JP2016224912A - Opening reinforcement method for axial pressure reinforcement rib cylindrical shell - Google Patents
Opening reinforcement method for axial pressure reinforcement rib cylindrical shell Download PDFInfo
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本発明は、航空宇宙構造における主耐荷部材の設計技術分野に関し、特に、軸方向圧力補強リブ円筒殻における開口補強方法に関する。 The present invention relates to the technical field of design of main load bearing members in an aerospace structure, and more particularly to an opening reinforcing method in an axial pressure reinforcing rib cylindrical shell.
薄肉補強構造は軽量で耐荷性能に優れる等の特徴があることから、現代の航空宇宙工業に広く応用されている。装置の取り付け、配管、放熱等の必要性から、航空宇宙構造の薄肉補強部分には開口の存在が不可避である。例えば、ミサイル、ロケット構造の段間部や計器室、飛行機体などがこれにあたる。開口に起因する構造材料及び剛性の不連続性によって、補強筐体の変位場及び応力場が部分的に乱れ、モーメント応力の無い状態が破壊されると、筐体の耐荷力は低下してしまう。特に、飛移座屈に対する極限耐荷力への影響は大きく、設計上の補強措置を余儀なくされる。しかし、国内外の大多数の研究では、開口付近領域について構造強度の安定角度を部分的に補強していることから、補強リブ円筒殻の設計案の多くが重量超過となっている。特に、開口が多い場合には重量超過が深刻である。この点において、従来の「部分補強」の考え方に基づく研究では構造設計全体への着目が不足している。特に、関連の構造を一体化して最適化するとの設計理論の枠組みに欠けている。また、従来の加工工程や設計理念に縛られて、現在の補強リブ円筒殻の構造設計は多くが「直線リブ」を適用しているため、リブの多様な形状変化に欠け、構造設計空間も制限されている。実際に、設計全体を考慮していない部分補強では、往々にして補強リブ円筒殻の開口付近領域で剛性が突然変化するため、部分的な破損が発生しやすい。注目すべきことに、本邦では重量型キャリアロケットや大型航空機における大直径、薄壁、超軽量等への設計要求が高まっているほか、耐荷構造の多機能性融合に起因する開口の拡大がみられる。よって、動力伝達経路の一部に着目した開口補強設計への要求はますます切実となっている。 Thin-walled reinforcing structures are widely applied to the modern aerospace industry because they are lightweight and have excellent load-bearing performance. Due to the necessity of installation of equipment, piping, heat dissipation, etc., the existence of openings in the thin-walled reinforcement portion of the aerospace structure is inevitable. For example, missiles, interstage parts of rocket structures, instrument rooms, and airplane bodies. Displacement and stress fields of the reinforced housing are partially disturbed by discontinuities in the structural material and rigidity resulting from the openings, and the load bearing capacity of the housing is reduced when the state without moment stress is destroyed. . In particular, the impact on the ultimate load bearing capacity against jump buckling is large, and design reinforcement measures are required. However, in the majority of studies in Japan and overseas, the stability angle of structural strength is partially reinforced in the region near the opening, so many of the design plans for reinforcing rib cylindrical shells exceed the weight. In particular, when there are many openings, excess weight is serious. In this regard, research based on the conventional concept of “partial reinforcement” lacks attention to the entire structural design. In particular, it lacks the framework of design theory to integrate and optimize related structures. In addition, the current structural design of the reinforced rib cylindrical shells, which are bound by the conventional processing processes and design philosophy, apply “straight ribs”, so that there is a lack of various shape changes of the ribs, and the structural design space is also small. Limited. Actually, in partial reinforcement not considering the entire design, since the rigidity suddenly changes in the region near the opening of the reinforcing rib cylindrical shell, partial breakage tends to occur. Of note, in Japan, design requirements for heavy-duty carrier rockets and large aircraft such as large diameters, thin walls, ultra-lightweight, etc. are increasing, and the opening due to multifunctional fusion of load-bearing structures is seen. It is done. Therefore, there is an increasing need for an aperture reinforcement design that focuses on a portion of the power transmission path.
近年、国外の学者Ｍｕｌａｎｉらが、全体型曲線補強リブ構造の概念を提起した。デジタル化製造技術の急速な発展によって、こうした不規則配置によるリブ加工成型が可能となっている。金属材料については、ＮＣ機械によるスライス加工、３Ｄプリント、電子ビームダイレスフォーミング等の技術で製造加工を完遂可能である。ＮＡＳＡラングレー研究センターは電子ビームダイレスフォーミング技術によって、湾曲リブプレートのアルミニウム合金サンプルを作製し、ｐａｎｅｌレベルでの実験検証を完了している。しかし、現在のところ、国外の学者らは湾曲リブプレート殻の耐荷重構造については深く研究していない。実際のところ、湾曲リブの設計柔軟性を、補強リブ円筒殻構造における開口補強要求に組み合わせれば、構造における動力伝達経路の一部が大きく改善されて、補強リブ円筒殻の軸方向圧力に対する耐性や、開口補強効率も向上するはずである。 In recent years, foreign scholars Mulani et al. Have proposed the concept of an overall curved reinforcing rib structure. Thanks to the rapid development of digitized manufacturing technology, rib processing and molding with such irregular arrangement is possible. For metal materials, manufacturing processing can be accomplished by techniques such as NC machine slicing, 3D printing, and electron beam dieless forming. The NASA Langley Research Center has produced aluminum alloy samples of curved rib plates using electron beam dieless forming technology, and has completed experimental verification at the panel level. At present, however, foreign scholars have not studied the load bearing structure of curved rib plate shells. In fact, combining the design flexibility of curved ribs with the opening reinforcement requirements in a reinforced rib cylindrical shell structure greatly improves some of the power transmission path in the structure and is resistant to the axial pressure of the reinforced rib cylindrical shell. In addition, the aperture reinforcement efficiency should be improved.
補強リブ円筒殻構造の開口補強効率は、軸方向圧力に対する耐荷力を算出することで評価する必要がある。現在、補強リブ円筒殻構造の耐荷力については、大部分が等価剛性モデルや精密な有限要素モデルに基づいて数値を予測している。等価剛性モデルとは、リブを密集させた周期性を有する補強リブ円筒殻を、均質化理論又は漸近的均質化理論に基づいて異方性又は等方性の光学殻に等価とすることであり、算出効率が極めて高い。しかし、例えばセルごとに周期性を有し、リブ密集条件を満たさねばならないなど、適用条件の制限が厳しい。軸方向圧力下での補強リブ円筒殻は、徐々に負荷がかかるにつれて、線形座屈−非線形飛移座屈−圧潰というように構造が変化する。精密な有限要素モデルでは、分析過程における材料の非線形性、幾何学的非線形性、及び各種欠陥に起因する非線形性要因を考慮して、境界条件、負荷のかかり方、構造的開口、リブ形状等の詳細を正確にシミュレーション可能である。しかし、精密な有限要素モデルでは、往々にして算出効率が非常に低くなる。結果として、開口された補強リブ円筒殻構造の軸方向圧力に対する耐荷能力分析及び最適化に多くの算出コストがかかり、最適化が失敗しやすくもなる。 The opening reinforcement efficiency of the reinforcing rib cylindrical shell structure needs to be evaluated by calculating the load bearing capacity against the axial pressure. Currently, most of the load bearing capacity of the reinforced rib cylindrical shell structure is predicted based on an equivalent stiffness model or a precise finite element model. The equivalent stiffness model is to make a reinforced rib cylindrical shell with periodicity with dense ribs equivalent to an anisotropic or isotropic optical shell based on homogenization theory or asymptotic homogenization theory. The calculation efficiency is extremely high. However, the application conditions are severely limited, for example, each cell must have periodicity and the rib dense condition must be satisfied. The structure of the reinforcing rib cylindrical shell under an axial pressure changes as linear buckling-nonlinear jump buckling-crushing as the load is gradually applied. In a precise finite element model, considering the nonlinearity of the material in the analysis process, geometrical nonlinearity, and nonlinearity factors caused by various defects, boundary conditions, loading method, structural opening, rib shape, etc. The details can be accurately simulated. However, precise finite element models often have very low calculation efficiency. As a result, the load carrying capacity analysis and optimization for the axial pressure of the opened reinforcing rib cylindrical shell structure requires a lot of calculation costs, and the optimization tends to fail.
