CN102622486B - Topological optimization design method taking drafting mold manufacturing constraint into consideration - Google Patents

Abstract

The invention discloses a topological optimization design method taking drafting mold manufacturing constraint into consideration and aims to solve the technical problem about introduction of drafting mold manufacturing constraint to the topological optimization design of an irregular network model. In the technical scheme, a topological optimization variable definition mode is adopted, and the topological optimization variable is defined as ratio of two adjacent cell densities in the same row in a drafting mold direction. Due to the mode, the drafting mold constraint is introduced into the design variable definition; the problem about introduction of a great number of constraints into topological optimization is solved; and a drafting mold constraint condition is introduced into the design variable, so that a design structure can meet the design requirement of drafting mold manufacturing.

Description

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 a kind of method of topological optimization design of considering 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 with Mould Machining manufacturing or sand casting, so need to consider the withdrawing pattern problem.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 to take out wooden model from sand.The result of traditional structural Topology Optimization 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 situations 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 namely on the withdrawing pattern direction, the pseudo-density of topology optimization design variable satisfies constraint:

Wherein,

Be the pseudo-density of model in the same unit that lists of withdrawing pattern direction.K is the total columns of model 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 namely finite element model has the K row in 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 is to have increased topological optimization sensitivity greatly to find the solution difficulty; The 2nd, constraint condition too much may cause process of topology optimization not restrain.

Summary of the invention

In order to solve the problem of introducing a large amount of constraints, the invention provides a kind of method of topological optimization design of considering withdrawing pattern manufacturing constraint, this method adopts topological optimization variable-definition mode, is the ratio that is in adjacent two cell densities of same row on the withdrawing pattern direction with the topology optimization design variable-definition.By this mode, the withdrawing pattern constraint is incorporated in the design variable definition.Can solve the problem of introducing a large amount of constraints in topological optimization, and withdrawing pattern constraint condition is incorporated in the design variable, reaching project organization can be by the designing requirement of withdrawing pattern manufacturing.

The technical solution adopted for the present invention to solve the technical problems is: a kind of method of topological optimization design of considering withdrawing pattern manufacturing constraint is characterized in may further comprise the steps:

(a) set up finite element model by 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 (1)

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

0＜δ≤x _i≤1，i＝1，K，n

Wherein, X is design variable; N is the design variable number; Φ (X) is objective function; K is finite element model global stiffness matrix; F is 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; δ=10 ^-3To avoid stiffness matrix unusual.

To being in the unit of same row on the withdrawing pattern direction, the order of its pseudo-density on the withdrawing pattern direction is followed successively by ρ _i, ρ _I+1..., ρ _I+m, (m=1, K, M).The withdrawing pattern direction is the normal orientation of the branch mould/profile 4 of model, and the branch mould/profile 4 of unit i distance model is nearest, the branch mould/profile 4 of unit i+m distance model farthest, then:

To being in the unit ρ of same row on the withdrawing pattern direction _i, ρ _I+1..., ρ _I+m, (m=1, K, M), 0＜δ≤x _i≤ 1:

$\left\{\begin{array}{c}0<{\mathrm{\&rho;}}_i\&le;1\\ 0<\frac{{\mathrm{\&rho;}}_{i+1}}{{\mathrm{\&rho;}}_i}\&le;1\\ M\\ 0<\frac{{\mathrm{\&rho;}}_{i+m}}{{\mathrm{\&rho;}}_{i+m-1}}\&le;1\end{array}\right.---\left(3\right)$

Can be got by following formula: 1＞ρ _i〉=ρ _I+1〉=..., 〉=ρ _I+m〉=0, (m=1, K M), namely satisfy withdrawing pattern constraint condition.

(c) model is carried out a finite element analysis; By optimizing sensitivity analysis, try to achieve the sensitivity of objective function and constraint condition; Be optimized design, the result is optimized.

The invention has the beneficial effects as follows: owing to adopt topology optimization design variable-definition method, design variable is defined as the ratio that is in adjacent two cell densities of same row on the withdrawing pattern direction, under the prerequisite that does not increase the topology optimization design constraint, the withdrawing pattern constraint is incorporated in the topology optimization design.For the two-dimentional cantilever beam structure in the embodiment, use method of the present invention and be optimized design, do not increase any topology optimization design constraint; And the method in the application background technical literature then needs to increase by 25 constraints (model in the embodiment has 25 row in the withdrawing pattern direction), and namely the design constraint of Zeng Jiaing is:

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

Description of drawings

Fig. 1 is can be by the structural representation of Mould Machining or sand casting manufacturing in the background technology.

Fig. 2 is cannot be by the structural representation of Mould Machining or sand casting manufacturing in the background technology.

Fig. 3 is cannot be by the structural representation of Mould Machining or sand casting manufacturing in the background technology.

Fig. 4 is the synoptic diagram that document is introduced the withdrawing pattern constraint in the background technology.

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

Fig. 6 is the element number synoptic diagram of a certain row on the model withdrawing pattern direction of the inventive method.

Fig. 7 adopts the topology optimization design result who does not add the withdrawing pattern constraint in the background technology.

Fig. 8 is the topology optimization design result that the inventive method adopts the withdrawing pattern constraint.

