力を与える方向に、最大温度から冷却までは、２次元対称モデル３０の内壁面４０に圧力を与える方向とすることが望ましい。また、与える圧力の大きさは、例えば、図８に示されるように、溶接部２０からの距離（軸方向位置）が近い程圧力を高く、離れるに従い圧力を低下させるように変化させる。   As shown in FIG. 9, the pressure condition set by the pressure condition setting unit 36, that is, the location and timing at which pressure is applied, simulates the welded structure 26 from the moment the heat is applied to the welding path 27 to the maximum temperature. The direction in which the pressure is applied to the outer wall surface 39 of the two-dimensional symmetric model 30 is preferably the direction in which the pressure is applied to the inner wall surface 40 of the two-dimensional symmetric model 30 from the maximum temperature to the cooling. Moreover, the magnitude | size of the pressure to apply is changed so that a pressure may become high, so that the distance (axial direction position) from the welding part 20 is so close that it leaves | separates, for example, as FIG. 8 shows.

このように第２の溶接残留応力解析システム１Ｂでは、圧力条件を決定して与えることによって、型枠モデル３１を用いて変形を拘束した第１の溶接残留応力解析システム１Ａと同様の作用および効果を得ることができる。すなわち、従来、解析精度が低下していた小口径配管等の３次元的な変形挙動が顕著に現れる形状を持つ溶接構造物２６に対する溶接残留応力解析の際に、仮想的な変形拘束条件を溶接残留応力解析手段３に与えることにより、溶接残留応力解析の精度を向上させることができる。   As described above, in the second welding residual stress analysis system 1B, the same actions and effects as those in the first welding residual stress analysis system 1A in which the deformation is constrained using the mold model 31 by determining and giving the pressure condition. Can be obtained. In other words, when performing a welding residual stress analysis on a welded structure 26 having a shape in which three-dimensional deformation behavior such as a small-diameter pipe, which has conventionally been reduced in analysis accuracy, appears, a virtual deformation constraint condition is welded. By giving the residual stress analysis means 3, the accuracy of the welding residual stress analysis can be improved.

次に、本発明の第２の実施形態に係る溶接残留応力解析方法（以下、第２の溶接残留応力解析方法とする）について説明する。   Next, a welding residual stress analysis method according to the second embodiment of the present invention (hereinafter referred to as a second welding residual stress analysis method) will be described.

図１０は、第２の溶接残留応力解析方法の一例として実行される溶接残留応力解析システム１Ｂの処理ステップ（以下、第２の溶接残留応力解析手順とする）を示した処理フロー図である。   FIG. 10 is a process flow diagram showing processing steps of the welding residual stress analysis system 1B executed as an example of the second welding residual stress analysis method (hereinafter referred to as a second welding residual stress analysis procedure).

図１０に示されるように第２の溶接残留応力解析手順では、図６に示される第１の溶接残留応力解析手順に対して、ステップＳ４の型枠モデル作成ステップの代わりに、ステップＳ１１の圧力条件設定ステップを備える点で相違するが、その他の処理ステップは実質的に相違しない。すなわち、図６に示される処理フロー図において、ステップＳ４とステップＳ１１とを置換した処理フロー図が、第２の溶接残留応力解析手順の処理フロー図となる。そこで、第２の溶接残留応力解析手順の説明では、ステップＳ１１を中心に説明し、その他の処理ステップについての説明は省略する。   As shown in FIG. 10, in the second welding residual stress analysis procedure, the pressure in step S11 is used instead of the mold model creation step in step S4, in contrast to the first welding residual stress analysis procedure shown in FIG. Although different in that it includes a condition setting step, the other processing steps are not substantially different. That is, in the processing flow diagram shown in FIG. 6, a processing flow diagram in which Step S4 and Step S11 are replaced becomes a processing flow diagram of the second welding residual stress analysis procedure. Therefore, in the description of the second welding residual stress analysis procedure, step S11 will be mainly described, and description of other processing steps will be omitted.

第２の溶接残留応力解析手順は、まず、ステップＳ１で３次元伝熱解析ステップが実行された後、３次元熱弾性解析ステップ（ステップＳ２）および変形補正量算出ステップ（ステップＳ３）が実行され、続いて、ステップＳ１１で圧力条件設定ステップが実行される。   In the second welding residual stress analysis procedure, first, after the three-dimensional heat transfer analysis step is executed in step S1, the three-dimensional thermoelastic analysis step (step S2) and the deformation correction amount calculation step (step S3) are executed. Subsequently, a pressure condition setting step is executed in step S11.

圧力条件設定ステップ（ステップＳ１１）では、圧力条件設定部３６がステップＳ３で算出された変形補正量を考慮して、２次元対称モデル３０の変形を仮想的に拘束するための圧力条件を設定する。圧力条件設定ステップ（ステップＳ１１）が完了すると、続いて、ステップＳ６に進む。   In the pressure condition setting step (step S11), the pressure condition setting unit 36 sets a pressure condition for virtually constraining the deformation of the two-dimensional symmetric model 30 in consideration of the deformation correction amount calculated in step S3. . When the pressure condition setting step (step S11) is completed, the process proceeds to step S6.

他方、第２の溶接残留応力解析手順においても、第１の溶接残留応力解析手順と同様、ステップＳ２とは別に、温度時刻歴情報取得ステップ（ステップＳ５）がステップＳ１に続いて実行される。温度時刻歴情報取得ステップ（ステップＳ５）が完了し、圧力条件設定ステップ（ステップＳ１１）が完了している場合には、ステップＳ６で２次元熱弾塑性解析ステップが実行される。２次元熱弾塑性解析ステップが完了すると、第２の溶接残留応力解析手順の全処理ステップが完了する。   On the other hand, also in the second welding residual stress analysis procedure, a temperature time history information acquisition step (step S5) is executed subsequent to step S1, as in the first welding residual stress analysis procedure. When the temperature time history information acquisition step (step S5) is completed and the pressure condition setting step (step S11) is completed, a two-dimensional thermoelastic-plastic analysis step is executed in step S6. When the two-dimensional thermoelastic-plastic analysis step is completed, all processing steps of the second welding residual stress analysis procedure are completed.

第２の溶接残留応力解析システム１Ｂおよび第２の溶接残留応力解析方法によれば、第１の溶接残留応力解析システム１Ａおよび第１の溶接残留応力解析方法と同様の効果を得ることができる。すなわち、従来、解析精度が低下していた小口径配管等の３次元的な変形挙動が顕著に現れる形状を持つ溶接構造物２６に対する溶接残留応力解析の際に、仮想的な変形拘束条件を溶接残留応力解析手段３に与えることにより、溶接残留応力解析の精度を向上させることができる。   According to the second welding residual stress analysis system 1B and the second welding residual stress analysis method, the same effects as those of the first welding residual stress analysis system 1A and the first welding residual stress analysis method can be obtained. In other words, when performing a welding residual stress analysis on a welded structure 26 having a shape in which three-dimensional deformation behavior such as a small-diameter pipe, which has conventionally been reduced in analysis accuracy, appears, a virtual deformation constraint condition is welded. By giving the residual stress analysis means 3, the accuracy of the welding residual stress analysis can be improved.

尚、圧力条件設定の際には、計算簡略化のため、板厚全体で仮想的な変形拘束条件を決定し、圧力値を溶接構造物２６の溶接パス２７の層の深さ毎、すなわち、溶接パス２７の層の厚さの割合に応じて変化させても良い。   When setting the pressure condition, for the sake of simplification of calculation, a virtual deformation constraint condition is determined for the entire plate thickness, and the pressure value is determined for each layer depth of the weld path 27 of the welded structure 26, that is, You may change according to the ratio of the thickness of the layer of the welding pass 27. FIG.

［第３の実施形態］
図１１は、本発明の第３の実施形態に係る溶接残留応力解析システムの一実施例である溶接残留応力解析システム１Ｃの機能的構成要素を概略的に示す機能ブロック図である。 [Third Embodiment]
FIG. 11 is a functional block diagram schematically showing functional components of a welding residual stress analysis system 1C which is an example of a welding residual stress analysis system according to the third embodiment of the present invention.

溶接残留応力解析システム１Ｃは、図２に示される３次元モデル２１の有限要素法の要素タイプがいわゆるソリッドタイプではなく板厚方向の計算点を簡略化したシェルタイプ（３次元シェル要素）となる点で異なる。３次元シェル要素の３次元モデル２１を使用する場合、溶接構造物２６の板厚方向の計算点が簡略化されているため、３次元伝熱解析部６が伝熱解析を行っても、溶接構造物２６の径方向の温度分布を得ることができないという点で溶接残留応力解析システム１Ａと違いがある。   In the welding residual stress analysis system 1C, the element type of the finite element method of the three-dimensional model 21 shown in FIG. 2 is not a so-called solid type but a shell type (three-dimensional shell element) in which calculation points in the plate thickness direction are simplified. It is different in point. When the three-dimensional model 21 of the three-dimensional shell element is used, the calculation points in the thickness direction of the welded structure 26 are simplified, so that even if the three-dimensional heat transfer analysis unit 6 performs the heat transfer analysis, welding is performed. It differs from the welding residual stress analysis system 1A in that the temperature distribution in the radial direction of the structure 26 cannot be obtained.

