CN102663163A - Topological optimization design method based on geometrical background meshes and with consideration of manufacturing constraints of drawing die - Google Patents

Topological optimization design method based on geometrical background meshes and with consideration of manufacturing constraints of drawing die Download PDF

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CN102663163A
CN102663163A CN2012100710622A CN201210071062A CN102663163A CN 102663163 A CN102663163 A CN 102663163A CN 2012100710622 A CN2012100710622 A CN 2012100710622A CN 201210071062 A CN201210071062 A CN 201210071062A CN 102663163 A CN102663163 A CN 102663163A
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finite element
grid
withdrawing pattern
profile
mould
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CN102663163B (en
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谷小军
朱继宏
高欢欢
张卫红
李军朔
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Northwestern Polytechnical University
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Abstract

The invention discloses a topological optimization design method based on geometrical background meshes and with consideration of manufacturing constraints of drawing die, which is used for solving technical problems of introducing drawing die constraints into topological optimization design of irregular mesh models. A technical scheme in the invention adopts a geometrical background mesh method, wherein mesh centroid of a finite element is projected to a geometrical background mesh along the direction of split dies or profiles of the drawing die, and pseudo-density of the finite element unit which constrains the centroid in a same geometrical background mesh decreases in order along the direction of split dies or profiles. The method disclosed by the invention effectively overcomes the problem that finite element models which is divided by free meshes can not apply drawing die constrains.