従来の開口された補強リブ円筒殻構造における部分補強設計では、往々にして有限要素解析に過度に依存することになり、設計及び最適化の過程で幾度も有限要素解析を用いねばならないため、最適化効率が非常に低い。本分野ではすでに多くの業務が展開されているが、軸方向圧力補強リブ円筒殻に適した高効率の開口補強方法についてはいまだ提供されていない。 In the conventional partial reinforcement design in the open-ended reinforcing rib cylindrical shell structure, the finite element analysis is often overly dependent on the finite element analysis, and the finite element analysis must be used many times in the design and optimization process. The conversion efficiency is very low. Although a lot of work has already been developed in this field, a highly efficient opening reinforcement method suitable for an axial pressure reinforcing rib cylindrical shell has not yet been provided.
本発明は主として、従来技術における軸方向圧力補強リブ円筒殻は開口補強設計の構造効率が低く、最適化設計の算出コストが嵩むとの技術的課題を解決するものであり、開口の部分補強設計の構造効率を高め、最適化設計の算出コストを削減するとの目的を達成すべく、軸方向圧力補強リブ円筒殻における開口補強方法を提供する。 The present invention mainly solves the technical problem that the axial pressure reinforcing rib cylindrical shell in the prior art has low structural efficiency of the opening reinforcing design and increases the calculation cost of the optimized design, and the partial reinforcing design of the opening In order to achieve the object of improving the structural efficiency of the material and reducing the calculation cost of the optimized design, an opening reinforcing method for an axial pressure reinforcing rib cylindrical shell is provided.
本発明は軸方向圧力補強リブ円筒殻における開口補強方法を提供し、当該軸方向圧力補強リブ円筒殻における開口補強方法が、開口を含む軸方向圧力補強リブ円筒殻を開口遠方領域と開口付近領域に区分するステップ１００を含み、当該ステップが、座屈固有値解析を用い、軸方向圧力補強リブ円筒殻におけるｎ次までの座屈モードを取得するステップ１０１と、ｎ次までの座屈モードのうち選別条件を満たすｍ次までの部分座屈モードを選別し、ｍ次までの部分座屈モードを重畳して混合モード形状を形成するステップ１０２であって、座屈変形が座屈変形閾値よりも大きな領域の面積が筐体総面積の１／ａ以下であり、ａが２〜４であることを選別条件とするステップ１０２と、形成された混合モードの形状に基づき、座屈変形が座屈変形閾値を超えている領域を開口付近領域、残りの領域を開口遠方領域として区分するステップ１０３と、開口遠方領域に等価剛性モデルを構築し、開口付近領域に精密な幾何モデルを構築して、軸方向圧力補強リブ円筒殻の混合分析モデルを得るステップ２００と、均質化理論又は漸近的均質化理論に基づく軸方向圧力補強リブ円筒殻構造の等価剛性モデルを構築し、開口遠方領域の軸方向圧力補強リブ円筒殻を、異方性又は等方性の光学殻に等価とするステップ２０１と、 非一様有理Ｂスプライン曲線で描いた湾曲リブに基づいて、開口付近領域に精密な幾何モデルを構築するステップ２０２と、開口付近領域と開口遠方領域の接続関係を設定し、開口を含む軸方向圧力補強リブ円筒殻の軸方向圧力に対する耐荷能力の混合分析モデルを取得するステップ２０３と、軸方向圧力補強リブ円筒殻について開口補強の最適化を行い、最適化結果をチェックするステップ３００と、を含む。 The present invention provides an opening reinforcing method in an axial pressure reinforcing rib cylindrical shell, the opening reinforcing method in the axial pressure reinforcing rib cylindrical shell includes an axial direction pressure reinforcing rib cylindrical shell including an opening, an opening far region and an opening vicinity region. Step 101, which includes buckling eigenvalue analysis, which obtains buckling mode up to the nth order in the axial pressure reinforcing rib cylindrical shell, and of the buckling modes up to the nth order In step 102, partial buckling modes up to m-th order satisfying the selection condition are selected, and a mixed mode shape is formed by superimposing the partial buckling modes up to m-th order, and the buckling deformation is less than the buckling deformation threshold. The buckling deformation is buckled based on the step 102 in which the area of the large region is 1 / a or less of the total housing area and a is 2 to 4 and the shape of the mixed mode formed. Strange Step 103, in which the region exceeding the threshold is classified as the near-opening region and the remaining region as the far-opening region, an equivalent stiffness model is constructed in the far-opening region, and a precise geometric model is constructed in the near-opening region. Step 200 to obtain a mixed analysis model of the directional pressure-reinforced rib cylindrical shell and an equivalent stiffness model of the axial pressure-reinforced rib cylindrical shell structure based on the homogenization theory or asymptotic homogenization theory A precise geometric model is constructed in the region near the aperture based on the step 201 that makes the reinforced cylindrical shell equivalent to an anisotropic or isotropic optical shell and the curved rib drawn by a non-uniform rational B-spline curve. Step 202, setting the connection relationship between the region near the opening and the region far from the opening, and taking a mixed analysis model of the load bearing capacity against the axial pressure of the cylindrical shell of the axial pressure reinforcing rib including the opening Obtaining step 203 and optimizing the opening reinforcement for the axial pressure reinforcing rib cylindrical shell and checking 300 the optimization result.
好ましくは、軸方向圧力補強リブ円筒殻について開口補強の最適化を行い、最適化結果をチェックするステップ３００は、第１層の最適化において、代理モデルを大域的最適化手法と組み合わせることで、リブ厚、リブ高さ、軸方向のリブ数と配置、周方向のリブ数と配置、及びプライ角度のうちの１又はこれらの組み合わせを設計変数とし、軸方向圧力補強リブ円筒殻構造の軸方向圧力に対する耐荷力を目標関数とし、構造重量及び／又は構造製造コストを制約条件として、軸方向圧力補強リブ円筒殻構造を最適化設計し、制約条件を満たした最適化設計を得るステップ３０１であって、軸方向のリブ配置が、単一の制御変数で描かれた配置関数で決定されるステップ３０１と、第２層の最適化において、第１層の最適化設計に基づいてリブ厚、リブ高さ、軸方向のリブ数及び周方向のリブ数を固定し、勾配別部分最適化法を用いて、各湾曲リブの制御点座標を設計変数とし、軸方向圧力補強リブ円筒殻構造の軸方向圧力に対する耐荷力を目標関数とし、構造重量及び／又は構造製造コストを制約条件として、軸方向圧力補強リブ円筒殻構造を最適化設計し、制約条件を満たす最適化結果を取得するステップ３０２と、精密な有限要素解析によって最適化結果をチェックするステップ３０３と、を含む。 Preferably, the step 300 of optimizing the opening reinforcement for the axial pressure-reinforced rib cylindrical shell and checking the optimization results is performed by combining the surrogate model with a global optimization method in the first layer optimization, The axial direction of the axial pressure reinforcing rib cylindrical shell structure with one or a combination of rib thickness, rib height, number and arrangement of ribs in the axial direction, number and arrangement of ribs in the circumferential direction, and ply angle as a design variable Step 301 is to optimize the axial pressure-reinforced rib cylindrical shell structure with the load bearing capacity against pressure as a target function and the structural weight and / or structure manufacturing cost as constraints, and obtain an optimized design that satisfies the constraints. Thus, in step 301 where the axial rib placement is determined by the placement function drawn with a single control variable, and in the optimization of the second layer, the optimization is based on the optimization design of the first layer. Fixed thickness, rib height, number of axial ribs and number of ribs in the circumferential direction, and using gradient-based partial optimization method, control point coordinates of each curved rib as design variables, and axial pressure reinforcing rib cylindrical shell Optimize the axial pressure reinforced rib cylindrical shell structure with the load bearing capacity against the axial pressure of the structure as the target function and the structure weight and / or structure manufacturing cost as constraints, and obtain optimization results that satisfy the constraints Step 302 and Step 303 for checking the optimization result by precise finite element analysis.