上記のような相違点を有することから、図１１に示される溶接残留応力解析システム１Ｃは、溶接残留応力解析システム１Ａに対して、溶接残留応力解析手段３の代わりに、溶接残留応力解析手段３Ｃを具備する点で相違する。より具体的には、図１１に示される溶接残留応力解析システム１Ｃは、温度情報取得部１１の代わりに、溶接構造物２６の２次元対称モデル３０を用いた２次元伝熱解析結果に基づいて、２次元温度分布および温度時刻歴を得る温度情報取得部１１Ｃを備える点で相違するが、その他の点については、実質的に相違しない。そこで、溶接残留応力解析システム１Ａの構成要素と実質的に相違しない構成要素については同じ符号を付して説明を省略する。   Because of the differences as described above, the welding residual stress analysis system 1C shown in FIG. 11 is different from the welding residual stress analysis system 1A in place of the welding residual stress analysis means 3 in that the welding residual stress analysis means 3C. Is different. More specifically, the welding residual stress analysis system 1 </ b> C shown in FIG. 11 is based on a two-dimensional heat transfer analysis result using a two-dimensional symmetric model 30 of the welded structure 26 instead of the temperature information acquisition unit 11. The difference is that a temperature information acquisition unit 11C that obtains a two-dimensional temperature distribution and temperature time history is provided, but the other points are not substantially different. Therefore, the constituent elements that are not substantially different from the constituent elements of the welding residual stress analysis system 1A are denoted by the same reference numerals and description thereof is omitted.

図１１によれば、溶接残留応力解析システム１Ｃは、変形拘束条件設定手段２Ｃと、変形拘束条件設定手段２Ｃが決定した変形拘束条件を考慮して解析対象物の２次元対称モデル３０を用いて溶接残留応力解析を行う溶接残留応力解析手段３Ｃとを具備する。変形拘束条件設定手段２Ｃは、図１に示される変形拘束条件設定手段２Ａと同じく３次元伝熱解析部６、３次元熱弾性解析部７、変形補正量算出部８および型枠モデル作成部９を備えており、３次元熱弾性解析手段７が３次元伝熱解析部６から３次元伝熱解析結果としての溶接構造物２６の３次元温度分布を取得して処理を実行する点を除き実質的に相違しない。すなわち、各手段６，７，８，９で実行される処理内容は実質的に同様である。   According to FIG. 11, the welding residual stress analysis system 1C uses the deformation constraint condition setting means 2C and the deformation constraint condition determined by the deformation constraint condition setting means 2C using the two-dimensional symmetric model 30 of the analysis object. Welding residual stress analysis means 3C for performing welding residual stress analysis. Similar to the deformation constraint condition setting means 2A shown in FIG. 1, the deformation constraint condition setting means 2C is a three-dimensional heat transfer analysis section 6, a three-dimensional thermoelastic analysis section 7, a deformation correction amount calculation section 8, and a formwork model creation section 9. Except that the three-dimensional thermoelastic analysis means 7 acquires the three-dimensional temperature distribution of the welded structure 26 as a three-dimensional heat transfer analysis result from the three-dimensional heat transfer analysis unit 6 and executes the process. There is no difference. That is, the processing contents executed by each means 6, 7, 8, 9 are substantially the same.

また、溶接残留応力解析手段３Ｃは、溶接構造物２６の２次元対称モデル３０を用いた２次元伝熱解析結果に基づいて、２次元温度分布および温度時刻歴を得る温度情報取得部１１Ｃと、熱弾塑性解析部１２とを備える。温度情報取得部１１Ｃは、２次元伝熱解析結果に基づいて、２次元温度分布および温度時刻歴を得る機能を有する（温度情報取得機能）。温度情報取得部１１Ｃは、温度情報取得機能を用いて、２次元対称モデル３０の２次元温度分布および温度時刻歴を示す情報を取得し、取得した情報を熱弾塑性解析部１２へ送る。   Further, the welding residual stress analysis means 3C includes a temperature information acquisition unit 11C that obtains a two-dimensional temperature distribution and a temperature time history based on a two-dimensional heat transfer analysis result using the two-dimensional symmetric model 30 of the welded structure 26; And a thermoelastic-plastic analysis unit 12. The temperature information acquisition unit 11C has a function of obtaining a two-dimensional temperature distribution and a temperature time history based on a two-dimensional heat transfer analysis result (temperature information acquisition function). The temperature information acquisition unit 11 </ b> C acquires information indicating the two-dimensional temperature distribution and temperature time history of the two-dimensional symmetrical model 30 using the temperature information acquisition function, and sends the acquired information to the thermoelastic-plastic analysis unit 12.

このように構成される溶接残留応力解析システム１Ｃによれば、３次元モデル２１として３次元シェル要素を用いれば、ソリッド要素の３次元モデル２１を用いて行う場合に比べて、解析時間の短縮化が図れるメリットがある。尚、溶接残留応力解析システム１Ｃでは、２次元伝熱解析結果を得るために別途２次元伝熱解析を行う必要があるが、変形拘束条件設定手段２Ｃが変形拘束条件を決定するまでの間に、２次元伝熱解析および２次元対称モデル３０の２次元温度分布および温度時刻歴を示す情報を取得することができるので、別途２次元伝熱解析を行う必要がある点は特段の不利益にはならない。   According to the weld residual stress analysis system 1C configured as described above, if a three-dimensional shell element is used as the three-dimensional model 21, the analysis time can be shortened compared to the case where the three-dimensional model 21 of solid elements is used. There is an advantage that can be achieved. In the welding residual stress analysis system 1C, it is necessary to separately perform a two-dimensional heat transfer analysis in order to obtain a two-dimensional heat transfer analysis result, but until the deformation constraint condition setting means 2C determines the deformation constraint condition. Since the information indicating the two-dimensional heat transfer analysis and the two-dimensional temperature distribution and temperature time history of the two-dimensional symmetric model 30 can be acquired, it is a special disadvantage that a separate two-dimensional heat transfer analysis needs to be performed. Must not.

次に、本発明の第３の実施形態に係る溶接残留応力解析方法（以下、第３の溶接残留応力解析方法とする）の一例として実行される溶接残留応力解析システム１Ｃの処理ステップ（以下、第３の溶接残留応力解析手順とする）について説明する。   Next, processing steps (hereinafter, referred to as a welding residual stress analysis system 1C) executed as an example of a welding residual stress analysis method (hereinafter referred to as a third welding residual stress analysis method) according to the third embodiment of the present invention. The third welding residual stress analysis procedure will be described.

第３の溶接残留応力解析手順は、図６に示される第１の溶接残留応力解析手順に対して、ステップＳ５の温度情報取得ステップの処理内容が相違するが、その他の処理ステップは実質的に相違しない。そこで、第３の溶接残留応力解析手順の説明では、ステップＳ５を中心に説明し、その他の処理ステップについての説明は省略する。   The third welding residual stress analysis procedure is different from the first welding residual stress analysis procedure shown in FIG. 6 in the processing contents of the temperature information acquisition step in step S5, but the other processing steps are substantially the same. No difference. Therefore, in the description of the third welding residual stress analysis procedure, step S5 will be mainly described, and description of other processing steps will be omitted.

第３の溶接残留応力解析手順では、まず、ステップＳ１で３次元伝熱解析ステップが実行される。その後、一方では、３次元熱弾性解析ステップ（ステップＳ２）、変形補正量算出ステップ（ステップＳ３）および型枠モデル作成ステップ（ステップＳ４）が実行される。他方では、ステップＳ１に引き続き温度情報取得ステップ（ステップＳ５）が実行される。   In the third welding residual stress analysis procedure, first, a three-dimensional heat transfer analysis step is executed in step S1. Thereafter, on the other hand, a three-dimensional thermoelastic analysis step (step S2), a deformation correction amount calculation step (step S3), and a form model creation step (step S4) are executed. On the other hand, a temperature information acquisition step (step S5) is executed subsequent to step S1.

