CN103412987A - Multi-component structural system distribution optimized design method based on KS function - Google Patents

Abstract

The invention discloses a multi-component structural system distribution optimized design method based on a KS function, which is used for solving the technical problem that the conventional multi-component structural system distribution optimized design method brings large quantities of constraint equations. The invention adopts the technical scheme that all the component interference constraint equations are integrated to one or more constraint equations, and in addition, the integrated constraint equations can satisfy constraint surely. The number of geometry constraint (i.e. constraint equations) in the multi-component structural system distribution optimized design can be greatly reduced. According to the embodiment of the multi-component structural system distribution optimized design of a suspension beam structure, four components are provided, the components 1-4 respectively use 2, 3, 1 and 3 circumcircle affinities, and a design domain edge uses 4 circumcircle affinities; by applying the method of citing reference, 30 constraint equations are needed to be led in, and the optimization can not be performed, while by applying the method, only 2 constraint equations are needed, and the optimization can be performed smoothly.

Description

Method for layout optimal design of multi-assembly structure system based on the KS function

Technical field

The present invention relates to a kind of method for layout optimal design of multi-assembly structure system, particularly relate to a kind of method for layout optimal design of multi-assembly structure system based on the KS function.

Background technology

With reference to Fig. 1.This Design Mode of multicomponent structures system has been contained most industrial products, as aerospace flight vehicle, boats and ships, automobile and machinery etc.Due to its complicated duty status and harsh performance requirement, the mechanical property design problem of multicomponent structures system is particularly outstanding in aerospace flight vehicle structural design field.Because assembly and structure all have himself quality and rigidity, thus assembly put the comprehensive mechanical characteristic that has fundamentally determined structural system with this two aspects factor of location of configuration of structure.For the balance and stability that guarantees aircraft and avoid equipment or the damage of structure, need to carry out rational optimal design to these two kinds of location problems, this work is called the monolithic construction system by the collaborative topological design of multicomponent structures system.

With reference to Fig. 2-3.Document " Zhu J.H.; Beckers P.Zhang W.H.; On the multi-component layout design with inertial force.Journal of Computational and Applied Mathematics.2010; 234 (7): 2222-2230 " discloses a kind of method for layout optimal design of multi-assembly structure system, this method combines structural Topology Optimization technology and filling layout optimization technique, has realized that the location layout of the regional inner assembly of certain filling and support and connection version design simultaneously.Document discloses and has used limited envelope circule method to solve the assembly interference problem.For the assembly of random appearance profile, adopt the profile of limited envelope circle (three-dimensional micromodule is the envelope ball) this assembly of approximate description, if any two envelopes circle between two assemblies is not interfered, these two assemblies are not interfered.N assembly even arranged, i assembly (i=1,2 .n.. N _iIndividual envelope circle is approximate, retrains this n assembly and does not interfere and need to have

Individual equation of constraint.

Interference constraint between assembly and assembly, the filling layout optimization also needs Assurance component to be included in design section inside fully, document adopts the larger envelope circle of radius to carry out piecewise approximation to the Polygonal Boundary of design section, now contains to retrain can be similar to equally to adopt center of circle distance function to describe.N assembly even arranged, i assembly (i=1,2 ..., n) use N _iIndividual envelope circle is approximate, and design domain is approximate by M envelope circle, retrains this n assembly and does not interfere and be included in design domain and need to have

Individual equation of constraint.

Although the disclosed method of document can solve between restraint assembly, the interference problem on assembly and design domain border, has introduced a large amount of equation of constraint.If for example judgement has 4 assemblies, each assembly approximate with 4 envelopes circles, design domain is with 4 approximate interference problems of envelopes circle, the distance of center circle that need to judge altogether 160 two circles from radius and relative size (160 equation of constraint).So many equation of constraint number causes topology optimization problem to be difficult to carry out or is difficult to convergence.

Summary of the invention

In order to overcome existing method for layout optimal design of multi-assembly structure system, introduce the deficiency that equation of constraint quantity is many, the invention provides a kind of method for layout optimal design of multi-assembly structure system based on the KS function.The method interferes equation of constraint to be integrated into one or more equation of constraint all component, can guarantee that again integrated equation of constraint can meet constraint simultaneously.Can reduce greatly geometrical constraint in multicomponent structures system layout optimal design is the number that assembly is interfered equation of constraint.

The technical solution adopted for the present invention to solve the technical problems is: a kind of method for layout optimal design of multi-assembly structure system based on the KS function is characterized in comprising the following steps:

Step 1, set up finite element model by the cad model of structure, the multicomponent structures finite element model is divided into to structured grid, background grid and component grid three parts, definition load and boundary condition.