好ましくは、前記代理モデルには、応答曲面モデル、クリギングモデル又は放射基底関数モデルが含まれ、前記大域的最適化手法には、粒子群最適化、遺伝的アルゴリズム、疑似アニーリング法、蟻コロニー最適化、タブーサーチ又は免疫アルゴリズムが含まれる。 Preferably, the surrogate model includes a response surface model, a kriging model, or a radial basis function model, and the global optimization method includes a particle swarm optimization, a genetic algorithm, a pseudo annealing method, and an ant colony optimization. , Tabu search or immune algorithm.
好ましくは、前記勾配別部分最適化法には、最急降下法、実行可能方向法、シンプレックス法、逐次線形計画法又は逐次二次計画法が含まれる。 Preferably, the gradient-based partial optimization method includes a steepest descent method, a feasible direction method, a simplex method, a sequential linear programming method, or a sequential quadratic programming method.
好ましくは、下記式によって軸方向のリブ配置関数が表される。 Preferably, an axial rib arrangement function is represented by the following formula.
Ｃｉは第１リブと第ｉリブとの距離、λはリブの配置係数、Ｎはリブ数、ＬＤは第１リブと最終リブとの距離をそれぞれ表す。 C i is the distance between the first rib and the i-th rib, λ is the rib placement coefficient, N is the number of ribs, and L D is the distance between the first rib and the final rib.
本発明が提供する軸方向圧力補強リブ円筒殻における開口補強方法は、従来の軸方向圧力補強リブ円筒殻の開口補強設計では構造効率が低く、最適化設計の算出コストが嵩むとの課題に対して、まず、ＮＵＲＢＳ湾曲リブの設計柔軟性を、軸方向圧力補強リブ円筒殻構造における開口補強要求に組み合わせることで、開口付近の動力伝達経路を大幅に改善するとともに、軸方向圧力補強リブ円筒殻構造における軸方向圧力への耐荷力を向上させる。続いて、開口付近領域と開口遠方領域につきアダプティブパーティショニング法を提供して、開口付近領域の範囲を合理的に決定することで、後続の開口付近領域の最適化のために適切な設計領域を特定する。最後に、混合分析モデルに基づいて、軸方向圧力補強リブ円筒殻の開口補強について２層最適化設計法を提供する。開口付近領域−開口遠方領域の混合分析モデルによれば、開口された補強リブ円筒殻構造の軸方向圧力に対する耐荷力の分析効率を大幅に向上させられるほか、算出時間を短縮可能となる。また、２層最適化法は、当該開口補強問題における変数特性を十分に組み合わせ、異なる最適化アルゴリズムを用いて段階的に適化設計を展開することから、最適化効率が向上する。本発明によれば、開口の部分補強設計における構造効率が高まり、最適化設計の算出コストを削減可能となる。よって、本邦のキャリアロケットやミサイルの設計といった航空宇宙分野において、軸方向圧力補強リブ円筒殻構造の開口補強方法の一つと十分になり得る。 The opening reinforcement method for the axial pressure-reinforced rib cylindrical shell provided by the present invention is for the problem that the structural efficiency is low in the conventional opening-reinforcement design of the axial pressure-reinforced rib cylindrical shell, and the calculation cost of the optimized design is increased. First, by combining the design flexibility of the NURBS curved rib with the opening reinforcement requirement in the axial pressure reinforcing rib cylindrical shell structure, the power transmission path near the opening is greatly improved, and the axial pressure reinforcing rib cylindrical shell is also improved. Improve load bearing capacity against axial pressure in the structure. Subsequently, an adaptive partitioning method is provided for the near-opening region and the far-opening region to rationally determine the range of the near-opening region, so that an appropriate design region for optimization of the subsequent near-opening region can be obtained. Identify. Finally, based on the mixed analysis model, a two-layer optimization design method is provided for the opening reinforcement of the axial pressure reinforcing rib cylindrical shell. According to the mixed analysis model of the region near the opening and the region far from the opening, the analysis efficiency of the load bearing capacity against the axial pressure of the opened reinforcing rib cylindrical shell structure can be greatly improved, and the calculation time can be shortened. In addition, the two-layer optimization method sufficiently improves the optimization efficiency because the variable characteristics in the opening reinforcement problem are sufficiently combined and the optimization design is developed step by step using different optimization algorithms. According to the present invention, the structural efficiency in the partial reinforcement design of the opening is increased, and the calculation cost of the optimized design can be reduced. Therefore, in the aerospace field such as the design of carrier rockets and missiles in Japan, it can be sufficient as one of the opening reinforcement methods of the axial pressure reinforcement rib cylindrical shell structure.
本発明が解決する技術的課題、適用する技術方案及び達成される技術的効果をより明確にすべく、以下に図面と実施例を組み合わせて本発明を更に詳細に説明する。なお、ここで述べる具体的実施例は本発明を説明するためのものにすぎず、本発明を限定する主旨ではないと解釈される。また、記載の便宜上、図面には本発明に関連する部分のみを表示しており、全ての内容を示しているわけではない。 In order to clarify the technical problem to be solved by the present invention, the technical solution to be applied, and the technical effect to be achieved, the present invention will be described in more detail below in combination with the drawings and embodiments. It should be noted that the specific examples described here are merely for explaining the present invention, and are not intended to limit the present invention. Further, for convenience of description, only the parts related to the present invention are displayed in the drawings, and not all the contents are shown.
図１は、本発明の実施例が提供する軸方向圧力補強リブ円筒殻における開口補強方法を実現するためのフローである。図１に示すように、本発明の実施例が提供する軸方向圧力補強リブ円筒殻における開口補強方法は、開口を含む軸方向圧力補強リブ円筒殻を開口遠方領域と開口付近領域に区分するステップ１００を含む。 FIG. 1 is a flowchart for realizing an opening reinforcing method in an axial pressure reinforcing rib cylindrical shell provided by an embodiment of the present invention. As shown in FIG. 1, the method for reinforcing an opening in an axial pressure reinforcing rib cylindrical shell provided by an embodiment of the present invention includes a step of dividing an axial pressure reinforcing rib cylindrical shell including an opening into an opening distant area and an opening vicinity area. 100 is included.
本発明では、開口を含む補強リブ円筒殻の開口を補強する。具体的に、補強リブ円筒殻は各種の補強構成を備えることが可能である。図２ａ〜ｄは、各種補強リブ円筒殻の構造を示す図である。図２ａは、正三角形の補強リブが正置された円筒殻の構造を示す図であり、図２ｂは、正三角形の補強リブが縦置きされた円筒殻の構造を示す図であり、図２ｃは、直交する補強リブが正置された円筒殻の構造を示す図であり、図２ｄは、任意の角度の補強リブ円筒殻の構造を示す図である。図２ａ〜ｄを参照して、本発明が提供する軸方向圧力補強リブ円筒殻における開口補強方法は、各種補強リブ円筒殻について開口補強の最適化設計が可能である。図３ａ〜ｃは、各種開口を示す図である。図３ａ〜ｃに示すように、開口の形状は矩形、円形又は楕円形が可能である。 In the present invention, the opening of the reinforcing rib cylindrical shell including the opening is reinforced. Specifically, the reinforcing rib cylindrical shell can have various reinforcing configurations. 2a to 2d are diagrams showing structures of various reinforcing rib cylindrical shells. Fig. 2a is a diagram showing the structure of a cylindrical shell in which equilateral triangular reinforcing ribs are arranged, and Fig. 2b is a diagram showing the structure of a cylindrical shell in which equilateral triangular reinforcing ribs are vertically arranged, Fig. 2c Fig. 2 is a diagram showing a structure of a cylindrical shell in which orthogonal reinforcing ribs are arranged in a straight line, and Fig. 2d is a diagram showing a structure of a reinforcing rib cylindrical shell having an arbitrary angle. Referring to FIGS. 2a to 2d, the opening reinforcing method in the axial pressure reinforcing rib cylindrical shell provided by the present invention can be optimized for opening reinforcing for various reinforcing rib cylindrical shells. 3a to 3c are diagrams showing various openings. As shown in FIGS. 3a-c, the shape of the opening can be rectangular, circular or elliptical.
