CN107895098A - A kind of parabola circular arc end enclosure structure Optimization Design - Google Patents

A kind of parabola circular arc end enclosure structure Optimization Design Download PDF

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CN107895098A
CN107895098A CN201711474495.1A CN201711474495A CN107895098A CN 107895098 A CN107895098 A CN 107895098A CN 201711474495 A CN201711474495 A CN 201711474495A CN 107895098 A CN107895098 A CN 107895098A
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circular arc
parabola
design parameters
mrow
end socket
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CN107895098B (en
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苏文献
陈嘉雯
李波
黄文彬
熊丽敏
季思园
凌玮
凌一玮
赵婉瑄
李业勤
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University of Shanghai for Science and Technology
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design

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  • Computer Hardware Design (AREA)
  • General Engineering & Computer Science (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Optimization (AREA)
  • Mathematical Analysis (AREA)
  • Computational Mathematics (AREA)
  • Vessels, Lead-In Wires, Accessory Apparatuses For Cathode-Ray Tubes (AREA)

Abstract

The invention provides a kind of parabola circular arc end enclosure structure Optimization Design, comprise the following steps：Step 1, set the characteristic parameter and initial design parameters of parabola circular arc end socket；Step 2, two-dimensional geometry model is established according to characteristic parameter and initial design parameters；Step 3, corresponding function during the stress minimum of two-dimensional geometry model is defined as object function；Step 4, set the range of variables of initial design parameters；Step 5, using finite element analysis software, set constraint and load that initial design parameters are optimized with analysis and obtains stress intensity value corresponding to initial design parameters；Step 6, stress intensity value is substituted into object function, judge whether object function restrains and meet constraints, initial design parameters and return to step five are changed if being unsatisfactory for；Step 7, when object function is restrained and meets constraints, obtain optimal design parameters.