第３の溶接残留応力解析手順における温度情報取得ステップでは、温度情報取得部１１Ｃが、２次元対称モデル３０の２次元温度分布および温度推移情報（温度時刻歴を示す情報）を取得する。この点が、２次元対称モデル３０の温度分布および温度推移情報（温度の時刻歴変化）を得る第１の溶接残留応力解析手順における温度情報取得ステップと異なる点である。   In the temperature information acquisition step in the third welding residual stress analysis procedure, the temperature information acquisition unit 11C acquires the two-dimensional temperature distribution and temperature transition information (information indicating the temperature time history) of the two-dimensional symmetry model 30. This point is different from the temperature information acquisition step in the first welding residual stress analysis procedure for obtaining the temperature distribution and temperature transition information (temperature time history change) of the two-dimensional symmetrical model 30.

第３の溶接残留応力解析システム１Ｃおよび第３の溶接残留応力解析方法によれば、第１の溶接残留応力解析システム１Ａおよび第１の溶接残留応力解析方法による効果に加え、解析時間の更なる短縮化を図ることができる。尚、図９に示される溶接残留応力解析システム１Ｃは、シェル要素の３次元モデル２１を用いた解析を溶接残留応力解析システム１Ａに適用した例であるが、他の実施形態に係る溶接残留応力解析システム１Ｂ，１Ｄ，１Ｅに適用しても良い。   According to the third welding residual stress analysis system 1C and the third welding residual stress analysis method, the analysis time is further increased in addition to the effects of the first welding residual stress analysis system 1A and the first welding residual stress analysis method. Shortening can be achieved. The welding residual stress analysis system 1C shown in FIG. 9 is an example in which the analysis using the three-dimensional model 21 of the shell element is applied to the welding residual stress analysis system 1A, but the welding residual stress according to another embodiment is used. You may apply to analysis system 1B, 1D, 1E.

［第４の実施形態］
図１２は、本発明の第４の実施形態に係る溶接残留応力解析システムの一実施例である溶接残留応力解析システム１Ｄの機能的構成要素を概略的に示す機能ブロック図である。 [Fourth Embodiment]
FIG. 12 is a functional block diagram schematically showing functional components of a welding residual stress analysis system 1D which is an example of a welding residual stress analysis system according to the fourth embodiment of the present invention.

図１２に示されるように、溶接残留応力解析システム１Ｄは、変形拘束条件設定手段２Ｄと、溶接残留応力解析手段３とを具備する。すなわち、図１に示される溶接残留応力解析システム１Ａに対して、変形拘束条件設定手段２Ａの代わりに変形拘束条件設定手段２Ｄを具備する点で相違するが、その他の点では実質的な相違は無い。そこで、本実施形態では、変形拘束条件設定手段２Ｄを中心に説明し、溶接残留応力解析システム１Ｄの構成要素と実質的に相違しない構成要素については同じ符号を付して説明を省略する。   As shown in FIG. 12, the welding residual stress analysis system 1 </ b> D includes a deformation constraint condition setting unit 2 </ b> D and a welding residual stress analysis unit 3. That is, the welding residual stress analysis system 1A shown in FIG. 1 is different from the welding residual stress analysis system 1A in that the deformation constraint condition setting unit 2D is provided instead of the deformation constraint condition setting unit 2A. No. Therefore, in the present embodiment, the deformation constraint condition setting unit 2D will be mainly described, and components that are not substantially different from the components of the welding residual stress analysis system 1D are denoted by the same reference numerals and description thereof is omitted.

溶接残留応力解析システム１Ｄの変形拘束条件設定手段２Ｄは、３次元伝熱解析部６と、この３次元伝熱解析部６が溶接構造物２６の３次元伝熱解析を行った結果得られる３次元温度分布情報（溶接構造物温度分布）５および溶接構造物２６である母材２６ａ，２６ｂの線膨張係数に基づいて３次元変形補正量を算出する変形補正量算出部８Ｄと、型枠モデル作成部９とを備える。すなわち、変形拘束条件設定手段２Ｄは、図１に示される変形拘束条件設定手段２Ａに対して変形量補正の方法が異なる。   The deformation constraint condition setting means 2D of the welding residual stress analysis system 1D is obtained as a result of the 3D heat transfer analysis unit 6 and the 3D heat transfer analysis unit 6 performing 3D heat transfer analysis of the welded structure 26 3 A deformation correction amount calculation unit 8D that calculates a three-dimensional deformation correction amount based on the three-dimensional temperature distribution information (weld structure temperature distribution) 5 and the linear expansion coefficients of the base materials 26a and 26b that are the welded structures 26, and a form model And a creation unit 9. That is, the deformation constraint condition setting unit 2D is different in a method of correcting the deformation amount from the deformation constraint condition setting unit 2A shown in FIG.

図１３は、変形拘束条件設定手段２Ｄにおいてなされる変形量補正の方法について説明する説明図である。より具体的には、図１３（Ａ）は、溶接構造物２６の２次元対称モデル３０の周方向温度分布を示す図であり、図１３（Ｂ）は、仮想的な変形状態を示す概略図である。尚、図１３（Ａ）において、符号４１は従来の２次元熱弾塑性解析において用いる２次元対称モデル３０（詳細は図５を参照）の周方向の温度分布であり、符号４２は実際の溶接構造物２６の周方向の温度分布である。   FIG. 13 is an explanatory diagram for explaining a deformation amount correction method performed in the deformation constraint condition setting unit 2D. More specifically, FIG. 13A is a diagram showing a circumferential temperature distribution of the two-dimensional symmetric model 30 of the welded structure 26, and FIG. 13B is a schematic diagram showing a virtual deformation state. It is. In FIG. 13A, reference numeral 41 denotes a circumferential temperature distribution of the two-dimensional symmetric model 30 (see FIG. 5 for details) used in the conventional two-dimensional thermal elastic-plastic analysis, and reference numeral 42 denotes actual welding. This is a temperature distribution in the circumferential direction of the structure 26.

図１３（Ａ）および図１３（Ｂ）を引用して、変形拘束条件設定手段２Ｄにおいてなされる変形量補正の方法について説明する。まず、従来の２次元対称モデル３０を用いての２次元熱弾塑性解析では、図１３（Ａ）に示されるように、周方向の温度を均一とみなした温度分布４１を使用していたが、実際の温度分布４２とは乖離していたため、現実の溶接構造物２６の変形と比較すると、当該溶接構造物２６の径方向および軸方向に対して過剰な変形が起き、熱弾塑性解析の精度の低下を招来していた。   With reference to FIGS. 13A and 13B, a deformation amount correction method performed in the deformation constraint condition setting unit 2D will be described. First, in the two-dimensional thermal elastic-plastic analysis using the conventional two-dimensional symmetric model 30, as shown in FIG. 13A, a temperature distribution 41 that considers the temperature in the circumferential direction to be uniform is used. Since the actual temperature distribution 42 deviates from that of the actual welded structure 26, excessive deformation occurs in the radial direction and the axial direction of the welded structure 26, and the thermal elastic-plastic analysis is performed. The accuracy was reduced.

そこで、変形拘束条件設定手段２Ｄでは、３次元温度分布情報（溶接構造物温度分布）５および母材２６ａ，２６ｂ（溶接構造物２６）の線膨張係数に基づいて３次元変形補正量を算出し、算出した３次元変形補正量を考慮した２次元熱弾塑性解析を行う。この結果、溶接残留応力解析システム１Ｄは、従来の２次元熱弾塑性解析よりも精度が良く、３次元熱弾塑性解析を行う場合よりも簡易な弾塑性解析の提供を実現する。   Therefore, the deformation constraint condition setting means 2D calculates the three-dimensional deformation correction amount based on the three-dimensional temperature distribution information (welded structure temperature distribution) 5 and the linear expansion coefficients of the base materials 26a and 26b (welded structure 26). Then, a two-dimensional thermal elastic-plastic analysis is performed in consideration of the calculated three-dimensional deformation correction amount. As a result, the welding residual stress analysis system 1D is more accurate than the conventional two-dimensional thermoelastic-plastic analysis, and provides a simpler elastoplastic analysis than when performing the three-dimensional thermoelastic-plastic analysis.

変形補正量算出部８Ｄが行う具体的な変形量補正方法は、まず、図１３（Ｂ）に示されるように、実際に周方向の温度勾配が存在する領域、すなわち、変形を生じる周方向側の長さ（以下、変形範囲長とする）Ｌを特定する。変形範囲長Ｌの特定は、溶接構造物温度分布５に基づいて行う。続いて、変形範囲長Ｌから推測される仮想的な径方向変形範囲４３を算出する。   A specific deformation amount correction method performed by the deformation correction amount calculation unit 8D is as follows. First, as shown in FIG. 13B, a region where a temperature gradient in the circumferential direction actually exists, that is, a circumferential side where deformation occurs. The length L (hereinafter referred to as the deformation range length) L is specified. The deformation range length L is specified based on the weld structure temperature distribution 5. Subsequently, a virtual radial deformation range 43 estimated from the deformation range length L is calculated.