ステップ１０１において、座屈固有値解析を用い、軸方向圧力補強リブ円筒殻におけるｎ次までの座屈モードを取得する。 In step 101, buckling modes up to the n-th order in the axial pressure reinforcing rib cylindrical shell are obtained using buckling eigenvalue analysis.
ステップ１０２において、ｎ次までの座屈モードのうち選別条件を満たすｍ次までの部分座屈モードを選別し、ｍ次までの部分座屈モードを重畳して混合モード形状を形成する。 In step 102, partial buckling modes up to the mth order satisfying the selection condition among the buckling modes up to the nth order are selected, and the mixed mode shape is formed by superimposing the partial buckling modes up to the mth order.
本ステップでは、座屈変形が座屈変形閾値よりも大きな領域の面積が筐体総面積の１／ａ以下であり、ａが２〜４であることを選別条件とする。実際の開口補強過程では、状況に応じて変形閾値が異なる数値を取るとともに、ａが異なる数値を取るよう調整する場合がある。本発明では、変形閾値を０．３５、ａを２とする。ａが２であることから、座屈変形が０．３５よりも大きな領域の面積が筐体総面積の半分以下であることが選別条件となる。本ステップでは、座屈変形が０．３５よりも大きな領域の面積を測定し、座屈変形が０．３５よりも大きな領域の面積が筐体総面積の半分よりも大きいか否かを判別することで、座屈変形が０．３５よりも大きな領域の面積が筐体総面積の半分以下である座屈モードを選別して、ｍ次までの部分座屈モードを形成する。本ステップにおける重畳では、ｍ次までの各部分座屈モードを取得して合わせることで混合モード形状が得られる。 In this step, the selection condition is that the area of the region where the buckling deformation is larger than the buckling deformation threshold is 1 / a or less of the total housing area, and a is 2 to 4. In the actual opening reinforcement process, the deformation threshold value may vary depending on the situation, and a may be adjusted to take a different value. In the present invention, the deformation threshold is 0.35 and a is 2. Since a is 2, the selection condition is that the area of the region where the buckling deformation is larger than 0.35 is not more than half of the total housing area. In this step, the area of the region where the buckling deformation is larger than 0.35 is measured, and it is determined whether the area of the region where the buckling deformation is larger than 0.35 is larger than half of the total housing area. Thus, the buckling mode in which the area of the region where the buckling deformation is larger than 0.35 is less than half of the total housing area is selected, and the partial buckling mode up to the mth order is formed. In the superposition in this step, a mixed mode shape is obtained by acquiring and combining the partial buckling modes up to the mth order.
ステップ１０３では、形成された混合モードの形状に基づき、座屈変形が座屈変形閾値を超えている領域を開口付近領域、残りの領域を開口遠方領域として区分する。 In step 103, based on the shape of the formed mixed mode, the region where the buckling deformation exceeds the buckling deformation threshold is classified as the opening vicinity region, and the remaining region is classified as the opening far region.
本ステップでは、主に座屈固有値解析を用いて開口遠方領域と開口付近領域を区分する。座屈固有値解析は線形座屈解析ともいい、応力剛性効果を考慮している。当該効果によれば、構造は面内圧応力を受けた後に平面負荷に抵抗する能力が低下してしまう。ある負荷レベルにおいて、こうしたマイナスの応力剛性が構造の線形剛性を上回った場合、構造は座屈不安定となる。 In this step, the area far from the aperture and the area near the aperture are mainly classified using buckling eigenvalue analysis. The buckling eigenvalue analysis is also called linear buckling analysis and considers the stress stiffness effect. This effect reduces the ability of the structure to resist planar loads after receiving in-plane pressure stress. If at some load level such negative stress stiffness exceeds the linear stiffness of the structure, the structure becomes buckling unstable.
ステップ２００では、開口遠方領域に等価剛性モデルを構築し、開口付近領域に精密な幾何モデルを構築して、軸方向圧力補強リブ円筒殻の混合分析モデルを得る。 In step 200, an equivalent stiffness model is constructed in the region far from the aperture, and a precise geometric model is constructed in the region near the aperture to obtain a mixed analysis model of the axial pressure reinforcing rib cylindrical shell.
ステップ２０１では、均質化理論又は漸近的均質化理論に基づく軸方向圧力補強リブ円筒殻構造の等価剛性モデルを構築し、開口遠方領域の軸方向圧力補強リブ円筒殻を、異方性又は等方性の光学殻に等価とする。 In step 201, an equivalent stiffness model of the axial pressure reinforcing rib cylindrical shell structure based on the homogenization theory or the asymptotic homogenization theory is constructed, and the axial pressure reinforcing rib cylindrical shell in the far opening region is made anisotropic or isotropic. Equivalent to the optical shell of sex.
ステップ２０２では、非一様有理Ｂスプライン曲線で描いた湾曲リブに基づいて、開口付近領域に精密な幾何モデルを構築する。 In step 202, a precise geometric model is constructed in the region near the opening based on the curved rib drawn by the non-uniform rational B-spline curve.
ステップ２０３では、開口付近領域と開口遠方領域の接続関係を設定し、開口を含む軸方向圧力補強リブ円筒殻の軸方向圧力に対する耐荷能力の混合分析モデルを取得する。 In step 203, a connection relationship between the opening vicinity region and the opening far region is set, and a mixed analysis model of the load bearing capacity against the axial pressure of the axial pressure reinforcing rib cylindrical shell including the opening is acquired.
本発明は、均質化理論又は漸近的均質化理論に基づいて、補強リブ円筒殻構造の等価剛性モデルを構築する。均質化理論では、マクロ構造を構成するセルエレメントの入手から着手し、セルエレメントが空間周期性を有すると仮定して、セルエレメントの構造を分析することで、元構造とマクロ力学性能が等価である均質材料を取得する。本発明は均質化の原理に基づいて、空間周期性を有するリブを、直交する異方性／等方性の光学殻に等価とすることで、軸方向圧力補強構造の座屈分析効率を大幅に向上させる。均質化理論又は漸近的均質化理論に基づいて取得される等価剛性モデルは、解を求めるプロセスが視覚的で簡潔なことから、ミサイル本体における補強リブ円筒殻構造の初期設計やパラメータ予備調査に常用される。 The present invention builds an equivalent stiffness model of a reinforced rib cylindrical shell structure based on homogenization theory or asymptotic homogenization theory. In the homogenization theory, we start by obtaining the cell elements that make up the macro structure, and assume that the cell elements have a spatial periodicity and analyze the structure of the cell elements so that the original structure and the macro mechanical performance are equivalent. Get a certain homogeneous material. Based on the principle of homogenization, the present invention greatly increases the buckling analysis efficiency of the axial pressure reinforcement structure by making the rib with spatial periodicity equivalent to an orthogonal anisotropic / isotropic optical shell. To improve. The equivalent stiffness model obtained based on homogenization theory or asymptotic homogenization theory is commonly used for initial design and preliminary parameter investigation of the reinforced rib cylindrical shell structure in the missile body because the solution-finding process is visual and simple. Is done.