Step 2, assembly and design domain boundary demarcation envelope is round, set up equation of constraint:

$\left\{\begin{array}{c}\∀i=\mathrm{1,2},...,n;j=i+1,...,n;\∀k=\mathrm{1,2},...,N_i;l=\mathrm{1,2},...,N_j\\ s.t.:C_{\mathrm{ij}}^{\mathrm{kl}}=\frac{\left|\right|O_{i\_k}{O}_{j\_l}\left|\right|}{R_{i\_k}+R_{j\_l}}\≥1\\ \∀\mathrm{\ϵ}=\mathrm{1,2},...,n;\∀\mathrm{\τ}=\mathrm{1,2},...,N_p;\mathrm{\ζ}=\mathrm{1,2},...,M\\ s.t.:C_{\mathrm{\ϵ}}^{\mathrm{\τ\ζ}}=\frac{\left|\right|O_{\mathrm{\ϵ}\_\mathrm{\τ}}{O}_{\mathrm{\ζ}}\left|\right|}{R_{\mathrm{\ϵ}\_\mathrm{\τ}}+R_{\mathrm{\ζ}}}\≥1\end{array}\right.$

In formula, n is component count; N _iFor being used for being similar to the envelope circle number of i assembly; O _{i_k}, R _{i_k}Be respectively the center of circle and the radius of k envelope circle of i assembly; M is the number of the envelope circle in Approximate Design zone; O _ζ, R _ζBe respectively the center of circle and the radius of τ the large envelope circle in Approximate Design zone.

Above-mentioned equation of constraint is integrated with a KS function constraint equation:

$C_{\mathrm{KS}}=\frac{1}{p}\ln [\underset{i=1}{\overset{n-1}{\mathrm{\Σ}}}\underset{j=i+1}{\overset{n}{\mathrm{\Σ}}}\underset{k=1}{\overset{N_i}{\mathrm{\Σ}}}\underset{l=1}{\overset{N_j}{\mathrm{\Σ}}}{e}^{p{C}_{\mathrm{ij}}^{\mathrm{kl}}}+\underset{\mathrm{\ϵ}=1}{\overset{n}{\mathrm{\Σ}}}\underset{\mathrm{\τ}=1}{\overset{N_{\mathrm{\ϵ}}}{\mathrm{\Σ}}}\underset{\mathrm{\ζ}=1}{\overset{M}{\mathrm{\Σ}}}{e}^{p{C}_{\mathrm{\ϵ}}^{\mathrm{\τ\ζ}}}]\≥1$

In formula, p is the parameter of KS function.

Step 3, set up Topological optimization model and be:

Find η=(η ₁, η ₂..., η _Enum); S=(s ₁, s ₂... s _n), s wherein _i=(x _i, y _i, θ _i)

min?φ(η,S)

s.t.KU＝F

$G_j(\mathrm{\η},S)\≤{\stackrel{\‾}{G}}_j,j=\mathrm{1,2},...,J$

C _KS≥1

In formula, η is the pseudo-intensity vector in the unit on design domain; Enum is design domain grid number; S is the Position Design variable of assembly, wherein s _i=(x _i, y _i, θ _i) represent respectively x coordinate, y coordinate and the direction coordinate of i assembly barycenter; N is component count; φ (η, S) is the objective function of topology optimization problem; K is finite element model global stiffness matrix; F is the node equivalent load vectors; U is node global displacement vector; G _j(η, S) is j constraint function;

It is the upper limit of j constraint function; J is the number of constraint; C _KSEquation of constraint for the KS construction of function.

Step 4, model is carried out to a finite element analysis: respectively how much variablees and pseudo-density variables are carried out to sensitivity analysis, try to achieve the sensitivity of objective function and constraint condition, choose gradient optimal method GCMMA and be optimized design, result is optimized.

The invention has the beneficial effects as follows: the method interferes equation of constraint to be integrated into one or more equation of constraint all component, can guarantee that again integrated equation of constraint can meet constraint simultaneously.Can reduce greatly geometrical constraint in multicomponent structures system layout optimal design is the number that assembly is interfered equation of constraint.Multicomponent structures system layout optimal design for cantilever beam structure in embodiment, have 4 assemblies, and assembly 1-4 is approximate with 2,3,1,3 envelope circles respectively, and the design domain border is approximate with 4 envelope circles; The method of application reference document, need to introduce 30 equation of constraint, makes optimization to carry out; And application the inventive method only needs 2 equation of constraint, optimization can be carried out smoothly.