径方向変形範囲４３の算出は、溶接構造物２６の材質（線膨張係数）およびその場所における板厚といった既知の物性値と、変形補正算出時に設定される溶接構造物２６における場所および当該場所の温度とに基づいて行う。ここで、溶接構造物２６に関する物性値の情報は、予め格納しておいた所定の場所から読み出される場合もあるし、変形補正算出を開始する際にユーザーの入力によって与えられる場合もある。   The calculation of the radial deformation range 43 is based on the known physical property values such as the material (linear expansion coefficient) of the welded structure 26 and the plate thickness at that location, the location in the welded structure 26 set at the time of deformation correction calculation, and the location of the location. Based on temperature. Here, the physical property value information related to the welded structure 26 may be read from a predetermined location stored in advance, or may be given by user input when starting the deformation correction calculation.

続いて、変形補正量算出部８Ｄは、算出した径方向変形範囲４３と周方向全長と比率を求め、この比率を周方向に対して一様に変形している径方向変位量に積算することにより、変形補正量を決定する。実際に周方向の温度勾配が存在する領域（変形範囲長Ｌ）は、実験的な温度測定結果および３次元伝熱解析の結果から、６０ｍｍであることが判っている。この変形補正量を基にして仮想的な変形拘束条件を設定する。すなわち、型枠モデル作成部９が２次元対称モデル３０の変形を仮想的に拘束する型枠モデル３１を作成する。   Subsequently, the deformation correction amount calculation unit 8D obtains the calculated radial deformation range 43 and the total length in the circumferential direction, and integrates this ratio with the radial displacement that is uniformly deformed in the circumferential direction. Thus, the deformation correction amount is determined. The region where the temperature gradient in the circumferential direction actually exists (deformation range length L) is found to be 60 mm from experimental temperature measurement results and three-dimensional heat transfer analysis results. Based on the deformation correction amount, a virtual deformation constraint condition is set. That is, the formwork model creation unit 9 creates a formwork model 31 that virtually restrains deformation of the two-dimensional symmetric model 30.

次に、本発明の第４の実施形態に係る溶接残留応力解析方法（以下、第４の溶接残留応力解析方法とする）について説明する。   Next, a welding residual stress analysis method according to the fourth embodiment of the present invention (hereinafter referred to as a fourth welding residual stress analysis method) will be described.

図１４は、第４の溶接残留応力解析方法の一例として実行される溶接残留応力解析システム１Ｄの処理ステップ（以下、第４の溶接残留応力解析手順とする）の処理フロー図である。尚、第４の溶接残留応力解析手順の説明において、上述した溶接残留応力解析手順と重複する処理ステップについての説明は省略する。   FIG. 14 is a process flow diagram of processing steps (hereinafter referred to as a fourth welding residual stress analysis procedure) of the welding residual stress analysis system 1D executed as an example of the fourth welding residual stress analysis method. In the description of the fourth welding residual stress analysis procedure, the description of the processing steps overlapping with the welding residual stress analysis procedure described above is omitted.

第４の溶接残留応力解析手順では、まず、ステップＳ１で３次元伝熱解析ステップが実行される。その後、一方では、ステップＳ２１に進み、変形補正量算出ステップ（ステップＳ２１）が実行される。変形補正量算出ステップ（ステップＳ２１）では、変形補正量算出部８Ｄが３次元温度分布情報（溶接構造物温度分布）５および母材２６ａ，２６ｂ（溶接構造物２６）の線膨張係数に基づいて３次元変形補正量を算出する。変形補正量算出部８Ｄが３次元変形補正量を算出すると、変形補正量算出ステップは完了し、続いて、ステップＳ４に進む。ステップＳ４以降の処理ステップおよびステップＳ１以降の他方の処理ステップ（ステップＳ５およびステップＳ６）は第１の溶接残留応力解析手順と同様である。   In the fourth welding residual stress analysis procedure, first, a three-dimensional heat transfer analysis step is executed in step S1. Thereafter, on the other hand, the process proceeds to step S21, and a deformation correction amount calculating step (step S21) is executed. In the deformation correction amount calculating step (step S21), the deformation correction amount calculating unit 8D is based on the three-dimensional temperature distribution information (welding structure temperature distribution) 5 and the linear expansion coefficient of the base materials 26a and 26b (welding structure 26). A three-dimensional deformation correction amount is calculated. When the deformation correction amount calculation unit 8D calculates the three-dimensional deformation correction amount, the deformation correction amount calculation step is completed, and then the process proceeds to step S4. The processing steps after step S4 and the other processing steps after step S1 (step S5 and step S6) are the same as those in the first welding residual stress analysis procedure.

尚、図１４に示される第４の溶接残留応力解析手順では、型枠モデル作成ステップ（ステップＳ４）を備えているが、型枠モデル作成ステップの代わりに圧力条件設定ステップ（ステップＳ１１）を備えても良い。   The fourth welding residual stress analysis procedure shown in FIG. 14 includes a mold model creation step (step S4), but includes a pressure condition setting step (step S11) instead of the mold model creation step. May be.

第４の溶接残留応力解析システム１Ｄおよび第４の溶接残留応力解析方法によれば、第１の溶接残留応力解析システム１Ａおよび第１の溶接残留応力解析方法と同様の効果を得ることができる。すなわち、従来、解析精度が低下していた小口径配管等の３次元的な変形挙動が顕著に現れる形状を持つ溶接構造物２６に対する溶接残留応力解析の際に、仮想的な変形拘束条件を溶接残留応力解析手段３に与えることにより、溶接残留応力解析の精度を向上させることができる。   According to the fourth welding residual stress analysis system 1D and the fourth welding residual stress analysis method, the same effects as those of the first welding residual stress analysis system 1A and the first welding residual stress analysis method can be obtained. In other words, when performing a welding residual stress analysis on a welded structure 26 having a shape in which three-dimensional deformation behavior such as a small-diameter pipe, which has conventionally been reduced in analysis accuracy, appears, a virtual deformation constraint condition is welded. By giving the residual stress analysis means 3, the accuracy of the welding residual stress analysis can be improved.

また、溶接構造物２６（母材２６ａ，２６ｂ）の温度と母材２６ａ，２６ｂの線膨張係数線に基づいて、３次元熱弾性解析を行うことなく、３次元変形補正量を算出するので、３次元熱弾性解析を行う第１の実施形態および第２の実施形態に係る溶接残留応力解析システムおよび溶接残留応力解析方法よりも簡易な弾塑性解析の提供を実現できる。   Further, since the three-dimensional deformation correction amount is calculated without performing the three-dimensional thermoelastic analysis based on the temperature of the welded structure 26 (the base materials 26a and 26b) and the linear expansion coefficient lines of the base materials 26a and 26b, It is possible to provide a simpler elasto-plastic analysis than the welding residual stress analysis system and the welding residual stress analysis method according to the first and second embodiments for performing a three-dimensional thermoelastic analysis.

尚、溶接残留応力解析システム１Ｄにおいて、変形拘束条件設定手段２Ｄは、型枠モデル作成部９を備えているが、第２の実施形態で説明したように、型枠モデル作成部９の代わりに圧力条件設定部３６を備えていても良い。この場合、溶接パス２７の層ごとに変形補正を求めても良いが、計算簡略化のために板厚全体で仮想的な変形拘束条件を決定し、圧力値を溶接パス２７の層の深さ率で変化させることも可能である。   In the welding residual stress analysis system 1D, the deformation constraint condition setting means 2D includes the formwork model creating unit 9, but as described in the second embodiment, instead of the formwork model creating unit 9 A pressure condition setting unit 36 may be provided. In this case, the deformation correction may be obtained for each layer of the welding pass 27, but for the sake of simplification of calculation, a virtual deformation restraint condition is determined for the entire plate thickness, and the pressure value is set to the depth of the layer of the welding pass 27. It is also possible to change at a rate.

また、第３の実施形態で説明したように、溶接残留応力解析手段３の代わりに、溶接残留応力解析手段３Ｃを具備して溶接残留応力解析システム１Ｄを構成しても良い。   Further, as described in the third embodiment, the welding residual stress analysis system 1D may be configured by including the welding residual stress analysis means 3C instead of the welding residual stress analysis means 3.

［第５の実施形態］
図１５は、本発明の第５の実施形態に係る溶接残留応力解析システムの一実施例である溶接残留応力解析システム１Ｅの機能的構成要素を概略的に示す機能ブロック図である。 [Fifth Embodiment]
FIG. 15 is a functional block diagram schematically showing functional components of a welding residual stress analysis system 1E, which is an example of a welding residual stress analysis system according to the fifth embodiment of the present invention.