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

Embodiment

With reference to Fig. 5～8.Be example explanation the present invention with two-dimentional free beam topology optimization design.The two dimension free beam is of a size of long 500mm, high 100mm.Two ends, free beam bottom freely-supported; The top mid point is subjected to concentrated force load F=100N vertically downward.The design simple beam structure makes its rigidity maximum, and volume fraction is 50%.The withdrawing pattern direction is for vertically upward.The method concrete steps are as follows:

(a) finite element modeling.

Cad model by structure is set up finite element model, and load is subjected to vertically downward concentrated force load F=100N for the top mid point; Boundary condition is two ends, free beam bottom freely-supporteds.

(b) set up the topological optimization model.

In the present embodiment, require project organization rigidity maximum, volume fraction is 50%.Volume fraction is defined as design constraint, is design object with the rigidity of beam, sets up and optimizes model, and its mathematic(al) representation is:

find X＝(x ₁，x ₂，K，x _n)

minC(X)

s.t.KU＝F (1)

V(X)-0.5≤0

0＜δ≤x _i≤1，i＝1，K，n

Wherein, X is design variable; N is the design variable number; C (X) is objective function, i.e. the rigidity of beam; K is finite element model global stiffness matrix; F is node equivalent load vector; U is the whole motion vector of node; V (X) is the volume fraction of structure; δ=10 ^-3To avoid stiffness matrix unusual.

To be in the unit 3 of same row in the withdrawing pattern direction, the order of its pseudo-density on the withdrawing pattern direction is followed successively by ρ _i, ρ _I+1..., ρ _I+4The withdrawing pattern direction is the normal orientation of the branch mould/profile 4 of model, so the unit i unit that to be the branch mould/profile 4 of distance model nearest design variable X=(x then ₁, x ₂, K, x _n) with the pass of the pseudo-density in unit be:

To being in the unit ρ of same row on the withdrawing pattern direction _i, ρ _I+1..., ρ _I+m, (m=1, K, 4) are because 0＜δ≤x _i≤ 1:

$\left\{\begin{array}{c}0<{\mathrm{\&rho;}}_i\&le;1\\ 0<\frac{{\mathrm{\&rho;}}_{i+1}}{{\mathrm{\&rho;}}_i}\&le;1\\ M\\ 0<\frac{{\mathrm{\&rho;}}_{i+m}}{{\mathrm{\&rho;}}_{i+m-1}}\&le;1\end{array}\right.---\left(3\right)$

Can be got by following formula: 0＜ρ ₅≤ ρ ₄≤ ρ ₃≤ ρ ₂≤ ρ ₁≤ 1, namely satisfy withdrawing pattern constraint condition.

(c) finite element analysis and optimization are found the solution

With finite element soft Ansys model is carried out a finite element analysis; Carry out design sensitivity analysis by structure optimization platform Boss-Quattro again, be optimized design, the result is optimized.

By optimizing the result as can be seen, considered the modelling result of withdrawing pattern constraint, can on the withdrawing pattern direction, create by the withdrawing pattern casting.There is not the design result of withdrawing pattern constraint can't create by the withdrawing pattern casting because there is the sealing cavity centre.And the topological optimization model that the present invention sets up, the definition mode of change design variable does not increase the number that retrains.

Claims (1)

1. method of topological optimization design of considering withdrawing pattern manufacturing constraint is characterized in that may further comprise the steps:

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

(b) set up the topological optimization model:

find X=(x ₁,x ₂,...，x _n)

min Φ(X)

s.t. KU＝F (1)

$G_j\left(X\right)-{\stackrel{\&OverBar;}{G}}_j\&le;0,j=1,...,J$

0＜δ≤x _i≤1，i＝1，...，n

Wherein, X is design variable; N is the design variable number; Φ (X) is objective function; K is finite element model global stiffness matrix; F is 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; δ=10 ^-3To avoid stiffness matrix unusual;

To being in the unit of same row on the withdrawing pattern direction, the order of its pseudo-density on the withdrawing pattern direction is followed successively by ρ _i, ρ _I+1..., ρ _I+m, m=1 ..., M; The withdrawing pattern direction is the normal orientation of the branch mould/profile (4) of model, and the branch mould/profile (4) of unit i distance model is nearest, the branch mould/profile (4) of unit i+m distance model farthest, then:

To being in the unit ρ of same row on the withdrawing pattern direction _i, ρ _I+1..., ρ _I+m, m=1 ..., M, 0＜δ≤x _i≤ 1:

$\left\{\begin{array}{c}0<{\mathrm{\&rho;}}_i\&le;1\\ 0<\frac{{\mathrm{\&rho;}}_{i+1}}{{\mathrm{\&rho;}}_i}\&le;1\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ 0<\frac{{\mathrm{\&rho;}}_{i+m}}{{\mathrm{\&rho;}}_{i+m-1}}\&le;1\end{array}\right.$

Got by following formula: 1＞ρ _i〉=ρ _I+1〉=..., 〉=ρ _I+m〉=0, m=1 ..., M namely satisfies withdrawing pattern constraint condition;

(c) model is carried out a finite element analysis; By optimizing sensitivity analysis, try to achieve the sensitivity of objective function and constraint condition; Be optimized design, the result is optimized.

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