Description

Based on the background geometry grid and consider the method for topological optimization design of withdrawing pattern manufacturing constraint
Technical field
The present invention relates to a kind of method of topological optimization design, particularly relate to a kind of based on the background geometry grid and consider the method for topological optimization design of withdrawing pattern manufacturing constraint.
Background technology
With reference to Fig. 1～3.In fields such as Aero-Space, automobile makings, there are a large amount of components of machine need be, so need to consider the withdrawing pattern problem with Mould Machining manufacturing or sand casting.The mould withdrawing pattern is in order to guarantee mould product demoulding smoothly in the process of producing product; The sand casting withdrawing pattern is not destroy sand mold in order from sand, to take out wooden model.Traditional structural Topology Optimization result of design can't create with the mode of Mould Machining or sand casting.Along with Topology Optimization Method is used widely, consider that the Topology Optimization Method of various manufacturing constraints such as withdrawing pattern constraint meets the requirement of structural design more, so need in topology optimization design, consider the withdrawing pattern problem in engineering.
Hinder several kinds of situation of withdrawing pattern: cap holes 1 is arranged in the structure, and cap holes 1 hinders withdrawing pattern; The angle 2 of the branch mould/profile 4 of structure outward flange and withdrawing pattern is less than 90 degree, and angle 2 hinders withdrawing pattern.
With reference to Fig. 4.Document " Zhou M; Shyy YK; Thomas HL (2001) Topology optimization with manufacturing constraints.In:4th world congress of structural and multidisciplinary optimization, Dalian " discloses a kind of method of topological optimization design of considering withdrawing pattern manufacturing constraint.Document is introduced withdrawing pattern and is made constraint condition, and promptly on the withdrawing pattern direction, the pseudo-density of topology optimization design variable satisfies constraint:
Figure BDA0000144470080000011
Wherein,
Figure BDA0000144470080000012
is the pseudo-density that on the withdrawing pattern direction, is in the unit 3 of same row.
Though the document disclosed method is incorporated into withdrawing pattern manufacturing constraint in the topology optimization design, this method require the finite element grid of design section must be on the withdrawing pattern direction complete matching, promptly finite element grid is necessary for the identical regular grid of size.Shortcoming is: this method can only be applied to simple structure; For the structure of dividing,, therefore can not use this method because its finite element grid can not complete matching on the withdrawing pattern direction with irregular finite element grid.
Summary of the invention
In order to solve in the topology optimization design of irregular grid model the technical matters of introducing withdrawing pattern manufacturing constraint, it is a kind of based on the background geometry grid and consider the method for topological optimization design of withdrawing pattern manufacturing constraint that the present invention provides.This method is through definition background geometry grid; The barycenter of finite element grid is mapped in the background geometry grid; Diminish successively along a minute mould/profile through the cell density that is in the same background geometry grid of constraint barycenter, can be implemented in the topology optimization design of irregular finite element grid model and introduce the withdrawing pattern constraint.
The technical solution adopted for the present invention to solve the technical problems is: a kind of based on the background geometry grid and consider the method for topological optimization design of withdrawing pattern manufacturing constraint, be characterized in may further comprise the steps:
(a) set up finite element model through the cad model of structure, definition load and boundary condition.
(b) the branch mould/profile 4 of withdrawing pattern is divided into the background geometry grid 7 measure-alike with finite element grid 6.For any finite element grid i on the design space, its barycenter divides the projection of mould/profile 4 normal direction necessarily to be under the jurisdiction of some background geometry grid m along withdrawing pattern, m ∈ (1,2 ..., 27).
(c) set up the topological optimization model:
find?X＝(x 1，x 2，K，x n)
min?Φ(X)
s.t.KU＝F
G j ( X ) - G ‾ j ≤ 0 , j＝1，2，K，J
(0＜x p≤x q...≤x w≤1) m，m＝1，2，K，M
(d p≥d q...≥d w) m，m＝1，2，K，M
In the formula, X is the pseudo-intensity vector in the unit on the design domain; N is the design variable number; Φ (X) is the objective function of topological optimization; K is a finite element model global stiffness matrix; F is a node equivalent load vector; U is the whole motion vector of node; G j(X) be j constraint function;
Figure BDA0000144470080000022
It is the upper limit of j constraint function; J is the quantity of constraint; x p, x q... x wFor barycenter divides the projection of mould/profile 4 normal direction to drop on the pseudo-density of the finite element grid among the background geometry grid m along withdrawing pattern; M is the total columns on the withdrawing pattern direction.d iBe unit x iCentroid distance divide the distance of mould/profile 4, i.e. d p, d q, d wBe respectively unit x p, x q, x wDistance is divided the distance of mould/profile 4.Drop on the unit x of same background geometry grid along the projection of branch mould/profile 4 normal direction of withdrawing pattern for barycenter p, x q... x w, its barycenter is big more apart from the distance of minute mould/profile 4, and the pseudo-density of its unit is more little.
(d) with finite element soft Ansys model is carried out a finite element analysis; Be optimized sensitivity analysis through structure optimization platform Boss-Quattro again, try to achieve the sensitivity of objective function constraints, choose gradient optimizing algorithm GCMMA and be optimized design, the result is optimized.
The dimension of said background geometry grid 7 is than the low one dimension of dimension of finite element grid 6.