非一様有理Ｂスプライン（ＮＵＲＢＳ）曲線で描かれた湾曲リブは、コンピュータグラフィックスで常用される数学的モデルであり、曲線や曲面を生成して表すために用いられる。通常、ＮＵＲＢＳ曲線は１の初期制御点、１又は複数の中間制御点及び１の終了制御点によって形状を描き、分析関数やモデル形状の処理に対し極めて高い柔軟性と精密性を提供する。ＮＵＲＢＳによる湾曲リブは、ＮＵＲＢＳ曲線を平面方向に引き伸ばし操作することで得られる。湾曲リブの制御点、即ちＮＵＲＢＳ曲線の制御点は、通常は１の初期制御点、１又は複数の中間制御点及び１の終了制御点であり、制御点の座標とは２次元座標軸上における制御点の座標値のことである。有限要素計算において、開口付近領域と開口遠方領域の関係接続は、一般的に共有ノード又は変形調和技術によって完遂される。即ち、開口付近領域と開口遠方領域の境界部分における有限要素のノードの自由度を併合することで、分析モデル全体を形成する。本ステップでは、ステップ２０１で得られた開口遠方領域モデルとステップ２０２で得られた開口付近領域モデルを重畳することで、混合分析モデルが得られる。 A curved rib drawn with a non-uniform rational B-spline (NURBS) curve is a mathematical model commonly used in computer graphics, and is used to generate and represent curves and curved surfaces. Normally, a NURBS curve is drawn with one initial control point, one or more intermediate control points, and one end control point, providing extremely high flexibility and precision for processing analytic functions and model shapes. The curved rib by NURBS can be obtained by extending the NURBS curve in the plane direction. The control point of the curved rib, that is, the control point of the NURBS curve is usually one initial control point, one or a plurality of intermediate control points, and one end control point, and the coordinates of the control points are the controls on the two-dimensional coordinate axis. It is the coordinate value of a point. In the finite element calculation, the relational connection between the near-opening region and the far-opening region is generally accomplished by a shared node or deformation matching technique. In other words, the entire analysis model is formed by merging the degrees of freedom of the finite element nodes at the boundary between the near-opening region and the far-opening region. In this step, a mixed analysis model is obtained by superimposing the aperture far region model obtained in step 201 and the aperture vicinity region model obtained in step 202.
ステップ３００において、軸方向圧力補強リブ円筒殻について開口補強の最適化を行い、最適化結果をチェックする。 In step 300, optimization of opening reinforcement is performed on the axial pressure reinforcing rib cylindrical shell, and the optimization result is checked.
ステップ３０１では、第１層の最適化において、代理モデルを大域的最適化手法と組み合わせることで、リブ厚、リブ高さ、軸方向のリブ数と配置、周方向のリブ数と配置、及びプライ角度のうちの１又はこれらの組み合わせを設計変数とし、軸方向圧力補強リブ円筒殻構造の軸方向圧力に対する耐荷力を目標関数とし、構造重量及び／又は構造製造コストを制約条件として、軸方向圧力補強リブ円筒殻構造を最適化設計し、制約条件を満たした最適化設計を得る。代理モデルを大域的最適化手法と組み合わせる方法では、まずサンプリングテスト設計手法で得られたテストポイントに基づいて代理モデルを構築してから、大域的最適化手法を用いて代理モデルに基づく最適化を実行する。 In step 301, in the optimization of the first layer, the surrogate model is combined with the global optimization method to obtain the rib thickness, rib height, the number and arrangement of the ribs in the axial direction, the number and arrangement of the ribs in the circumferential direction, and the ply. One of the angles or a combination thereof is used as a design variable, the load resistance against the axial pressure of the axial pressure-reinforcing rib cylindrical shell structure is a target function, and the structural weight and / or structure manufacturing cost is a constraint. Optimized design of the reinforced rib cylindrical shell structure and obtain an optimized design that satisfies the constraints. In the method of combining the surrogate model with the global optimization method, the surrogate model is first constructed based on the test points obtained by the sampling test design method, and then the optimization based on the surrogate model is performed using the global optimization method. Run.
具体的には、本発明の実施例が提供する第１層面の最適化は、下記式で表される。
設計変数：ｄ＝［ｈ，ｔｒ，Ｎａ，Ｎｃ，λａｓ，λａｍ，λｃｓ，λｃｍ］
目標関数：Ｐｃｏ
制約条件：Ｗ≦Ｗ０
ここで、ｈはリブ高さ、ｔｒはリブ厚、Ｎａは軸方向のリブ数、Ｎｃは周方向のリブ数、λａｓは軸方向のリブ始点の配置制御係数、λａｍは軸方向のリブ中間制御点の配置制御係数、λｃｓは周方向のリブ始点の配置制御係数、λｃｍは周方向のリブ中間制御点の配置制御係数、Ｐｃｏは構造の軸方向圧力に対する耐荷力、Ｗは構造重量、Ｗ０は初期設計の構造重量をそれぞれ表している。
Specifically, the optimization of the first layer surface provided by the embodiment of the present invention is expressed by the following formula.
Design variable: d = [h, tr , N a , N c , λ as , λ am , λ cs , λ cm ]
Target function: P co
Constraint: W ≦ W 0
Here, h is the rib height, t r is rib thickness, N a is the number of axial ribs, N c rib number of circumferential, lambda the as the arrangement control coefficient of axial ribs start, lambda am the shaft Is the placement control coefficient of the rib intermediate control point in the direction, λ cs is the placement control coefficient of the rib start point in the circumferential direction, λ cm is the placement control coefficient of the rib intermediate control point in the circumferential direction, and P co is the load bearing capacity against the axial pressure of the structure , W represents the structural weight, and W 0 represents the structural weight of the initial design.
軸方向のリブ配置は、単一の制御変数で描かれた配置関数で決定される。軸方向のリブの配置関数は、
ステップ３０２では、第２層の最適化において、第１層の最適化設計に基づいてリブ厚、リブ高さ、軸方向のリブ数及び周方向のリブ数を固定し、勾配別部分最適化法を用いて、各湾曲リブの制御点座標を設計変数とし、補強リブ円筒殻構造の軸方向圧力に対する耐荷力を目標関数とし、構造重量及び／又は構造製造コストを制約条件として、補強リブ円筒殻構造を最適化設計し、制約条件を満たす最適化結果を取得する。 In step 302, in the optimization of the second layer, the rib thickness, the rib height, the number of ribs in the axial direction and the number of ribs in the circumferential direction are fixed based on the optimization design of the first layer, and the partial optimization method by gradient The control point coordinates of each curved rib is used as a design variable, the load bearing force against the axial pressure of the reinforcing rib cylindrical shell structure is a target function, and the structural weight and / or the structure manufacturing cost are used as constraints. Optimize the structure and obtain optimization results that satisfy the constraints.
具体的には、本発明の実施例が提供する第２層面の最適化は、下記式で表される。
設計変数：ｄ＝［ｘａｓ，ｘａｍ，ｙｃｓ，ｙｃｍ］
目標関数：Ｐｃｏ
制約条件：Ｗ≦Ｗ０
ここで、ｘａｓは軸方向のリブ初期制御点におけるｘ座標、ｘａｍは軸方向のリブ中間制御点におけるｘ座標、ｙｃｓは周方向のリブ初期制御点におけるｙ座標、ｙｃｍは周方向のリブ中間制御点におけるｙ座標、Ｐｃｏは構造の軸方向圧力に対する耐荷力、Ｗは構造重量、Ｗ０は初期設計の構造重量をそれぞれ表している。
Specifically, the optimization of the second layer surface provided by the embodiment of the present invention is expressed by the following formula.
Design variable: d = [x as , x am , y cs , y cm ]
Target function: P co
Constraint: W ≦ W 0
Here, x as is the x coordinate at the axial initial rib control point, x am is the x coordinate at the axial intermediate rib control point, y cs is the y coordinate at the circumferential initial rib control point, and y cm is the circumferential direction. Y coordinate at the rib intermediate control point, P co is the load bearing capacity against the axial pressure of the structure, W is the structure weight, and W 0 is the structure weight of the initial design.