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

The accompanying drawing explanation

Fig. 1 is the structural representation of background technology method for layout optimal design of multi-assembly structure system design.

Fig. 2 is the schematic diagram that the limited envelope circle in background technology assembly and design section border is divided.

Fig. 3 is that in the background technology multicomponent structures, grid is divided schematic diagram.

Fig. 4 is moulded dimension and the Boundary Conditions in Structures schematic diagram of the inventive method embodiment.

Fig. 5 is that the limited envelope circle of the inventive method embodiment is divided schematic diagram.

Fig. 6 is the inventive method embodiment Cooperative Optimization result schematic diagram.

Embodiment

With reference to Fig. 4-6.The multicompartment cantilever beam structure under fixed load of take is example explanation the present invention.The plane cantilever beam structure is of a size of long 90mm, high 30mm, and its Young modulus is 7 * 10 ¹⁰Mpa, Poisson ratio is 0.3.Four assemblies of the inner embedding of cantilever beam structure, be respectively rectangular module, convex shape assembly, cruciform component and L shaped assembly.Initial center position and the inceptive direction of rectangular module is (15,15,360); Initial center position and the inceptive direction of convex shape assembly is (35,15,360); Initial center position and the inceptive direction of cruciform component is (55,15,360); Center initial position and the inceptive direction of L shaped assembly is (75,15,360).The size of each assembly is with reference to Fig. 4, and the Young modulus of each assembly is 2 * 10 ¹¹Mpa, Poisson ratio is 0.3.The load boundary condition that semi-girder applies and displacement boundary conditions are with reference to shown in Figure 4.Design semi-girder load-carrying construction and the position of assembly in load-carrying construction, make its rigidity maximum, and overall material usage volume fraction is 50% to the maximum.Method step is as follows:

(a) finite element modeling.

Cad model by structure is set up finite element model: setting the grid length of side is 1mm, and the finite element model of multicompartment cantilever beam structure is divided into to structured grid, component grid, three parts of background grid.Definition boundary condition: right-hand member summit, cantilever beam structure coboundary and coboundary are fixed apart from right endpoint 30mm place node; On cantilever beam structure lower boundary left end summit and lower boundary, apply along the load of x axle negative sense and y axle negative sense apart from left end point formula place node, magnitude of load is 100000N.

(b) by assembly and design domain boundary demarcation envelope circle, set up equation of constraint.

Respectively with 2,3,1 and 3 next being similar to of envelope circle, with 4 envelopes circles, come approximate the design domain border rectangular module, convex shape assembly, cruciform component and L shaped assembly border.The method of application reference document, set up interference equation of constraint between assembly and the containing equation of constraint between assembly and design domain border, has 127 equation of constraint:

$\left\{\begin{array}{c}\∀i=\mathrm{1,2},\mathrm{3,4};j=i+1,...,4;\∀k=\mathrm{1,2},...,N_i;l=\mathrm{1,2},...,N_j\\ s.t.:C_{\mathrm{ij}}^{\mathrm{kl}}=\frac{\left|\right|O_{i\_k}{O}_{j\_l}\left|\right|}{R_{i\_k}+R_{j\_l}}\≥1\\ \∀\mathrm{\ϵ}=\mathrm{1,2},\mathrm{3,4};\∀\mathrm{\τ}=\mathrm{1,2},...,N_{\mathrm{\ϵ}};\mathrm{\ζ}=\mathrm{1,2},\mathrm{3,4}\\ s.t.:C_{\mathrm{\ϵ}}^{\mathrm{\τ\ζ}}=\frac{\left|\right|O_{\mathrm{\ϵ}\_\mathrm{\τ}}{O}_{\mathrm{\ζ}}\left|\right|}{R_{\mathrm{\ϵ}\_\mathrm{\τ}}+R_{\mathrm{\ζ}}}\≥1\end{array}\right.$

O wherein _{i_k}, R _{i_k}Be respectively the center of circle and the radius of k envelope circle of i assembly; O _ζ, R _ζBe respectively the center of circle and the radius of τ the large envelope circle in Approximate Design zone; Be that interference between l envelope of k envelope circle of i assembly and j assembly justified retrains;

Be that containing between ζ the envelope circle on τ envelope circle of ε assembly and design domain border retrains.