溶接残留応力解析システム１Ｅは、溶接構造物２６の実物が存在し、例えば、溶接構造物２６の残留変形量や残留ひずみの測定結果といった溶接構造物２６の変形量に関する実際の測定データが存在する場合に有効なシステムであり、具体的には、図１５に示されるように、溶接構造物２６の実測した変形量のデータ（以下、単に実測データとする）に基づき、２次元対称モデル３０の変形拘束条件を決定する変形拘束条件設定手段２Ｅと、溶接残留応力解析手段３とを具備する。すなわち、図１に示される溶接残留応力解析システム１Ａに対して、変形拘束条件設定手段２Ａの代わりに変形拘束条件設定手段２Ｅを具備する点で相違するが、その他の点では実質的な相違は無い。そこで、本実施形態では、変形拘束条件設定手段２Ｅを中心に説明し、溶接残留応力解析システム１Ｅの構成要素と実質的に相違しない構成要素については同じ符号を付して説明を省略する。   In the welding residual stress analysis system 1E, the actual welded structure 26 exists, and actual measurement data relating to the deformation amount of the welded structure 26 such as, for example, the residual deformation amount and residual strain measurement result of the welded structure 26 exists. Specifically, as shown in FIG. 15, the two-dimensional symmetric model 30 is based on the measured deformation data of the welded structure 26 (hereinafter simply referred to as measured data). Deformation constraint condition setting means 2E for determining deformation constraint conditions and welding residual stress analysis means 3 are provided. That is, the welding residual stress analysis system 1A shown in FIG. 1 is different from the welding residual stress analysis system 1A in that the deformation constraint condition setting unit 2E is provided instead of the deformation constraint condition setting unit 2A. No. Therefore, in the present embodiment, the deformation constraint condition setting unit 2E will be mainly described, and the constituent elements that are not substantially different from the constituent elements of the welding residual stress analysis system 1E are denoted by the same reference numerals and description thereof is omitted.

溶接残留応力解析システム１Ｅの変形拘束条件設定手段２Ｅは、図１５に示されるように、３次元伝熱解析部６と、溶接構造物２６の実測データに基づき、２次元対称モデル３０の変形拘束条件としての変形補正量を決定する変形補正量算出部８Ｅと、型枠モデル作成部９とを備える。すなわち、図１に示される変形拘束条件設定手段２Ａでは、３次元熱弾性解析結果に基づき２次元対称モデル３０の変形拘束条件としての変形補正量を決定する点に対して、変形拘束条件設定手段２Ｅは、溶接構造物２６の実測データに基づき２次元対称モデル３０の変形拘束条件としての変形補正量を決定する点で異なる。尚、その他の点については実質的に相違しない。   As shown in FIG. 15, the deformation constraint condition setting means 2E of the welding residual stress analysis system 1E is based on the three-dimensional heat transfer analysis unit 6 and the measurement data of the welded structure 26, and the deformation constraint of the two-dimensional symmetric model 30. A deformation correction amount calculation unit 8E that determines a deformation correction amount as a condition and a formwork model creation unit 9 are provided. That is, in the deformation constraint condition setting means 2A shown in FIG. 1, the deformation constraint condition setting means is used for determining the deformation correction amount as the deformation constraint condition of the two-dimensional symmetric model 30 based on the three-dimensional thermoelastic analysis result. 2E is different in that a deformation correction amount as a deformation constraint condition of the two-dimensional symmetric model 30 is determined based on actually measured data of the welded structure 26. Other points are not substantially different.

このように、構成される溶接残留応力解析システム１Ｅでは、溶接構造物２６の溶接前後の変形を実際に測定した測定データがある場合、３次元熱弾性解析を行うことなく当該測定データを用いて変形補正量を決定することができるので、溶接残留応力解析システム１Ａ，１Ｂ，１Ｄよりも簡易な弾塑性解析の提供を実現できる。   As described above, in the welding residual stress analysis system 1E configured as described above, when there is measurement data obtained by actually measuring the deformation of the welded structure 26 before and after welding, the measurement data is used without performing a three-dimensional thermoelastic analysis. Since the deformation correction amount can be determined, it is possible to provide a simpler elastoplastic analysis than the welding residual stress analysis systems 1A, 1B, and 1D.

尚、図１５に示される溶接残留応力解析システム１Ｅでは、変形拘束条件設定手段２Ｅが型枠モデル作成部９を備えているが、型枠モデル作成部９の代わりに圧力条件設定部３６を備える変形拘束条件設定手段２Ｅを構成しても構わない。この場合、測定データが板厚全体に対する変形量であるため、溶接パス２７の層を順次盛っていく過程段階で溶接パス圧力値を溶接パス２７の層の深さ率で変化させるが望ましい。   In the welding residual stress analysis system 1E shown in FIG. 15, the deformation constraint condition setting unit 2E includes the formwork model creation unit 9, but includes a pressure condition setting unit 36 instead of the formwork model creation unit 9. You may comprise the deformation | transformation constraint condition setting means 2E. In this case, since the measurement data is the deformation amount with respect to the entire plate thickness, it is desirable to change the welding pass pressure value by the depth ratio of the layer of the welding pass 27 in the process step of successively depositing the layers of the welding pass 27.

次に、本発明の第５の実施形態に係る溶接残留応力解析方法（以下、第５の溶接残留応力解析方法とする）について説明する。   Next, a welding residual stress analysis method according to the fifth embodiment of the present invention (hereinafter referred to as a fifth welding residual stress analysis method) will be described.

図１６は、第５の溶接残留応力解析方法の一例として実行される溶接残留応力解析システム１Ｅの処理ステップ（以下、第５の溶接残留応力解析手順とする）の処理フロー図である。尚、第５の溶接残留応力解析手順の説明において、上述した溶接残留応力解析手順と重複する処理ステップについての説明は省略する。   FIG. 16 is a process flow diagram of processing steps (hereinafter referred to as a fifth welding residual stress analysis procedure) of the welding residual stress analysis system 1E executed as an example of the fifth welding residual stress analysis method. In the description of the fifth welding residual stress analysis procedure, the description of the processing steps overlapping with the welding residual stress analysis procedure described above is omitted.

第５の溶接残留応力解析手順は、図１４に示される第４の溶接残留応力解析手順に対して、変形補正量算出ステップ（ステップＳ２１）の代わりに、変形補正量算出ステップ（ステップＳ３１）を備える点で相違するが、その他の点では実質的に相違しないので、ステップＳ３１の変形補正量算出ステップについて説明し、その他の箇所については説明を省略する。   The fifth welding residual stress analysis procedure differs from the fourth welding residual stress analysis procedure shown in FIG. 14 in that a deformation correction amount calculating step (step S31) is used instead of the deformation correction amount calculating step (step S21). Although it differs in the point provided, since it is not substantially different in another point, the deformation | transformation amount calculation step of step S31 is demonstrated and description is abbreviate | omitted about another part.

第５の溶接残留応力解析手順は、では、まず、ステップＳ１で３次元伝熱解析ステップが実行される。その後、一方では、ステップＳ３１に進み、溶接構造物２６の実測データに基づき、２次元対称モデル３０の変形補正量を決定する変形補正量算出ステップ（ステップＳ３１）が実行される。変形補正量算出ステップ（ステップＳ３１）では、変形補正量算出部８Ｅが溶接構造物２６の実測の３次元熱変形量のデータに基づき、２次元対称モデル３０の変形拘束条件となる３次元変形補正量を算出する。変形補正量算出部８Ｅが３次元変形補正量を算出すると、変形補正量算出ステップは完了し、続いて、ステップＳ４に進む。ステップＳ４以降の処理ステップおよびステップＳ１以降の他方の処理ステップ（ステップＳ５およびステップＳ６）は第１の溶接残留応力解析手順と同様である。   In the fifth welding residual stress analysis procedure, first, a three-dimensional heat transfer analysis step is executed in step S1. Thereafter, on the other hand, the process proceeds to step S31, and a deformation correction amount calculating step (step S31) for determining the deformation correction amount of the two-dimensional symmetric model 30 based on the actual measurement data of the welded structure 26 is executed. In the deformation correction amount calculation step (step S31), the deformation correction amount calculation unit 8E uses the three-dimensional thermal deformation amount data measured for the welded structure 26 as a deformation constraint condition for the two-dimensional symmetric model 30. Calculate the amount. When the deformation correction amount calculation unit 8E calculates the three-dimensional deformation correction amount, the deformation correction amount calculation step is completed, and then the process proceeds to step S4. The processing steps after step S4 and the other processing steps after step S1 (step S5 and step S6) are the same as those in the first welding residual stress analysis procedure.