前記の勾配別部分最適化法には、最急降下法、実行可能方向法、シンプレックス法、逐次線形計画法又は逐次二次計画法が含まれる。逐次二次計画法では、元の制約最適化問題に類似した二次計画部分問題を反復点に構築し、当該部分問題の解を求めることで、制約最適化問題における１の改良反復点を取得する。この過程は、要求を満たす反復点が求められるまで繰り返される。 The gradient-based partial optimization method includes steepest descent method, feasible direction method, simplex method, sequential linear programming, or sequential quadratic programming. In sequential quadratic programming, a quadratic programming subproblem similar to the original constraint optimization problem is constructed at the iteration point, and the solution of the subproblem is obtained to obtain one improved iteration point in the constraint optimization problem. To do. This process is repeated until an iteration point that satisfies the requirement is found.
ステップ３０３では、精密な有限要素に基づいて、最適化結果をチェックする。 In step 303, the optimization result is checked based on the precise finite element.
チェックの具体的過程としては、精密な有限要素に基づいて、最適化結果について精密なモデリング及び軸方向圧力に対する耐荷能力分析を行い、その幾何モデル及び分析結果をチェックする。本ステップで最適化結果をチェックするのは、加工困難な断裂リブや小さいリブ、応力集中現象の発生有無や、最小特徴サイズ、曲率といったその他の工程要求を満たしているか否かを確認するためである。 As a specific process of the check, based on a precise finite element, the optimization result is subjected to precise modeling and load bearing capacity analysis for axial pressure, and the geometric model and analysis result are checked. The optimization results are checked in this step in order to confirm whether other process requirements such as fractured ribs, small ribs, stress concentration phenomenon, minimum feature size, and curvature are difficult to process. is there.
本発明の方法によれば、軸方向圧力補強リブ円筒殻における開口補強効率が高まり、算出コストを削減可能となる。 According to the method of the present invention, the opening reinforcement efficiency in the axial pressure reinforcing rib cylindrical shell is increased, and the calculation cost can be reduced.
以下に、実例形式で本実施例が提供する方案について説明する。 Below, the method which a present Example provides with an example form is demonstrated.
例示的に、図４は開口された補強リブ円筒殻の構造を示す図である。図４を参照して、直交する補強リブが正置された半径Ｒ＝１５００ｍｍ、長さＬ＝２０００ｍｍ、被覆厚ｔｓ＝４．０ｍｍ、リブ厚ｔｒ＝９．０ｍｍ、リブ高さｈ＝１５．０ｍｍ、軸方向のリブ数Ｎａ＝９０、周方向のリブ数Ｎｃ＝２５の円筒殻について考える。なお、開口形状は正方形であり、辺の長さｂ＝５００ｍｍであった。また、構造材料としては、弾性率Ｅ＝７０ＧＰａ、ボアソン比υ＝０．３３、密度ρ＝２．７Ｅ−６ｋｇ／ｍｍ３のアルミニウム合金を用いた。初期設計の構造重量は３５０ｋｇであり、有限要素モデルに基づき予測される構造の軸方向圧力に対する耐荷力は１００００ｋＮであった。 Illustratively, FIG. 4 is a diagram illustrating the structure of an open reinforcing rib cylindrical shell. Referring to FIG. 4, radius R = 1500 mm, length L = 2000 mm, covering thickness t s = 4.0 mm, rib thickness t r = 9.0 mm, and rib height h = Consider a cylindrical shell with 15.0 mm, axial rib number N a = 90, and circumferential rib number N c = 25. The opening shape was a square, and the side length b was 500 mm. As a structural material, an aluminum alloy having an elastic modulus E = 70 GPa, a Boisson ratio υ = 0.33, and a density ρ = 2.7E−6 kg / mm 3 was used. The structure weight of the initial design was 350 kg, and the load bearing capacity against the axial pressure of the structure predicted based on the finite element model was 10000 kN.
まず、有限要素モデルに基づいて座屈固有値解析を行い、１０次までの固有値の座屈モードを取得した。図５は、本発明の実施例が提供する開口された補強リブ円筒殻における１０次までの固有値の座屈モードである。図５に示すように、４次までが本実施例の選別条件を満たすため、４次までを部分座屈モードとし、５次以降を全体座屈モードとした。５次以降は全体座屈モードのため、開口付近領域と開口遠方領域を区分するためのガイダンス情報は提供されない。そこで、４次までのモードを重畳して混合モード形状を形成し、図６に示すように、変形が所定の閾値０．３５を上回る領域を開口付近領域、残りの領域を開口遠方領域として区分した。図６は、本発明の実施例が提供する開口された補強リブ円筒殻の混合分析モデルである。続いて、開口遠方領域に漸近的均質化理論に基づいて取得した等価剛性モデルを用い、リブを異方性の光学殻に等価とするとともに、開口付近領域にＮＵＲＢＳ湾曲リブを用いて精密な幾何モデルを構築することで、図６に示すように、開口された補強リブ円筒殻の混合分析モデルを取得した。各湾曲リブは、１の初期制御点、１の中間制御点及び１の終了制御点により描画された。なお、現在主流とされているコンピュータ（４コア、クロック周波数２．９ＧＨｚ、メモリ８Ｇ）を用いたところ、精密な有限要素モデル及び混合分析モデルによる明示的飛移座屈分析の算出に要した時間はそれぞれ１．８時間及び０．２時間であった。 First, buckling eigenvalue analysis was performed based on a finite element model, and buckling modes of eigenvalues up to the 10th order were obtained. FIG. 5 is an eigenvalue buckling mode up to the 10th order in an open reinforcing rib cylindrical shell provided by an embodiment of the present invention. As shown in FIG. 5, since the conditions up to the fourth order satisfy the selection conditions of the present embodiment, the parts up to the fourth order are set as the partial buckling mode, and the fifth order and later are set as the whole buckling mode. Since the fifth and subsequent modes are in the overall buckling mode, guidance information for distinguishing between the aperture vicinity region and the aperture far region is not provided. Therefore, a mixed mode shape is formed by superimposing the modes up to the fourth order, and as shown in FIG. 6, the region where the deformation exceeds a predetermined threshold value 0.35 is classified as the near-opening region, and the remaining region is classified as the far-opening region. did. FIG. 6 is a mixed analysis model of an open reinforced rib cylindrical shell provided by an embodiment of the present invention. Subsequently, the equivalent stiffness model obtained based on the asymptotic homogenization theory is used for the far region of the aperture, the rib is made equivalent to an anisotropic optical shell, and a precise geometrical shape using a NURBS curved rib in the region near the aperture. By constructing the model, a mixed analysis model of the opened reinforcing rib cylindrical shell was obtained as shown in FIG. Each curved rib was drawn with one initial control point, one intermediate control point, and one end control point. In addition, when a computer (4 cores, clock frequency 2.9 GHz, memory 8G), which is currently mainstream, is used, the time required for calculation of explicit jump buckling analysis using a precise finite element model and a mixed analysis model Were 1.8 hours and 0.2 hours, respectively.