Description

A kind of parabola-circular arc end enclosure structure Optimization Design
Technical field
The present invention relates to a kind of Optimization Design, and in particular to a kind of parabola-circular arc end enclosure structure optimization design Method.
Background technology
End socket is the important component of pressure vessel, standard GB/T 150《Pressure vessel》In end socket have ellipse End socket, dished (torispherical) head, spherical seal head and hemispherical head.Wherein ellipsoidal head recommend use ratio of long axis to short axis for 2 mark Pseudotype ellipsoidal head, its combination property is preferable, most widely used；Dome head is mostly used for the higher pressure vessel of pressure, Its stress distribution is good, but manufacture difficulty is larger；Dished (torispherical) head is made up of middle sphere and radius for the corner of certain value, its by Power state is good not as ellipsoidal head, using being restricted；Spherical seal head stress can not show a candle to hemispherical head, but due to Its depth as shallow, shaping is easy, and some occasions also have application.
To solve the above problems, the structure of parabola-circular arc end socket is proposed, but parabola-circular arc type end socket Parabola and circular arc slightly change, and the shape of end socket will change, and slight change in shape is sometimes for load performance shadow Sound is huge.Existing design method is usually that classically, parabola-circular arc type is sealed with reference to the experience of designer The structure of head is improved design, it is clear that such design method can not obtain really optimal structure.
The content of the invention
The present invention is, and it is an object of the present invention to provide a kind of parabola-circular arc end socket knot in order to solving the above problems and carry out Structure Optimization Design.
The invention provides a kind of parabola-circular arc end enclosure structure Optimization Design, have the feature that, including Following steps：Step 1, the characteristic parameter and initial design parameters of parabola-circular arc end socket are set, characteristic parameter is cylinder The physical dimension of body, initial design parameters are the coordinate value and radius of curvature of the center of curvature of parabola-circular arc end socket；Step Rapid two, establish two-dimensional geometry model according to characteristic parameter and initial design parameters；Step 3, by the stress of two-dimensional geometry model Corresponding function is defined as object function when minimum；Step 4, set the range of variables of initial design parameters；Step 5, use Finite element analysis software, set constraint and load that initial design parameters are optimized with analysis and obtains initial design parameters correspondingly Stress intensity value；Step 6, stress intensity value is substituted into object function, judge whether object function restrains and meet to constrain bar Part, initial design parameters and return to step five are changed if being unsatisfactory for；Step 7, when object function is restrained and meets constraints When, optimal design parameters are obtained, the optimal design parameters are center of curvature C coordinate (α, β) and radius of curvature R；Step 8, The median surface of parabola-circular arc end socket is built according to the center of curvature C coordinate (α, β) and radius of curvature R.
In parabola provided by the invention-circular arc end enclosure structure Optimization Design, can also have such special Sign：Wherein, the forming step of median surface is as follows：In plane rectangular coordinates, make curve y=f (x)=Axn(A ＞ 0, x >=0,2 ＜ n≤3), the center of curvature C of a point M (1, A) coordinate is (α, β) on curve, radius of curvature R,β =A2(2n2- n)+1,As n ＞ 2, A ＞ 0,α ＜ 0 are made, then C points are left in y-axis Side, using C points as the center of circle, using R as radius, mistake M points make circular arc and hand over straight line y=β to meet at point O` in point O``, straight line y=β and y-axis, O`O``=h, O`O=r=β are made, using y=β as rotary shaft, the curve that is made up of parabolic segment OM and circular arc line segment MO``, around y =β axles rotate end socket median surface OMO``.
In parabola provided by the invention-circular arc end enclosure structure Optimization Design, can also have such special Sign：Wherein, in step 5, the mathematic optimal model for optimizing analysis is：
In formula, f is the stress value for parabola-circular arc type end socket that numerical computations obtain, and α, β, R are parabola-circular arc types The center of curvature C of end socket abscissa value, ordinate value and radius of curvature, P are the internal pressures that end socket is born, σmaxFor parabola- The maximum stress value of circular arc type end socket.
In parabola provided by the invention-circular arc end enclosure structure Optimization Design, can also have such special Sign：Wherein, constraint and internal pressure of the primary condition of analysis for parabola-circular arc end socket are optimized.
The effect of invention and effect
According to parabola involved in the present invention-circular arc end enclosure structure Optimization Design, because employing finite element Analysis software optimizes design to parabola-circular arc end socket, and in end socket stress minimum, the load performance of end socket is carried out Numerical simulation and analysis, save time and material, and obtained design result is more accurate relative to traditional experiment.
In addition, parabola-circular arc the end socket designed according to the Optimization Design of the present invention, substitutes roundlet with parabola Arc, eliminate between changeover portion and cylinder and between changeover portion and middle circular arc first and second curvature mutation, so as to subtract Lack to meet compatibility of deformation and caused local membrane stress and second order buckling stress, improved mechanical property, improve pole Limit for tonnage lotus.
Brief description of the drawings