尚、図１６に示される第５の溶接残留応力解析手順でも、第４の溶接残留応力解析手順と同様に、型枠モデル作成ステップ（ステップＳ４）の代わりに圧力条件設定ステップ（ステップＳ１１）を備えていても良い。   In the fifth welding residual stress analysis procedure shown in FIG. 16, as in the fourth welding residual stress analysis procedure, a pressure condition setting step (step S11) is performed instead of the mold model creation step (step S4). You may have.

第５の溶接残留応力解析システム１Ｅおよび第５の溶接残留応力解析方法によれば、第１の溶接残留応力解析システム１Ａおよび第１の溶接残留応力解析方法と同様の効果を得ることができる。すなわち、従来、解析精度が低下していた小口径配管等の３次元的な変形挙動が顕著に現れる形状を持つ溶接構造物２６に対する溶接残留応力解析の際に、仮想的な変形拘束条件を溶接残留応力解析手段３に与えることにより、溶接残留応力解析の精度を向上させることができる。   According to the fifth welding residual stress analysis system 1E and the fifth welding residual stress analysis method, the same effects as those of the first welding residual stress analysis system 1A and the first welding residual stress analysis method can be obtained. In other words, when performing a welding residual stress analysis on a welded structure 26 having a shape in which three-dimensional deformation behavior such as a small-diameter pipe, which has conventionally been reduced in analysis accuracy, appears, a virtual deformation constraint condition is welded. By giving the residual stress analysis means 3, the accuracy of the welding residual stress analysis can be improved.

また、溶接構造物２６の溶接前後の変形を実際に測定した測定データがある場合、既存のデータを有効に活用することができ、溶接構造物２６の溶接残留応力の解析時間を短縮することができるので、特に有効である。   Further, when there is measurement data obtained by actually measuring the deformation of the welded structure 26 before and after welding, the existing data can be used effectively, and the analysis time of the welding residual stress of the welded structure 26 can be shortened. It is particularly effective because it can.

以上、本発明によれば、従来、解析精度が低下していた小口径配管等の３次元的な変形挙動が顕著に現れる形状を持つ溶接構造物２６に対する溶接残留応力解析の際に、仮想的な変形拘束条件を溶接残留応力解析手段３に与えることにより、溶接残留応力解析の精度を向上させることができる。   As described above, according to the present invention, when performing a welding residual stress analysis on a welded structure 26 having a shape in which a three-dimensional deformation behavior such as a small-bore pipe or the like in which analysis accuracy has been lowered has remarkably appeared, By providing the welding residual stress analysis means 3 with various deformation constraint conditions, the accuracy of the welding residual stress analysis can be improved.

尚、本発明は上記の各実施形態そのままに限定されるものではなく、実施段階ではその要旨を逸脱しない範囲で構成要素を変形して具体化しても良い。また、上記の各実施形態に開示されている複数の構成要素の適宜な組み合わせにより、種々の発明を形成できる。例えば、実施形態に示される全構成要素から幾つかの構成要素を削除しても良い。さらに、異なる実施形態にわたる構成要素を適宜組み合わせても良い。   Note that the present invention is not limited to the above-described embodiments as they are, and may be embodied by modifying constituent elements without departing from the scope of the invention in the implementation stage. In addition, various inventions can be formed by appropriately combining a plurality of constituent elements disclosed in the above embodiments. For example, you may delete a some component from all the components shown by embodiment. Furthermore, the constituent elements over different embodiments may be appropriately combined.

本発明の第１の実施形態に係る溶接残留応力解析システムの機能的構成要素を概略的に示した機能ブロック図。The functional block diagram which showed schematically the functional component of the welding residual stress analysis system which concerns on the 1st Embodiment of this invention. 本発明に係る溶接残留応力解析システムにおける変形拘束条件設定手段（３次元伝熱解析部）が行う３次元伝熱解析の概念を説明する模式図。The schematic diagram explaining the concept of the three-dimensional heat transfer analysis which the deformation | transformation constraint condition setting means (three-dimensional heat transfer analysis part) in the welding residual stress analysis system concerning this invention performs. 図２に示される３次元モデルとしてモデル化された溶接構造物の溶接部およびその周辺を拡大して示した概略図。Schematic which expanded and showed the welding part and its periphery of the welding structure modeled as a three-dimensional model shown by FIG. 図２に示される３次元モデルを回転軸Ｌと平行な方向（高さ方向）から見た場合における平面図。FIG. 3 is a plan view when the three-dimensional model shown in FIG. 2 is viewed from a direction (height direction) parallel to the rotation axis L. 本発明に係る溶接残留応力解析システムにおける残留応力解析手段が熱弾塑性解析時に使用する２次元対称モデルおよび型枠モデル作成部が作成する型枠モデルについて概略的に表した概略図。FIG. 3 is a schematic diagram schematically illustrating a two-dimensional symmetry model used by a residual stress analysis unit in a thermal elastic-plastic analysis and a form model created by a form model creation unit in a welding residual stress analysis system according to the present invention. 本発明に係る溶接残留応力解析方法の一例である第１の溶接残留応力解析手順を示した処理フロー図。The processing flow figure showing the 1st welding residual stress analysis procedure which is an example of the welding residual stress analysis method concerning the present invention. 本発明に係る残留応力分布解析の解析精度を評価するための説明図であり、（Ａ）が溶接構造物の内径側表面の溶接残留応力解析結果（残留応力分布）を示す図、（Ｂ）が外径側表面の溶接残留応力解析結果（残留応力分布）を示す図。It is explanatory drawing for evaluating the analysis accuracy of the residual stress distribution analysis which concerns on this invention, (A) is a figure which shows the welding residual stress analysis result (residual stress distribution) of the internal diameter side surface of a welded structure, (B) FIG. 4 is a view showing a welding residual stress analysis result (residual stress distribution) on the outer diameter side surface. 本発明の第２の実施形態に係る溶接残留応力解析システムの機能的構成要素を概略的に示した機能ブロック図。The functional block diagram which showed schematically the functional component of the welding residual stress analysis system which concerns on the 2nd Embodiment of this invention. 本発明の第２の実施形態に係る溶接残留応力解析システムが溶接残留応力解析を行う際に２次元対称モデルに加えられる圧力条件と当該２次元モデルの関係を説明する説明図。Explanatory drawing explaining the relationship between the pressure conditions applied to a two-dimensional symmetrical model when the welding residual stress analysis system which concerns on the 2nd Embodiment of this invention performs a welding residual stress analysis, and the said two-dimensional model. 本発明に係る溶接残留応力解析方法の一例である第２の溶接残留応力解析手順を示した処理フロー図。The processing flowchart which showed the 2nd welding residual stress analysis procedure which is an example of the welding residual stress analysis method which concerns on this invention. 本発明の第３の実施形態に係る溶接残留応力解析システムの機能的構成要素を概略的に示した機能ブロック図。The functional block diagram which showed schematically the functional component of the welding residual stress analysis system which concerns on the 3rd Embodiment of this invention. 本発明の第４の実施形態に係る溶接残留応力解析システムの機能的構成要素を概略的に示した機能ブロック図。The functional block diagram which showed schematically the functional component of the welding residual stress analysis system which concerns on the 4th Embodiment of this invention. 本発明の第４の実施形態に係る溶接残留応力解析システムの変形拘束条件設定手段においてなされる変形量補正の方法について説明する説明図であり、（Ａ）は、溶接構造物の２次元対称モデルの周方向温度分布を示す図、（Ｂ）は、仮想的な変形状態を示す概略図。It is explanatory drawing explaining the deformation | transformation amount correction | amendment method made in the deformation | transformation constraint condition setting means of the welding residual stress analysis system which concerns on the 4th Embodiment of this invention, (A) is a two-dimensional symmetrical model of a welded structure The figure which shows the circumferential direction temperature distribution of (B), (B) is the schematic which shows a virtual deformation | transformation state. 本発明に係る溶接残留応力解析方法の一例である第４の溶接残留応力解析手順を示した処理フロー図。The processing flow figure showing the 4th welding residual stress analysis procedure which is an example of the welding residual stress analysis method concerning the present invention. 本発明の第５の実施形態に係る溶接残留応力解析システムの機能的構成要素を概略的に示した機能ブロック図。The functional block diagram which showed schematically the functional component of the welding residual stress analysis system which concerns on the 5th Embodiment of this invention. 本発明に係る溶接残留応力解析方法の一例である第５の溶接残留応力解析手順を示した処理フロー図。The processing flow figure showing the 5th welding residual stress analysis procedure which is an example of the welding residual stress analysis method concerning the present invention.