次に、軸方向圧力補強リブ円筒殻の開口補強について２層最適化設計を展開した。収束基準を満たすまで、第１層につき大域的最適化を、第２層につき部分最適化を実施した。第１層面の最適化においては、構造の軸方向圧力に対する耐荷力を最大化することを最適化目標とし、構造重量が初期重量を超えないことを制約条件とした。設計変数には、リブ高さ、リブ厚、軸方向及び周方向のリブ数、軸方向と周方向におけるリブの配置制御係数（初期制御点と中間制御点をそれぞれ含む）の計８項目が含まれた。特定の設計変数区間内において、最適ラテン方格法を用いて３００のサンプルを抽出し、放射基底関数代理モデルを構築した。続いて、多島遺伝的アルゴリズムを用い、代理モデルに基づく開口付近領域の最適化設計を実行した。図７は、本発明の実施例が提供する開口された補強リブ円筒殻における第１層面の最適化反復図である。図７に示すように、外層を４回更新した後に、最適化の反復を収束終了させた。最適化設計の構造重量は３５０ｋｇであり、等価剛性モデルと有限要素モデルに基づき予測される軸方向圧力に対する耐荷力はそれぞれ１１１０７ｋＮ及び１１１５８ｋＮであった。最適化設計の変数値としては、リブ高さが２３．０ｍｍ、リブ厚が６．３ｍｍ、軸方向及び周方向のリブ数がそれぞれ１３及び７、軸方向のリブにおける初期制御点と中間制御点の配置制御係数がそれぞれ０．８５８１及び１．３１５０、周方向のリブにおける初期制御点と中間制御点の配置制御係数がそれぞれ１．２７４８及び０．７４０９であった。
Next, a two-layer optimization design was developed for opening reinforcement of the axial pressure reinforcing rib cylindrical shell. Global optimization was performed for the first layer and partial optimization was performed for the second layer until convergence criteria were met. In the optimization of the first layer surface, the optimization target was to maximize the load bearing capacity against the axial pressure of the structure, and the constraint was that the structure weight did not exceed the initial weight. The design variables include a total of 8 items: rib height, rib thickness, number of ribs in the axial direction and circumferential direction, and rib placement control coefficients in the axial direction and circumferential direction (including initial control points and intermediate control points, respectively). It was. Within a specific design variable interval, 300 samples were extracted using the optimal Latin square method, and a radial basis function surrogate model was constructed. Subsequently, using the archipelago genetic algorithm, optimization design of the area near the opening based on the surrogate model was performed. FIG. 7 is an optimized iterative view of the first layer surface in an open reinforcing rib cylindrical shell provided by an embodiment of the present invention. As shown in FIG. 7, after the outer layer was updated four times, the optimization iterations were converged. The structural weight of the optimized design was 350 kg, and the load bearing capacity against the axial pressure predicted based on the equivalent stiffness model and the finite element model was 11107 kN and 11158 kN, respectively. The optimization design variable values are: rib height 23.0 mm, rib thickness 6.3 mm, axial and
第２層面の最適化においては、構造の軸方向圧力に対する耐荷力を最大化することを最適化目標とし、構造重量が初期重量を上回らないことを制約条件とした。また、軸方向及び周方向のリブ数、リブ高及びリブ厚を固定して、各湾曲リブの制御点座標を計１８の設計変数とした。図８は、本発明の実施例が提供する開口された補強リブ円筒殻における第２層面の最適化反復図である。図８に示すように、逐次二次計画法を用いて、最適化を１００回反復した後に収束終了した。最適化設計の構造重量は３５０ｋｇであり、等価剛性モデルと有限要素モデルに基づき予測される軸方向圧力に対する耐荷力はそれぞれ１１５５９ｋＮ及び１１６１４ｋＮであった。 In optimizing the second layer surface, the optimization goal was to maximize the load bearing capacity against the axial pressure of the structure, and the constraint was that the structure weight would not exceed the initial weight. Further, the number of ribs in the axial direction and the circumferential direction, the rib height, and the rib thickness were fixed, and the control point coordinates of each curved rib were used as a total of 18 design variables. FIG. 8 is an optimized iterative view of the second layer surface in an open reinforcing rib cylindrical shell provided by an embodiment of the present invention. As shown in FIG. 8, convergence was completed after 100 iterations of optimization using sequential quadratic programming. The structural weight of the optimized design was 350 kg, and the load bearing capacity against the axial pressure predicted based on the equivalent stiffness model and the finite element model was 11559 kN and 11614 kN, respectively.
最後に、精密な有限要素解析によって最適化設計をチェックした。チェックの結果、当該設計は変形モードと応力分布が合理的であり、工程要求を満たしていた。 Finally, the optimization design was checked by precise finite element analysis. As a result of checking, the design was reasonable in deformation mode and stress distribution, and satisfied the process requirements.
比較として、本発明の最適化方法に基づき、直線リブによる補強設計について最適化設計を行った。最適化設計の構造重量は３５０ｋｇ、軸方向圧力に対する耐荷力は１０９１７ｋＮであった。これに対し、本発明の技術方案による最適化設計の構造重量は３５０ｋｇ、軸方向圧力に対する耐荷力は１１６１４ｋＮであった。比較より、本発明の技術方案は、従来技術よりも構造効率の高い開口された補強設計方案を提供可能なことがわかった。 As a comparison, based on the optimization method of the present invention, an optimization design was performed for the reinforcement design using straight ribs. The structural weight of the optimized design was 350 kg, and the load bearing capacity against axial pressure was 10917 kN. In contrast, the structural weight of the optimized design according to the technical scheme of the present invention was 350 kg, and the load bearing capacity against the axial pressure was 11614 kN. From the comparison, it has been found that the technical solution of the present invention can provide an open reinforcing design method having a higher structural efficiency than the conventional technology.
非線形性飛移座屈分析の使用回数からみると、本発明の技術方案では４０４回であったのに対し、類似の最適化構造重量及び軸方向圧力に対する耐荷力獲得を前提とした場合、従来技術では２２００回の分析が必要であった。比較より、本発明の技術方案によれば、従来技術よりも高い最適化効率を提供可能なことがわかった。 In terms of the number of times the nonlinear jump buckling analysis is used, it was 404 times in the technical method of the present invention, whereas in the case of assuming a load capacity against a similar optimized structure weight and axial pressure, The technique required 2200 analyzes. From the comparison, it was found that according to the technical solution of the present invention, it is possible to provide higher optimization efficiency than the conventional technology.
算出コスト面では、提示した２層最適化設計法を適用し、現在主流とされているコンピュータ（４コア、クロック周波数２．９ＧＨｚ、メモリ８Ｇ）を用いた場合、本発明の技術方案の所要時間が８０．８ｈであったのに対し、従来技術では７２７．２ｈを要した。比較より、本発明の技術方案によれば算出コストが大幅に削減され、最適化効率が従来技術よりも大きく向上することがわかった。 In terms of calculation cost, when the proposed two-layer optimization design method is applied and a currently mainstream computer (4 cores, clock frequency 2.9 GHz, memory 8 G) is used, the time required for the technical method of the present invention Was 80.8 h, whereas the conventional technology required 727.2 h. From the comparison, it was found that according to the technical solution of the present invention, the calculation cost is greatly reduced, and the optimization efficiency is greatly improved as compared with the prior art.
本実施例が提供する軸方向圧力補強リブ円筒殻における開口補強方法では、まず、ＮＵＲＢＳ湾曲リブの設計柔軟性を、軸方向圧力補強リブ円筒殻構造における開口補強要求に組み合わせることで、開口付近の動力伝達経路を大幅に改善するとともに、軸方向圧力補強リブ円筒殻構造における軸方向圧力への耐荷力を向上させる。続いて、開口付近領域と開口遠方領域につきアダプティブパーティショニング法を提供して、開口付近領域の範囲を合理的に決定することで、後続の開口付近領域の最適化のために適切な設計領域を特定する。最後に、混合分析モデルに基づいて、軸方向圧力補強リブ円筒殻の開口補強について２層最適化設計法を提供する。開口付近領域−開口遠方領域の混合分析モデルによれば、開口された補強リブ円筒殻構造の軸方向圧力に対する耐荷力の分析効率を大幅に向上させられるほか、算出時間を短縮可能となる。また、２層最適化法は、当該開口補強問題における変数特性を十分に組み合わせ、異なる最適化アルゴリズムを用いて段階的に適化設計を展開することから、最適化効率が向上する。本発明によれば、開口の部分補強設計における構造効率が高まり、最適化設計の算出コストを削減可能となる。よって、本邦のキャリアロケットやミサイルの設計といった航空宇宙分野において、軸方向圧力補強リブ円筒殻構造の開口補強方法の一つとなり得る。 In the opening reinforcing method in the axial pressure reinforcing rib cylindrical shell provided by the present embodiment, first, the design flexibility of the NURBS curved rib is combined with the opening reinforcing requirement in the axial pressure reinforcing rib cylindrical shell structure, so that The power transmission path is greatly improved and the load resistance against the axial pressure in the axial pressure reinforcing rib cylindrical shell structure is improved. Subsequently, an adaptive partitioning method is provided for the near-opening region and the far-opening region to rationally determine the range of the near-opening region, so that an appropriate design region for optimization of the subsequent near-opening region can be obtained. Identify. Finally, based on the mixed analysis model, a two-layer optimization design method is provided for the opening reinforcement of the axial pressure reinforcing rib cylindrical shell. According to the mixed analysis model of the region near the opening and the region far from the opening, the analysis efficiency of the load bearing capacity against the axial pressure of the opened reinforcing rib cylindrical shell structure can be greatly improved, and the calculation time can be shortened. In addition, the two-layer optimization method sufficiently improves the optimization efficiency because the variable characteristics in the opening reinforcement problem are sufficiently combined and the optimization design is developed step by step using different optimization algorithms. According to the present invention, the structural efficiency in the partial reinforcement design of the opening is increased, and the calculation cost of the optimized design can be reduced. Therefore, in the aerospace field such as the design of carrier rockets and missiles in Japan, it can be one of the methods of reinforcing the opening of the axial pressure reinforcing rib cylindrical shell structure.
