CN102663163B - Topological optimization design method based on geometrical background meshes and with consideration of manufacturing constraints of drawing die - Google Patents

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 background geometry grid and consider the method for topological optimization design of withdrawing pattern manufacturing constraints

Technical field

The present invention relates to a kind of method of topological optimization design, particularly relate to a kind of based on background geometry grid and consider the method for topological optimization design of withdrawing pattern manufacturing constraints.

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 to be with Mould Machining manufacture or sand casting, so need to consider withdrawing pattern problem.Mould withdrawing pattern is in order to guarantee mould product demoulding smoothly in the process of producing product; Sand casting withdrawing pattern is not destroy sand mold in order to take out wooden model from sand.The result of traditional Structural Topology Optimization Design, cannot create by the mode of Mould Machining or sand casting.Along with Topology Optimization Method is used widely in engineering, consider that the Topology Optimization Method of the various manufacturing constraints such as withdrawing pattern constraint meets the requirement of structural design more, so need to consider withdrawing pattern problem in topology optimization design.

Hinder several situations of withdrawing pattern: in structure, have cap holes 1, cap holes 1 hinders withdrawing pattern; The angle 2 of the parting/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 constraints.Document is introduced withdrawing pattern manufacturing constraints condition, and, in withdrawing pattern direction, the pseudo-density of topology optimization design variable meets constraint:

Wherein, pseudo-density for the unit in same row 3 in withdrawing pattern direction.

Although the disclosed method of document is incorporated into withdrawing pattern manufacturing constraints in topology optimization design, the method require the finite element grid of design section must be in withdrawing pattern direction complete matching, finite element grid is necessary for the regular grid that size is identical.Shortcoming is: the method can only be applied to simple structure; For the structure of dividing with irregular finite element grid, because its finite element grid can not complete matching in withdrawing pattern direction, therefore can not apply the method.

Summary of the invention

In order to solve the technical matters of introducing withdrawing pattern manufacturing constraints in the topology optimization design of irregular grid model, the invention provides a kind of based on background geometry grid and consider the method for topological optimization design of withdrawing pattern manufacturing constraints.The method is by definition background geometry grid, the barycenter of finite element grid is mapped in background geometry grid, cell density by constraint barycenter in same background geometry grid diminishes successively along parting/profile, can realize and in the topology optimization design of irregular finite element grid model, introduce withdrawing pattern constraint.

The technical solution adopted for the present invention to solve the technical problems is: a kind of based on background geometry grid and consider the method for topological optimization design of withdrawing pattern manufacturing constraints, be characterized in comprising the following steps:

(a) by the cad model of structure, set up finite element model, definition load and boundary condition.

(b) parting/profile of withdrawing pattern 4 is divided into the background geometry grid 7 measure-alike with finite element grid 6.For any one the finite element grid i on design space, its barycenter is necessarily under the jurisdiction of some background geometry grid m along the projection of withdrawing pattern parting/profile 4 normal direction, m ∈ (1,2 ..., 27).

(c) set up Topological optimization model:

find X＝(x ₁，x ₂，K，x _n)

min Φ(X)

s.t.KU＝F

$G_j\left(X\right)-{\stackrel{\‾}{G}}_j\≤0,$ 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 formula, X is the pseudo-intensity vector in the unit in design domain; N is design variable number; The objective function that Φ (X) is topological optimization; K is finite element model global stiffness matrix; F is node equivalent load vectors; U is node global displacement vector; 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 drops on the pseudo-density of the finite element grid in background geometry grid m along the projection of withdrawing pattern parting/profile 4 normal direction; M is the total columns in withdrawing pattern direction.D _ifor unit x _ithe distance of centroid distance parting/profile 4, i.e. d _p, d _q, d _wbe respectively unit x _p, x _q, x _wdistance apart from parting/profile 4.For barycenter, along the projection of parting/profile 4 normal direction of withdrawing pattern, drop on the unit x of same background geometry grid _p, x _q... x _w, its barycenter is larger apart from the distance of parting/profile 4, and the pseudo-density of its unit is less.

(d) by finite element soft Ansys, model is carried out to a finite element analysis; By structure optimization platform Boss-Quattro, be optimized sensitivity analysis again, try to achieve the sensitivity of objective function and constraint condition, choose gradient optimal method GCMMA and be optimized design, result is optimized.

The dimension of described background geometry grid 7 is than the low one dimension of the dimension of finite element grid 6.

The invention has the beneficial effects as follows: owing to having adopted the method for background geometry grid in topological optimization, finite element grid barycenter is mapped on background geometry grid along withdrawing pattern parting/profile, the pseudo-density of the finite element unit of constraint barycenter in same background geometry grid reduces successively along parting/profile direction, and the finite element model that has effectively overcome free grid division can not be applied the problem of withdrawing pattern constraint.

Below in conjunction with drawings and Examples, the present invention is elaborated.

Accompanying drawing explanation

Fig. 1 is the structural representation that can manufacture by Mould Machining or sand casting in background technology.

Fig. 2 is one of the structure that cannot manufacture by Mould Machining or sand casting in background technology schematic diagram.

Fig. 3 is two schematic diagram that cannot pass through the structure of Mould Machining or sand casting manufacture in background technology.

Fig. 4 is the schematic diagram that the disclosed method of background technology document is introduced withdrawing pattern constraint.

Fig. 5 is the stress model of the inventive method.

Fig. 6 is finite element grid and the background grid schematic diagram of the inventive method.

Fig. 7 is the topology optimization design result that the inventive method is introduced withdrawing pattern constraint.