符号の説明Explanation of symbols

１Ａ，１Ｂ，１Ｃ，１Ｄ，１Ｅ 溶接残留応力解析システム
２（２Ａ，２Ｂ，２Ｃ，２Ｄ，２Ｅ） 変形拘束条件設定手段
３，３Ｃ 溶接残留応力解析手段
４ 表示手段
５ 溶接構造物温度分布
６ ３次元伝熱解析部
７ ３次元熱弾性解析部
８，８Ｄ，８Ｅ 変形補正量算出部
９ 型枠モデル作成部
１１ 温度情報取得部
１２ 熱弾塑性解析部
２０ 溶接部
２０ａ 溶接完了部分
２０ｂ 溶接未完了部分
２１ 溶接構造物の３次元モデル
２２ 溶接棒
２３ 熱源
２６ 溶接構造物
２６ａ，２６ｂ 母材（被溶接金属）
２７ 溶接パス
３０ ２次元対称モデル
３１ 型枠モデル
３２ 本発明を適用した場合における残留応力分布
３３ ３次元熱弾塑性解析を行った場合における残留応力分布
３４ 従来の２次元熱弾塑性解析を行った場合における残留応力分布
３６ 圧力条件設定部
３９ ２次元対称モデルの外壁面
４０ ２次元対称モデルの内壁面
４１ ２次元対称モデルの周方向の温度分布
４２ 実際の溶接構造物の周方向の温度分布
４３ 径方向変形範囲
Ｌ ３次元モデルの対称軸
Ｓ ２次元対称モデルと型枠モデルとの接触面 1A, 1B, 1C, 1D, 1E Welding residual stress analysis system 2 (2A, 2B, 2C, 2D, 2E) Deformation constraint condition setting means 3, 3C Welding residual stress analysis means 4 Display means 5 Welded structure temperature distribution 6 3 Dimensional heat transfer analysis unit 7 Three-dimensional thermoelastic analysis unit 8, 8D, 8E Deformation correction amount calculation unit 9 Formwork model creation unit 11 Temperature information acquisition unit 12 Thermoelastic-plastic analysis unit 20 Welding part 20a Welding completion part 20b Welding incomplete Portion 21 Three-dimensional model of welded structure 22 Welding rod 23 Heat source 26 Welded structures 26a and 26b Base material (metal to be welded)
27 Welding path 30 Two-dimensional symmetric model 31 Formwork model 32 Residual stress distribution 33 when the present invention is applied Residual stress distribution 34 when three-dimensional thermoelastic-plastic analysis is performed A conventional two-dimensional thermoelastic-plastic analysis is performed Residual stress distribution 36 in the case Pressure condition setting unit 39 Outer wall surface 40 of the two-dimensional symmetric model Inner wall surface 41 of the two-dimensional symmetric model Temperature distribution 42 in the circumferential direction of the two-dimensional symmetric model Temperature distribution 43 in the circumferential direction of the actual welded structure Radial deformation range L Axis of symmetry S of 3D model Contact surface of 2D symmetry model and formwork model

Claims (15)