The invention has the beneficial effects as follows: owing in topological optimization, adopted the method for background geometry grid; Divide mould/profile to be mapped on the background geometry grid along withdrawing pattern the finite element grid barycenter; The pseudo-density that the constraint barycenter is in the finite element unit of same background geometry grid reduces along a minute mould/profile direction successively, and the finite element model that has effectively overcome free grid dividing can not be used the problem of withdrawing pattern constraint.
Below in conjunction with accompanying drawing and embodiment the present invention is elaborated.
Description of drawings
Fig. 1 is can be through the structural representation of Mould Machining or sand casting manufacturing in the background technology.
Fig. 2 is one of the structure that cannot make through Mould Machining or sand casting in a background technology synoptic diagram.
Fig. 3 is two synoptic diagram that cannot pass through the structure of Mould Machining or sand casting manufacturing in the background technology.
Fig. 4 is the synoptic diagram that background technology document disclosed method is introduced the withdrawing pattern constraint.
Fig. 5 is the stress model of the inventive method.
Fig. 6 is the finite element grid and the background grid synoptic diagram of the inventive method.
Fig. 7 is the topology optimization design result that the inventive method is introduced the withdrawing pattern constraint.
Among the figure, the 1-hole, 2-angle, 3-are in the unit of same row on the withdrawing pattern direction, and 4-divides mould/profile, 5-border, 6-finite element grid, 7-background geometry grid.
Embodiment
With reference to Fig. 5～7.With two-dimentional semi-girder topology optimization design is example explanation the present invention.The two dimension semi-girder is of a size of long 500mm, high 100mm.The semi-girder left side is complete fixing; The base angle, right side receives concentrated force load F=100N vertically upward.The design cantilever beam structure makes its rigidity maximum, and volume fraction is 60%.The withdrawing pattern direction is for vertically upward.The method concrete steps are following:
(a) finite element modeling.
Cad model through structure is set up finite element model, definition load and boundary condition.The suffered load of model receives concentrated force load F=100N vertically upward for the base angle, right side; The boundary condition of model is that the semi-girder left side is all fixing.
(b) divide the background geometry grid.
Branch mould/the profile 4 of withdrawing pattern is divided into the background geometry grid 7 measure-alike with finite element grid 6.It both can be the division that meets certain rule that background geometry grid 7 is divided, and also can be to divide arbitrarily.Because the branch mould/profile 4 of a three-dimensional model is a two dimensional surface, so the background geometry grid 7 of three-dimensional finite element model is a two dimension; The background geometry grid 7 of corresponding two-dimensional finite element model is an one dimension.Be the dimension low one dimension of the dimension of background geometry grid 7 than model finite element grid 6.Background geometry grid 7 sizes are suitable with the finite element unit size, suppose total M background geometry grid 7, and present embodiment has been divided 27 background geometry grids 7 altogether.For any finite element grid i on the design space, its barycenter divides the projection of mould/profile 4 normal direction necessarily to be under the jurisdiction of some background geometry grid m along withdrawing pattern, (m ∈ (1,2 ..., 27)).
(c) setting up the topological optimization model is:
find?X＝(x 1，x 2，K，x n)
minΦ(X)
s.t.KU＝F
G j ( X ) - G ‾ j ≤ 0 , j＝1，2，K，J
(0＜x p≤x q...≤x w≤1) m，m＝1，2，K，M
(d p≥d q...≥d w) m，m＝1，2，K，M
Wherein, X is the pseudo-intensity vector in unit on the design domain; N is the design variable number; Φ (X) is the objective function of topological optimization; K is a finite element model global stiffness matrix; F is a node equivalent load vector; U is the whole motion vector of node; G j(X) be j constraint function; It is the upper limit of j constraint function; J is the quantity of constraint; x p, x q... x wFor barycenter divides the projection of mould/profile 4 normal direction to drop on the pseudo-density of the finite element grid 6 (unit) among the background geometry grid m along withdrawing pattern, wherein the border of model geometric background grid is border 5; M is the total columns on the withdrawing pattern direction, the i.e. sum of background geometry grid 7.d iBe unit x iCentroid distance divide the distance of mould/profile 4, i.e. d p, d q, d wBe respectively unit x p, x q, x wDistance is divided the distance of mould/profile 4.Then drop on the unit x of same background geometry grid 7 along the projection of branch mould/profile 4 normal direction of withdrawing pattern for barycenter p, x q... x w, its barycenter is big more apart from the distance of minute mould/profile 4, and the pseudo-density of unit is more little.
The topological optimization model that present embodiment is set up is:
find?X＝(x 1，x 2，K，x n)
min C(X)
s.t.?KU＝F
V(X)-0.6≤0
(0＜x p≤x q...≤x w≤1) m，m＝1，2，K，27
(d p≥d q...≥d w) m，m＝1，2，K，27
(d) finite element analysis and optimization are found the solution.
Model is carried out a finite element analysis; Through optimizing sensitivity analysis, try to achieve the sensitivity of objective function constraints, choose certain optimized Algorithm and be optimized design, the result is optimized.
With finite element soft Ansys model is carried out a finite element analysis; Be optimized sensitivity analysis through structure optimization platform Boss-Quattro again; Try to achieve the sensitivity of objective function constraints; Choose gradient optimizing algorithm GCMMA (Globally Convergent Method of Moving Asymptotes) and be optimized design, the result is optimized.
Can find out by Optimization result: through introducing the background geometry gridding technique, can apply withdrawing pattern manufacturing constraint, rather than only be confined to the finite element model of regular grid the finite element model of any cell type.

