CN102637223A - Topological optimization design method on basis of pseudo-density sequencing and with consideration of draft manufacturing constraints - Google Patents

Abstract

The invention discloses a topological optimization design method on the basis of pseudo-density sequencing and with consideration of draft manufacturing constraints, which is used for realizing introducing draft manufacturing constraints in a topological optimization design of an irregular grid model. The technical scheme includes that the topological optimization design method includes sequencing the pseudo-densities of units on the same row in a draft direction again by the aid of a unit pseudo-density sequencing method; leading the pseudo-densities of the units to be distributed from large to small in the draft direction; and accordingly realizing draft constraint. By the aid of the method, design requirements of the draft constraints can be met without introducing a large quantity of constraints. The topological optimization design method solves the problems that a large quantity of constraint conditions are introduced into an existing method and a topological optimization process is not converged due to the excessive constraint conditions.

Description

Method of topological optimization design based on pseudo-density ordering and consideration withdrawing pattern manufacturing constraint

Technical field

The present invention relates to a kind of method of topological optimization design, particularly a kind of method of topological optimization design based on pseudo-density ordering and consideration 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; Structure outward flange and withdrawing pattern divide the angle 2 of mould/profile 4 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:

Wherein,

is the pseudo-density in the same unit that lists 3 of withdrawing pattern direction.K is total columns of unit on the withdrawing pattern direction.

Though the document disclosed method is incorporated into withdrawing pattern manufacturing constraint in the topology optimization design, this method has been introduced K and has been tied in the topological optimization.If promptly finite element model has the K row on the withdrawing pattern direction, then just there be K to retrain and be introduced in during topological optimization finds the solution.Shortcoming is: this method has been introduced a large amount of constraint conditions, and the problem of bringing owing to a large amount of constraint conditions of introducing one is to have increased topological optimization sensitivity greatly to find the solution difficulty; The 2nd, constraint condition too much possibly cause process of topology optimization not restrain.

Summary of the invention

In prior art, there is the technical matters of introducing a large amount of constraints; The present invention provides a kind of method of topological optimization design based on pseudo-density ordering and consideration withdrawing pattern manufacturing constraint; This method adopts the pseudo-density ranking method in unit; The pseudo-density in unit that will be in same row on the withdrawing pattern direction through this method is resequenced, and makes the descending distribution on the withdrawing pattern direction of the pseudo-density in unit, thereby can realize the withdrawing pattern constraint.This method can realize the designing requirement of withdrawing pattern constraint, but does not introduce a large amount of constraints.Can solve not convergence problem of the process of topology optimization introducing a large amount of constraint conditions and too much cause owing to constraint condition.

The technical solution adopted for the present invention to solve the technical problems is: a kind of method of topological optimization design based on pseudo-density ordering and consideration withdrawing pattern manufacturing constraint is 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) set up the topological optimization model:

find?X＝(x ₁，x ₂，K，x _n)

minΦ(X)

s.t.KU＝F

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

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.

(c) to the pseudo-density (x of the unit 3 that on the withdrawing pattern direction, is in same row _p, x _q... x _w) _k, k=1 ..., the K rearrangement makes the pseudo-density in the same unit that lists on the withdrawing pattern direction, satisfy Relation, first branch mould/profile 4 from withdrawing pattern is far away more, its pseudo-density value is more little.Wherein k is the k row of model on the withdrawing pattern direction, and K is the total columns on the withdrawing pattern direction.

(d) 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.

The invention has the beneficial effects as follows:, can under the prerequisite that does not increase the topology optimization design constraint,, the withdrawing pattern constraint be incorporated in the topology optimization design through the pseudo-density rearrangement in unit through introducing the pseudo-density ranking method in a kind of unit.For the two-dimentional cantilever beam structure in the embodiment, use the inventive method and be optimized design, do not increase any constraint; And the method in the application reference document then need increase by 25 constraints (model in the embodiment has 25 row on the withdrawing pattern direction), and the constraint condition that promptly increases is:

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 cannot be through the structural representation of Mould Machining or sand casting manufacturing in the background technology.

Fig. 3 is cannot be through the structural representation 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 topology optimization design result that background technology does not add the withdrawing pattern constraint.

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

Among the figure, the 1-hole; The 2-angle; 3-is in the unit of same row on the withdrawing pattern direction; 4-divides mould/profile.

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% to the maximum.The withdrawing pattern direction is for vertically upward.Method step is following:

The present invention proposes a kind of method of topological optimization design of considering withdrawing pattern manufacturing constraint, comprise following three key links:

(a) finite element modeling.

Cad model through structure is set up finite element model.Load receives concentrated force load F=100N vertically upward for the base angle, right side; Boundary condition is that the semi-girder left side is complete fixing.

(b) set up the topological optimization model

find?X＝(x ₁，x ₂，K，x _n)

minΦ(X)

s.t.KU＝F

G(X)-0.6≤0

Wherein, X is a design variable---the pseudo-intensity vector in unit on the design domain; N is the design variable number; Φ (X) is an objective function; 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 (X) is the volume fraction of finite element model.

(c) pseudo-density ordering in unit and renewal.

To being positioned at the pseudo-density (x in the same unit that lists on the withdrawing pattern direction _p, x _q... x _w) _k, k=1 ..., the K rearrangement makes the pseudo-density in the same unit that lists on the withdrawing pattern direction, satisfy

Relation, promptly the unit is far away more far from the branch mould/profile 4 of withdrawing pattern, its pseudo-density value is more little.Wherein k is the k row of model on the withdrawing pattern direction, and K is the total columns on the withdrawing pattern direction.

(d) finite element analysis and optimization are found the solution.

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) optimized Algorithm and be optimized design, the result is optimized.

Can find out by Optimization result, consider the modelling result of withdrawing pattern constraint, can on the withdrawing pattern direction, create through the withdrawing pattern casting.There is not the design result of withdrawing pattern constraint can't create through the withdrawing pattern casting because of there is the sealing cavity centre.And the topological optimization model that the present invention sets up does not increase the number of constraint.

Claims (1)

1. one kind based on the ordering of pseudo-density 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) set up the topological optimization model:

find?X＝(x ₁，x ₂，K，x _n)

min?Φ(X)

s.t.KU＝F

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

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;

(c) to the pseudo-density (x of the unit (3) that on the withdrawing pattern direction, is in same row _p, x _q... x _w) _k, k=1 ..., the K rearrangement makes the pseudo-density in the same unit that lists on the withdrawing pattern direction, satisfy Relation, first branch mould/profile (4) from withdrawing pattern is far away more, its pseudo-density value is more little; Wherein k is the k row of model on the withdrawing pattern direction, and K is the total columns on the withdrawing pattern direction;

(d) 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.

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