３次元溶接構造物の有限要素法による残留応力解析方法において、
前記３次元溶接構造物の３次元熱変形量を取得する３次元熱変形量取得ステップと、
前記３次元熱変形量取得ステップで取得した３次元熱変形量に基づき、前記溶接構造物の回転軸を対称軸として２次元にモデル化された２次元対称モデルの変形補正量を算出する変形補正量算出ステップと、
前記変形補正量算出ステップで算出された変形補正量に基づき前記２次元対称モデルの変形拘束条件を設定する変形拘束条件設定ステップと、
前記変形拘束条件設定ステップで設定された条件下で前記２次元対称モデルの２次元熱弾塑性解析を行い、前記溶接構造物の溶接残留応力を得る２次元熱弾塑性解析ステップと、を備えることを特徴とする溶接残留応力解析方法。 In the residual stress analysis method of the three-dimensional welded structure by the finite element method,
A three-dimensional thermal deformation amount acquisition step of acquiring a three-dimensional thermal deformation amount of the three-dimensional welded structure;
Deformation correction for calculating a deformation correction amount of a two-dimensional symmetric model modeled two-dimensionally with the rotation axis of the welded structure as a symmetric axis based on the three-dimensional thermal deformation amount acquired in the three-dimensional thermal deformation amount acquisition step A quantity calculating step;
A deformation constraint condition setting step of setting a deformation constraint condition of the two-dimensional symmetric model based on the deformation correction amount calculated in the deformation correction amount calculation step;
A two-dimensional thermoelastic-plastic analysis step of performing a two-dimensional thermoelastic-plastic analysis of the two-dimensional symmetrical model under the conditions set in the deformation constraint condition setting step to obtain a welding residual stress of the welded structure. A welding residual stress analysis method characterized by 前記３次元熱変形量取得ステップは、溶接過程の伝熱解析を熱源と同じ速度で移動する移動座標系、および、熱源と同じ角速度で回転する回転座標系の何れかの座標系を用いて伝熱計算を実施し、溶接構造物の温度分布と温度時刻歴の温度情報を得る温度情報取得ステップと、
前記温度情報取得ステップで求めた温度情報に基づき３次元熱変形解析を実施して前記溶接構造物の３次元熱変形量を求める３次元熱弾性解析ステップと、を有することを特徴とする請求項１記載の溶接残留応力解析方法。 The three-dimensional thermal deformation amount acquisition step transfers heat transfer analysis of the welding process using either a moving coordinate system that moves at the same speed as the heat source or a rotating coordinate system that rotates at the same angular speed as the heat source. A temperature information acquisition step for performing heat calculation and obtaining temperature information of temperature distribution and temperature time history of the welded structure;
3. A three-dimensional thermoelastic analysis step for obtaining a three-dimensional thermal deformation amount of the welded structure by performing a three-dimensional thermal deformation analysis based on the temperature information obtained in the temperature information acquisition step. The welding residual stress analysis method according to 1. 前記３次元熱変形量取得ステップは、溶接過程の伝熱解析を熱源と同じ速度で移動する移動座標系、および、熱源と同じ角速度で回転する回転座標系の何れかの座標系を用いて伝熱計算を実施し、溶接構造物の温度分布と温度時刻歴の温度情報を得る温度情報取得ステップと、
前記温度情報取得ステップで求めた温度情報および前記溶接構造物の母材の線膨張率および板厚に基づいて前記溶接構造物の３次元熱変形量を求めるステップと、を有することを特徴とする請求項１記載の溶接残留応力解析方法。 The three-dimensional thermal deformation amount acquisition step transfers heat transfer analysis of the welding process using either a moving coordinate system that moves at the same speed as the heat source or a rotating coordinate system that rotates at the same angular speed as the heat source. A temperature information acquisition step for performing heat calculation and obtaining temperature information of temperature distribution and temperature time history of the welded structure;
Obtaining the three-dimensional thermal deformation amount of the welded structure based on the temperature information obtained in the temperature information obtaining step and the linear expansion coefficient and plate thickness of the base material of the welded structure. The welding residual stress analysis method according to claim 1. 温度情報取得ステップは、前記溶接構造物の３次元伝熱解析を行い、当該溶接構造物の３次元温度分布を得るステップと、
取得した３次元温度分布と溶接速度に基づいて前記溶接構造物の２次元対称モデルの温度推移情報を得るステップ、および、前記溶接構造物の２次元伝熱解析を行った結果に基づいて当該溶接構造物の２次元対称モデルの温度推移情報を得るステップの何れかのステップを備えることを特徴とする請求項２または３記載の溶接残留応力解析方法。 The temperature information acquisition step performs a three-dimensional heat transfer analysis of the welded structure to obtain a three-dimensional temperature distribution of the welded structure,
Obtaining temperature transition information of a two-dimensional symmetrical model of the welded structure based on the acquired three-dimensional temperature distribution and welding speed, and the welding based on the result of performing two-dimensional heat transfer analysis of the welded structure The welding residual stress analysis method according to claim 2, further comprising any one of steps of obtaining temperature transition information of a two-dimensional symmetrical model of the structure. 前記３次元熱変形量取得ステップは、前記溶接構造物の残留変形量および残留ひずみの測定結果の少なくとも一方から前記３次元熱変形量を取得するステップであることを特徴とする請求項１記載の溶接残留応力解析方法。 The said three-dimensional thermal deformation amount acquisition step is a step of acquiring the said three-dimensional thermal deformation amount from at least one of the measurement results of the residual deformation amount and the residual strain of the welded structure. Welding residual stress analysis method. 前記変形拘束条件決定ステップは、前記２次元熱弾塑性解析ステップ実行の際に、前記２次元対称モデルの変形を仮想的に拘束する型枠モデルを作成する型枠モデル作成ステップであり、前記型枠モデルは、前記残留応力解析を行う座標系に完全固定されており、外部負荷に対して変形せず、接触する前記２次元対称モデルと熱的に絶縁する物体として模擬された２次元モデルであることを特徴とする請求項１記載の溶接残留応力解析方法。 The deformation constraint condition determining step is a mold model creating step for creating a mold model that virtually restrains deformation of the two-dimensional symmetric model when the two-dimensional thermoelastic-plastic analysis step is performed. The frame model is completely fixed to the coordinate system for performing the residual stress analysis, and is a two-dimensional model that is not deformed against an external load and is simulated as an object that is thermally insulated from the two-dimensional symmetrical model that is in contact with the frame model. The welding residual stress analysis method according to claim 1, wherein: 前記型枠モデルは、溶接作業により生じる前記溶接構造物の径方向の変形に対して、前記溶接構造物の内径側表面にのみ配置されることを特徴とする請求項６記載の溶接残留応力解析方法。 The welding residual stress analysis according to claim 6, wherein the mold model is disposed only on a radially inner surface of the welded structure against a radial deformation of the welded structure caused by a welding operation. Method. 前記変形拘束条件決定ステップは、前記２次元熱弾塑性解析ステップ実行の際に、前記２次元対称モデルの変形を仮想的に拘束するため、前記２次元対称モデルに加える圧力条件を設定する圧力条件設定ステップであることを特徴とする請求項１記載の溶接残留応力解析方法。 The deformation constraint condition determining step is a pressure condition for setting a pressure condition to be applied to the two-dimensional symmetric model in order to virtually constrain deformation of the two-dimensional symmetric model when executing the two-dimensional thermoelastic-plastic analysis step. The welding residual stress analysis method according to claim 1, wherein the welding residual stress analysis method is a setting step. 前記圧力条件設定ステップで設定される圧力条件とは、前記変形補正量算出ステップで算出された変形補正量と圧力による変位量とが同等となる圧力分布および圧力値であることを特徴とする請求項８記載の溶接残留応力解析方法。 The pressure condition set in the pressure condition setting step is a pressure distribution and a pressure value in which the deformation correction amount calculated in the deformation correction amount calculation step is equal to the displacement amount due to pressure. Item 9. A welding residual stress analysis method according to Item 8. 前記圧力値は、前記溶接構造物の溶接層の深さ毎に変化させたことを特徴とする請求項９記載の溶接残留応力解析方法。 The welding residual stress analysis method according to claim 9, wherein the pressure value is changed for each depth of a weld layer of the welded structure. 溶接残留応力解析の対象となる溶接構造物の２次元対称モデルを用いて２次元熱弾塑性解析を行う際に設定する前記２次元対称モデルの変形拘束条件を決定する変形拘束条件設定手段と、
前記変形拘束条件設定手段が決定した変形拘束条件を考慮して前記２次元対称モデルを用いた２次元熱弾塑性解析を行い前記溶接構造物の溶接残留応力解析結果を得る溶接残留応力解析手段とを具備することを特徴とする溶接残留応力解析システム。 A deformation constraint condition setting means for determining a deformation constraint condition of the two-dimensional symmetric model that is set when performing a two-dimensional thermoelastic-plastic analysis using a two-dimensional symmetric model of a welded structure to be subjected to welding residual stress analysis;
Welding residual stress analysis means for obtaining a welding residual stress analysis result of the welded structure by performing a two-dimensional thermoelastic-plastic analysis using the two-dimensional symmetry model in consideration of the deformation constraint condition determined by the deformation constraint condition setting means; A welding residual stress analysis system comprising: 前記変形拘束条件設定手段は、溶接過程の伝熱解析を熱源と同じ速度で移動する移動座標系、および、熱源と同じ角速度で回転する回転座標系の何れかの座標系を用いて伝熱計算を実施し、前記溶接構造物の温度分布と温度時刻歴を示す温度情報を得る３次元伝熱解析部と、
前記温度情報に基づき３次元熱変形解析を実施して前記溶接構造物の３次元熱変形量を求める３次元熱弾性解析部と、
前記３次元熱弾性解析部が求めた３次元熱変形量に基づき前記溶接構造物の３次元変形補正量を算出する変形補正量算出部と、
前記変形補正量算出部が算出した変形補正量を考慮して前記２次元対称モデルの変形を仮想的に拘束する拘束条件を決定する拘束条件決定部とを備えることを特徴とする請求項１１記載の溶接残留応力解析システム。 The deformation constraint condition setting means performs heat transfer calculation using either a moving coordinate system that moves the heat transfer analysis of the welding process at the same speed as the heat source or a rotating coordinate system that rotates at the same angular speed as the heat source. 3D heat transfer analysis unit for obtaining temperature information indicating the temperature distribution and temperature time history of the welded structure,
A three-dimensional thermoelastic analysis unit for performing a three-dimensional thermal deformation analysis based on the temperature information to obtain a three-dimensional thermal deformation amount of the welded structure;
A deformation correction amount calculation unit that calculates a three-dimensional deformation correction amount of the welded structure based on the three-dimensional thermal deformation amount obtained by the three-dimensional thermoelastic analysis unit;
12. A constraint condition determination unit that determines a constraint condition for virtually constraining deformation of the two-dimensional symmetric model in consideration of the deformation correction amount calculated by the deformation correction amount calculation unit. Welding residual stress analysis system. 前記変形拘束条件決定部は、前記変形補正量算出部が算出した変形補正量を考慮して前記２次元対称モデルの変形を仮想的に拘束する拘束条件を具現化するとともに、前記残留応力解析を行う座標系に完全固定されており、外部負荷に対して変形せず、接触する前記２次元対称モデルと熱的に絶縁される型枠モデルを作成する型枠モデル作成部、および、前記拘束条件を前記２次元対称モデルへ加える圧力条件として設定する圧力条件設定部の一方を備えることを特徴とする請求項１２記載の溶接残留応力解析システム。 The deformation constraint condition determination unit embodies a constraint condition for virtually constraining deformation of the two-dimensional symmetric model in consideration of the deformation correction amount calculated by the deformation correction amount calculation unit, and performs the residual stress analysis. A formwork model creation unit for creating a formwork model that is completely fixed to a coordinate system to be performed, is not deformed with respect to an external load, and is thermally insulated from the two-dimensional symmetrical model that is in contact; and the constraint condition The welding residual stress analysis system according to claim 12, further comprising: a pressure condition setting unit that sets a pressure condition as a pressure condition to be applied to the two-dimensional symmetric model. 前記変形拘束条件設定手段は、溶接過程の伝熱解析を熱源と同じ速度で移動する移動座標系、および、熱源と同じ角速度で回転する回転座標系の何れかの座標系を用いて伝熱計算を実施し、前記溶接構造物の温度分布と温度時刻歴を示す温度情報を得る３次元伝熱解析部と、
前記温度情報および前記溶接構造物を形成する母材の物性値に基づき前記溶接構造物の３次元熱変形量を求め、求めた３次元熱変形量に基づき前記溶接構造物の３次元変形補正量を算出する変形補正量算出部と、
前記変形補正量算出部が算出した変形補正量を考慮して前記２次元対称モデルの変形を仮想的に拘束する拘束条件を決定する拘束条件決定部とを備えることを特徴とする請求項１１記載の溶接残留応力解析システム。 The deformation constraint condition setting means performs heat transfer calculation using either a moving coordinate system that moves the heat transfer analysis of the welding process at the same speed as the heat source or a rotating coordinate system that rotates at the same angular speed as the heat source. 3D heat transfer analysis unit for obtaining temperature information indicating the temperature distribution and temperature time history of the welded structure,
A three-dimensional thermal deformation amount of the welded structure is obtained based on the temperature information and a physical property value of a base material forming the welded structure, and a three-dimensional deformation correction amount of the welded structure is obtained based on the obtained three-dimensional thermal deformation amount. A deformation correction amount calculation unit for calculating
12. A constraint condition determination unit that determines a constraint condition for virtually constraining deformation of the two-dimensional symmetric model in consideration of the deformation correction amount calculated by the deformation correction amount calculation unit. Welding residual stress analysis system. 前記変形拘束条件設定手段は、前記溶接構造物の残留変形量および残留ひずみの測定結果の少なくとも一方から前記３次元熱変形量を取得する変形補正量算出部と、
前記変形補正量算出部が算出した変形補正量を考慮して前記２次元対称モデルの変形を仮想的に拘束する拘束条件を決定する拘束条件決定部とを備えることを特徴とする請求項１１記載の溶接残留応力解析システム。 The deformation constraint condition setting means includes a deformation correction amount calculation unit that acquires the three-dimensional thermal deformation amount from at least one of a measurement result of a residual deformation amount and a residual strain of the welded structure;
12. A constraint condition determination unit that determines a constraint condition for virtually constraining deformation of the two-dimensional symmetric model in consideration of the deformation correction amount calculated by the deformation correction amount calculation unit. Welding residual stress analysis system.
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