Fig. 1 is the flow chart of parabola in embodiments of the invention-circular arc end enclosure structure Optimization Design；
Fig. 2 is the median surface structural representation of parabola in embodiments of the invention-circular arc end socket；And
Fig. 3 is the structural representation of parabola in embodiments of the invention-circular arc end socket.
Embodiment
In order that the technical means, the inventive features, the objects and the advantages of the present invention are easy to understand, it is attached below Figure embodiment combines and parabola of the present invention-circular arc end enclosure structure Optimization Design is specifically addressed.
Fig. 1 is the flow chart of parabola in embodiments of the invention-circular arc end enclosure structure Optimization Design.
As shown in figure 1, the flow of parabola-circular arc end enclosure structure Optimization Design comprises the following steps：
Step 1, the characteristic parameter and initial design parameters of parabola-circular arc end socket are set, characteristic parameter is cylinder Physical dimension, initial design parameters for parabola-circular arc end socket the center of curvature coordinate value and radius of curvature.At this In embodiment, end socket and cylinder material are S30408,300 DEG C of design temperature, and the size of end socket is internal diameter 1600mm, depth 400mm, thickness 10mm, the barrel lenght 500mm being connected with end socket.
Step 2, two-dimensional geometry model is established according to characteristic parameter and initial design parameters.
Step 3, corresponding function during the stress minimum of two-dimensional geometry model is defined as object function.
Step 4, set the range of variables of initial design parameters.
Step 5, using finite element analysis software, mesh generation is carried out, can be only because end enclosure structure meets symmetry Symmetry axis side is entered to set constraint and load to optimize initial design parameters analysis and obtain the initial design parameters pair The stress intensity value answered.
The primary condition of optimization analysis is excellent for the constraint of parabola-circular arc end socket and internal pressure, the mathematics for optimizing analysis Changing model is：
In formula, f is the stress value for parabola-circular arc type end socket that numerical computations obtain, and α, β, R are parabola-circular arc types The center of curvature C of end socket abscissa value, ordinate value and radius of curvature, P are the internal pressures that end socket is born, σmaxFor parabola- The maximum stress value of circular arc type end socket.
In the present embodiment, the material property of input is：E=1.76 × 105, μ=0.31, select eight Node Quadrilateral Element lists First PLANE183, consider that the stress distribution of end socket corner is complex, suitably encrypt during dividing elements, end socket and cylinder it is interior Surface applies uniform pressure, and the end socket plane of symmetry gives symmetry constraint, and cylinder lower end applies axial restraint constraint.To end socket and cylinder Body thickness direction divides 5 parts, and barrel lenght direction divides 300 parts, and end socket divides 400 parts, and it is excellent to carry out structure after constraint and loading Change analysis, the stress intensity value of parabola-circular arc type end socket is calculated.
Step 6, the stress intensity value that step 5 is obtained substitute into object function, judge whether object function restrains, if not Meet then to change initial design parameters and return to step five.
Step 7, judges whether object function meets constraints, and initial design parameters are changed if being unsatisfactory for and are returned Step 5.
Step 8, when object function is restrained and meets constraints, optimal design parameters are obtained, the optimal design parameters For the center of curvature C coordinate (α, β) and radius of curvature R；
Step 9, built according to the center of curvature C coordinate (α, β) and radius of curvature R in parabola-circular arc end socket Between face.
Fig. 2 is the median surface structural representation of parabola in embodiments of the invention-circular arc end socket, and Fig. 3 is the present invention Embodiment in parabola-circular arc end socket structural representation.
As shown in Figure 2,3, the forming step of median surface is as follows：
In plane rectangular coordinates, make curve y=f (x)=Axn(A ＞ 0, x >=0,2 ＜ n≤3), a point M on curve (1, A the coordinate of center of curvature C) is (α, β), radius of curvature R,β=A2(2n2- n)+1,As n ＞ 2, A ＞ 0,Making α ＜ 0, then C points are on the left of y-axis, using C points as the center of circle, Using R as radius, mistake M points make circular arc and hand over straight line y=β to meet at point O` in point O``, straight line y=β and y-axis, make O`O``=h, O`O= R=β, using y=β as rotary shaft, the curve that is made up of parabolic segment OM and circular arc line segment MO``, rotate to obtain end socket around y=β axles Median surface OMO``.
The effect of embodiment and effect
Parabola-circular arc end enclosure structure Optimization Design in above-described embodiment, because employing finite element Analysis software optimizes design to parabola-circular arc end socket, and in end socket stress minimum, the load performance of end socket is carried out Numerical simulation and analysis, save time and material, and obtained design result is more accurate relative to traditional experiment.
In addition, parabola-circular arc the end socket designed according to the Optimization Design of the present invention, substitutes roundlet with parabola Arc, eliminate between changeover portion and cylinder and between changeover portion and middle circular arc first and second curvature mutation, so as to subtract Lack to meet compatibility of deformation and caused local membrane stress and second order buckling stress, improved mechanical property, improve pole Limit for tonnage lotus.
Above-mentioned embodiment is the preferred case of the present invention, is not intended to limit protection scope of the present invention.