Claims (2)

1. one kind based on the background geometry grid and consider the method for topological optimization design of withdrawing pattern manufacturing constraint, it is characterized in that may further comprise the steps:
(a) set up finite element model through the cad model of structure, definition load and boundary condition;
(b) the branch mould/profile (4) with withdrawing pattern is divided into and the measure-alike background geometry grid (7) of finite element grid (6); For any finite element grid i on the design space, its barycenter necessarily is under the jurisdiction of some background geometry grid m along the projection of branch mould/profile (4) normal direction of withdrawing pattern, m ∈ (1,2 ..., 27);
(c) set up the topological optimization model:
find?X＝(x 1，x 2，K，x n)
min?Φ(X)
s.t.?KU＝F
G j ( X ) - G ‾ j ≤ 0 , j＝1，2，K，J
(0＜x p≤x q...≤x w≤1) m，m＝1，2，K，M
(d p≥d q...≥d w) m，m＝1，2，K，M
In the formula, X is the pseudo-intensity vector in the unit on the design domain; N is the design variable number; Φ (X) is the objective function of topological optimization; K is a finite element model global stiffness matrix; F is a node equivalent load vector; U is the whole motion vector of node; G j(X) be j constraint function;
Figure FDA0000144470070000012
It is the upper limit of j constraint function; J is the quantity of constraint; x p, x q... x wDrop on the pseudo-density of the finite element grid among the background geometry grid m along the projection of branch mould/profile (4) normal direction of withdrawing pattern for barycenter; M is the total columns on the withdrawing pattern direction; d iBe unit x iThe centroid distance distance of dividing mould/profile (4), i.e. d p, d q, d wBe respectively unit x p, x q, x wDistance is divided the distance of mould/profile (4); Drop on the unit x of same background geometry grid along the projection of branch mould/profile (4) normal direction of withdrawing pattern for barycenter p, x q... x w, its barycenter is big more apart from the distance of a minute mould/profile (4), and the pseudo-density of its unit is more little;
(d) with finite element soft Ansys model is carried out a finite element analysis; Be optimized sensitivity analysis through structure optimization platform Boss-Quattro again, try to achieve the sensitivity of objective function constraints, choose gradient optimizing algorithm GCMMA and be optimized design, the result is optimized.
2. according to claim 1 based on the background geometry grid and consider the method for topological optimization design of withdrawing pattern manufacturing constraint, it is characterized in that: the dimension of said background geometry grid (7) is than the low one dimension of dimension of finite element grid (6).
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CN103559740A (en) * 2013-08-26 2014-02-05 空气动力学国家重点实验室 Prismatic grid generation method with realization of interactive operation
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Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103207940A (en) * 2013-04-23 2013-07-17 西北工业大学 Topology optimization design method for cyclic symmetry cylindrical grid structure
CN103207940B (en) * 2013-04-23 2015-07-22 西北工业大学 Topology optimization design method for cyclic symmetry cylindrical grid structure
CN103559740A (en) * 2013-08-26 2014-02-05 空气动力学国家重点实验室 Prismatic grid generation method with realization of interactive operation
CN103559740B (en) * 2013-08-26 2016-06-29 空气动力学国家重点实验室 A kind of prism mess generation method realizing interactive operation
CN109002598A (en) * 2018-06-29 2018-12-14 华中科技大学 Consider the self-supporting micro-structure Topology Optimization Method at overhanging angle and minimum dimension constraint
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