最後に、以上の各実施例は本発明の技術方案を説明するためのものであって、本発明を制限する主旨ではない。前記各実施例を参照して本発明を詳細に説明したが、当業者であれば、前記各実施例に記載される技術方案を補正、或いはその一部又は全ての技術的特徴につき等価の置き換えを実施したとしても、対応する技術方案の本質が本発明の各実施例における技術方案の範囲を逸脱することはないものと理解可能である。 Finally, each of the above embodiments is for explaining the technical solution of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to each of the above embodiments, those skilled in the art will correct the technical solutions described in each of the above embodiments, or equivalently replace some or all of the technical features. However, it can be understood that the essence of the corresponding technical solution does not depart from the scope of the technical solution in each embodiment of the present invention.
Claims (5)
開口を含む軸方向圧力補強リブ円筒殻を開口遠方領域と開口付近領域に区分するステップ１００を含み、当該ステップが、
座屈固有値解析を用い、軸方向圧力補強リブ円筒殻におけるｎ次までの座屈モードを取得するステップ１０１と、
ｎ次までの座屈モードのうち選別条件を満たすｍ次までの部分座屈モードを選別し、ｍ次までの部分座屈モードを重畳して混合モード形状を形成するステップ１０２であって、座屈変形が座屈変形閾値よりも大きな領域の面積が筐体総面積の１／ａ以下であり、ａが２〜４であることを選別条件とするステップ１０２と、
形成された混合モードの形状に基づき、座屈変形が座屈変形閾値を超えている領域を開口付近領域、残りの領域を開口遠方領域として区分するステップ１０３と、
開口遠方領域に等価剛性モデルを構築し、開口付近領域に精密な幾何モデルを構築して、軸方向圧力補強リブ円筒殻の混合分析モデルを得るステップ２００と、
均質化理論又は漸近的均質化理論に基づく軸方向圧力補強リブ円筒殻構造の等価剛性モデルを構築し、開口遠方領域の軸方向圧力補強リブ円筒殻を、異方性又は等方性の光学殻に等価とするステップ２０１と、
非一様有理Ｂスプライン曲線で描いた湾曲リブに基づいて、開口付近領域に精密な幾何モデルを構築するステップ２０２と、
開口付近領域と開口遠方領域の接続関係を設定し、開口を含む軸方向圧力補強リブ円筒殻の軸方向圧力に対する耐荷能力の混合分析モデルを取得するステップ２０３と、
軸方向圧力補強リブ円筒殻について開口補強の最適化を行い、最適化結果をチェックするステップ３００と、を含むことを特徴とする方法。 A method of reinforcing an opening in an axial pressure reinforcing rib cylindrical shell,
Partitioning the axial pressure reinforcing rib cylindrical shell including the aperture into an aperture remote region and a region near the aperture, the step comprising:
Using buckling eigenvalue analysis to obtain a buckling mode up to the nth order in the axial pressure-reinforced rib cylindrical shell 101;
a step 102 of selecting a partial buckling mode up to an m-th order satisfying a selection condition from buckling modes up to an n-th order, and forming a mixed mode shape by superimposing the partial buckling modes up to the m-th order; A step 102 in which the area of the region where the bending deformation is larger than the buckling deformation threshold is 1 / a or less of the total housing area, and a is 2 to 4,
Dividing the region where the buckling deformation exceeds the buckling deformation threshold based on the shape of the formed mixed mode, as a region near the opening, and the remaining region as a region far from the opening; and
Building an equivalent stiffness model in the far opening region and building a precise geometric model in the near opening region to obtain a mixed analysis model of the axial pressure-reinforced rib cylindrical shell;
An equivalent stiffness model of the axial pressure-reinforced rib cylindrical shell structure based on the homogenization theory or asymptotic homogenization theory was constructed, and the axial pressure-reinforced rib cylindrical shell in the far region of the aperture was changed to an anisotropic or isotropic optical shell. Step 201 equivalent to
Building a precise geometric model 202 in the region near the opening based on curved ribs drawn with non-uniform rational B-spline curves;
Setting a connection relationship between the region near the opening and the region far from the opening, and obtaining a mixed analysis model 203 of the load bearing capacity against the axial pressure of the axial pressure reinforcing rib cylindrical shell including the opening; and
Optimizing aperture reinforcement for the axial pressure reinforcing rib cylindrical shell and checking 300 for optimization results.
第１層の最適化において、代理モデルを大域的最適化手法と組み合わせることで、リブ厚、リブ高さ、軸方向のリブ数と配置、周方向のリブ数と配置、及びプライ角度のうちの１又はこれらの組み合わせを設計変数とし、軸方向圧力補強リブ円筒殻構造の軸方向圧力に対する耐荷力を目標関数とし、構造重量及び／又は構造製造コストを制約条件として、軸方向圧力補強リブ円筒殻構造を最適化設計し、制約条件を満たした最適化設計を得るステップ３０１であって、軸方向のリブ配置が、単一の制御変数で描かれた配置関数で決定されるステップ３０１と、
第２層の最適化において、第１層の最適化設計に基づいてリブ厚、リブ高さ、軸方向のリブ数及び周方向のリブ数を固定し、勾配別部分最適化法を用いて、各湾曲リブの制御点座標を設計変数とし、軸方向圧力補強リブ円筒殻構造の軸方向圧力に対する耐荷力を目標関数とし、構造重量及び／又は構造製造コストを制約条件として、軸方向圧力補強リブ円筒殻構造を最適化設計し、制約条件を満たす最適化結果を取得するステップ３０２と、
精密な有限要素解析によって最適化結果をチェックするステップ３０３と、を含むことを特徴とする請求項１記載の軸方向圧力補強リブ円筒殻における開口補強方法。 The step 300 of optimizing the opening reinforcement for the axial pressure reinforcing rib cylindrical shell and checking the optimization result comprises:
In the optimization of the first layer, by combining the surrogate model with the global optimization method, the rib thickness, the rib height, the number and arrangement of the ribs in the axial direction, the number and arrangement of the ribs in the circumferential direction, and the ply angle One or a combination of these is used as a design variable, the load bearing capacity of the axial pressure reinforcing rib cylindrical shell structure against the axial pressure is set as a target function, and the structural weight and / or the structure manufacturing cost are used as constraint conditions. A step 301 for optimizing the structure and obtaining an optimized design satisfying the constraints, wherein the axial rib placement is determined by a placement function drawn with a single control variable;
In the optimization of the second layer, the rib thickness, the rib height, the number of ribs in the axial direction and the number of ribs in the circumferential direction are fixed based on the optimization design of the first layer, and a gradient-specific partial optimization method is used. The axial pressure reinforcement ribs are designed with the control point coordinates of each curved rib as design variables, the load bearing capacity against the axial pressure of the axial pressure reinforcement rib cylindrical shell structure as a target function, and the structural weight and / or structure manufacturing cost as constraints. A step 302 of optimizing the cylindrical shell structure and obtaining an optimization result that satisfies the constraint conditions;
The method of reinforcing an opening in an axial pressure reinforcing rib cylindrical shell according to claim 1, further comprising a step 303 of checking an optimization result by a precise finite element analysis.
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