Claims (4)

  1. A kind of 1. parabola-circular arc end enclosure structure Optimization Design, for designing parabola-circular arc end socket, its feature It is, comprises the following steps：
    Step 1, the characteristic parameter and initial design parameters of parabola-circular arc end socket are set, the characteristic parameter is cylinder Physical dimension, the initial design parameters for the parabola-circular arc end socket the center of curvature coordinate value and curvature Radius；
    Step 2, two-dimensional geometry model is established according to the characteristic parameter and the initial design parameters；
    Step 3, corresponding function during the stress minimum of the two-dimensional geometry model is defined as object function；
    Step 4, set the range of variables of the initial design parameters；
    Step 5, using finite element analysis software, constraint and load is set to optimize analysis to the initial design parameters Obtain stress intensity value corresponding to initial design parameters；
    Step 6, the stress intensity value is substituted into the object function, judges whether the object function is restrained and met about Beam condition, the initial design parameters and return to step five are changed if being unsatisfactory for；
    Step 7, when the object function is restrained and meets constraints, optimal design parameters are obtained, the optimal design parameters For the center of curvature C coordinate (α, β) and radius of curvature R；
    Step 8, the parabola-circular arc end socket is built according to the coordinate (α, β) and radius of curvature R of the center of curvature C Median surface.
  2. 2. parabola according to claim 1-circular arc end enclosure structure Optimization Design, it is characterised in that：
    Wherein, the forming step of the median surface is as follows：
    In plane rectangular coordinates, make curve y=f (x)=Axn(A ＞ 0, x >=0,2 ＜ n≤3),
    The center of curvature C of a point M (1, A) coordinate is (α, β) on the curve, radius of curvature R,β =A2(2n2- n)+1,
    As n ＞ 2, A ＞ 0,Making α ＜ 0, then C points are on the left of y-axis, using C points as the center of circle, using R as radius, Cross M points make circular arc hand over straight line y=β meet at point O` in point O``, straight line y=β and y-axis,
    O`O``=h, O`O=r=β are made, using y=β as rotary shaft, the curve that is made up of parabolic segment OM and circular arc line segment MO``, Around y=β axles rotate end socket median surface OMO``.
  3. 3. parabola according to claim 1-circular arc end enclosure structure Optimization Design, it is characterised in that：
    Wherein, in step 5, the mathematic optimal model for optimizing analysis is：
    <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>f</mi> <mi>i</mi> <mi>n</mi> <mi>d</mi> <mi>f</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mi>&amp;alpha;</mi> <mo>,</mo> <mi>&amp;beta;</mi> <mo>,</mo> <mi>R</mi> <mo>,</mo> <mi>P</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>min</mi> <mi> </mi> <mi>M</mi> <mrow> <mo>(</mo> <mrow> <mi>&amp;alpha;</mi> <mo>,</mo> <mi>&amp;beta;</mi> <mo>,</mo> <mi>R</mi> <mo>,</mo> <mi>P</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>S</mi> <mo>.</mo> <mi>T</mi> <mo>.</mo> <msub> <mi>&amp;sigma;</mi> <mi>max</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>
    In formula, f is the stress value for parabola-circular arc type end socket that numerical computations obtain, and α, β, R are parabola-circular arc type end sockets Center of curvature C abscissa value, ordinate value and radius of curvature, P is the internal pressure that end socket is born, σmaxFor parabola-circular arc The maximum stress value of type end socket.
  4. 4. parabola according to claim 1-circular arc end enclosure structure Optimization Design, it is characterised in that：
    Wherein, in step 5, constraint and internal pressure of the primary condition of analysis for parabola-circular arc end socket are optimized.
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Cited By (3)

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Publication number Priority date Publication date Assignee Title
CN110516330A (en) * 2019-08-15 2019-11-29 上海理工大学 A kind of planar design method
CN111576350A (en) * 2020-05-21 2020-08-25 中国电建集团成都勘测设计研究院有限公司 Automatic optimization method for arch dam body shape
CN113221287A (en) * 2021-05-28 2021-08-06 南通职业大学 Three-arc convex seal head and optimal design method thereof

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Cited By (3)

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Publication number Priority date Publication date Assignee Title
CN110516330A (en) * 2019-08-15 2019-11-29 上海理工大学 A kind of planar design method
CN111576350A (en) * 2020-05-21 2020-08-25 中国电建集团成都勘测设计研究院有限公司 Automatic optimization method for arch dam body shape
CN113221287A (en) * 2021-05-28 2021-08-06 南通职业大学 Three-arc convex seal head and optimal design method thereof

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