In figure, 1-hole, 2-angle, 3-is the unit in same row in withdrawing pattern direction, 4-parting/profile, 5-border, 6-finite element grid, 7-background geometry grid.

Embodiment

With reference to Fig. 5～7.Take two-dimentional semi-girder topology optimization design as example explanation the present invention.Two dimension semi-girder is of a size of long 500mm, high 100mm.Semi-girder left side is complete fixing; Base angle, right side is subject to concentrated force load F=100N vertically upward.Design cantilever beam structure, makes its rigidity maximum, and volume fraction is 60%.Withdrawing pattern direction is for vertically upward.Method concrete steps are as follows:

(a) finite element modeling.

Cad model by structure is set up finite element model, definition load and boundary condition.It is that base angle, right side is subject to concentrated force load F=100N vertically upward that model is subject to load; The boundary condition of model is that semi-girder left side is all fixing.

(b) divide background geometry grid.

Parting/the profile of withdrawing pattern 4 is divided into the background geometry grid 7 measure-alike with finite element grid 6.It can be both the division that meets certain rule that background geometry grid 7 is divided, and can be also to divide arbitrarily.Because the parting/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 two dimension; The background geometry grid 7 of corresponding two-dimensional finite element model is one dimension.Be that the dimension of background geometry grid 7 is than the low one dimension of the dimension of model finite element grid 6.Background geometry grid 7 sizes are suitable with finite element unit size, suppose total M background geometry grid 7, and the present embodiment has been divided 27 background geometry grids 7 altogether.For any one the finite element grid i on design space, its barycenter is necessarily under the jurisdiction of some background geometry grid m along the projection of withdrawing pattern parting/profile 4 normal direction, (m ∈ (1,2 ..., 27)).

(c) setting up Topological optimization model is:

find X＝(x ₁，x ₂，K，x _n)

minΦ(X)

s.t.KU＝F

$G_j\left(X\right)-{\stackrel{\‾}{G}}_j\≤0,$ 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 in design domain; N is design variable number; The objective function that Φ (X) is topological optimization; K is finite element model global stiffness matrix; F is node equivalent load vectors; U is node global displacement vector; 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 drops on the pseudo-density of the finite element grid 6 (unit) in background geometry grid m along the projection of withdrawing pattern parting/profile 4 normal direction, wherein the border of model geometric background grid is border 5; M is the total columns in withdrawing pattern direction, the i.e. sum of background geometry grid 7.D _ifor unit x _ithe distance of centroid distance parting/profile 4, i.e. d _p, d _q, d _wbe respectively unit x _p, x _q, x _wdistance apart from parting/profile 4.For barycenter, along the projection of parting/profile 4 normal direction of withdrawing pattern, drop on the unit x of same background geometry grid 7 _p, x _q... x _w, its barycenter is larger apart from the distance of parting/profile 4, and the pseudo-density of unit is less.

The Topological optimization model that the 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 Solution.

Model is carried out to a finite element analysis; By optimizing sensitivity analysis, try to achieve the sensitivity of objective function and constraint condition, choose certain optimized algorithm and be optimized design, result is optimized.

By finite element soft Ansys, model is carried out to a finite element analysis; By structure optimization platform Boss-Quattro, be optimized sensitivity analysis again, try to achieve the sensitivity of objective function and constraint condition, choose gradient optimal method GCMMA (Globally Convergent Method of Moving Asymptotes) and be optimized design, result is optimized.

By optimum results, can be found out: by introducing background geometry gridding technique, can apply withdrawing pattern manufacturing constraints to the finite element model of any cell type, rather than only be confined to the finite element model of regular grid.

Claims (1)

1. based on background geometry grid and consider the method for topological optimization design of withdrawing pattern manufacturing constraints, it is characterized in that comprising the following steps:

(a) by the cad model of structure, set up finite element model, definition load and boundary condition;

(b) parting/profile of withdrawing pattern (4) is divided into the background geometry grid (7) measure-alike with finite element grid (6); For any one the finite element grid i on design space, its barycenter is necessarily under the jurisdiction of some background geometry grid m along the projection of parting/profile (4) normal direction of withdrawing pattern, m ∈ (1,2 ..., 27);

(c) set up Topological optimization model:

find X＝(x ₁，x ₂，...，x _n)

min Φ(X)

s.t.KU＝F

$G_j\left(X\right)-{\stackrel{\‾}{G}}_j\≤0,j=\mathrm{1,2},...,J$

(0＜x _p≤x _q...≤x _w≤1) _m,m＝1,2,...,M

(d _p≥d _q...≥d _w) _m,m＝1,2,...,M

In formula, X is the pseudo-intensity vector in the unit in design domain; N is design variable number; The objective function that Φ (X) is topological optimization; K is finite element model global stiffness matrix; F is node equivalent load vectors; U is node global displacement vector; 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 drops on the pseudo-density of the finite element grid in background geometry grid m along the projection of parting/profile (4) normal direction of withdrawing pattern; M is the total columns in withdrawing pattern direction; d _ifor unit x _ithe distance of centroid distance parting/profile (4), i.e. d _p, d _q, d _wbe respectively unit x _p, x _q, x _wdistance apart from parting/profile (4); For barycenter, along the projection of parting/profile (4) normal direction of withdrawing pattern, drop on the unit x of same background geometry grid _p, x _q... x _w, its barycenter is larger apart from the distance of parting/profile (4), and the pseudo-density of its unit is less;

(d) by finite element soft Ansys, model is carried out to a finite element analysis; By structure optimization platform Boss-Quattro, be optimized sensitivity analysis again, try to achieve the sensitivity of objective function and constraint condition, choose gradient optimal method GCMMA and be optimized design, result is optimized.