Above-mentioned 127 equation of constraint are integrated into to an equation of constraint with the KS function:

$C_{\mathrm{KS}}=\frac{1}{p}\ln [\underset{i=1}{\overset{3}{\mathrm{\Σ}}}\underset{j=i+1}{\overset{4}{\mathrm{\Σ}}}\underset{k=1}{\overset{N_i}{\mathrm{\Σ}}}\underset{l=1}{\overset{N_j}{\mathrm{\Σ}}}{e}^{p\·C_{\mathrm{ij}}^{\mathrm{kl}}}+\underset{\mathrm{\ϵ}=1}{\overset{4}{\mathrm{\Σ}}}\underset{\mathrm{\τ}=1}{\overset{N_{\mathrm{\ϵ}}}{\mathrm{\Σ}}}\underset{\mathrm{\ζ}=1}{\overset{4}{\mathrm{\Σ}}}{e}^{p\·C_{\mathrm{\ϵ}}^{\mathrm{\τ\ζ}}}]\≥1$

(c) setting up Topological optimization model is:

Find η=(η ₁, η ₂..., η _Enum); S=(s ₁, s ₂... s _n), s wherein _i=(x _i, y _i, θ _i)

min $\mathrm{\φ}(\mathrm{\η},S,U)=\mathrm{UKU}=\underset{e=1}{\overset{\mathrm{enum}}{\mathrm{\Σ}}}{u}_e{k}_e{u}_e$

s.t.KU＝F

$V(\mathrm{\η},S)\≤\stackrel{\‾}{V}$

C _KS≥1

Wherein, η is the pseudo-intensity vector in unit on design domain; Enum is design domain grid number; S is the Position Design variable of assembly, wherein s _i=(x _i, y _i, θ _i) represent respectively x coordinate, y coordinate and the direction coordinate of i assembly barycenter; N is component count; φ (η, S, U) is the objective function of topology optimization problem, is the structure compliance in this problem, is numerically equal to the bulk strain energy of structure; K is finite element model global stiffness matrix; F is the node equivalent load vectors; U is node global displacement vector; V (η, S) is the volume constraint function;

For the upper limit of volume constraint, namely V wherein ₀For the volume of material cell is arranged; C _KSEquation of constraint for the KS construction of function.

(d) finite element analysis and Optimization Solution.

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 function, choose gradient optimal method GCMMA(Globally Convergent Method of Moving Asymptotes) optimized algorithm is optimized design, and result is optimized.

As seen from Figure 6, carry out multicomponent structures system layout optimal design by the inventive method, a large amount of equation of constraint can be condensed into to one or more KS function constraint equations, and can guarantee that the equation of constraint after cohesion meets institute's Constrained.With the method in list of references, compare, method used in the present invention can solve because of component count and envelope circle number and too much introduce a large amount of equation of constraint, causes optimization problem to be difficult to the problem of carrying out or being difficult to restrain.Therefore, the method applied in the present invention applicability is wider.

Claims (1)

1. method for layout optimal design of multi-assembly structure system based on the KS function is characterized in that comprising the following steps:

Step 1, set up finite element model by the cad model of structure, the multicomponent structures finite element model is divided into to structured grid, background grid and component grid three parts, definition load and boundary condition;

Step 2, assembly and design domain boundary demarcation envelope is round, set up equation of constraint:

$\left\{\begin{array}{c}\∀i=\mathrm{1,2},...,n;j=i+1,...,n;\∀k=\mathrm{1,2},...,N_i;l=\mathrm{1,2},...,N_j\\ s.t.:C_{\mathrm{ij}}^{\mathrm{kl}}=\frac{\left|\right|O_{i\_k}{O}_{j\_l}\left|\right|}{R_{i\_k}+R_{j\_l}}\≥1\\ \∀\mathrm{\ϵ}=\mathrm{1,2},...,n;\∀\mathrm{\τ}=\mathrm{1,2},...,N_p;\mathrm{\ζ}=\mathrm{1,2},...,M\\ s.t.:C_{\mathrm{\ϵ}}^{\mathrm{\τ\ζ}}=\frac{\left|\right|O_{\mathrm{\ϵ}\_\mathrm{\τ}}{O}_{\mathrm{\ζ}}\left|\right|}{R_{\mathrm{\ϵ}\_\mathrm{\τ}}+R_{\mathrm{\ζ}}}\≥1\end{array}\right.$

In formula, n is component count; N _iFor being used for being similar to the envelope circle number of i assembly; O _{i_k}, R _{i_k}Be respectively the center of circle and the radius of k envelope circle of i assembly; M is the number of the envelope circle in Approximate Design zone; O _ζ, R _ζBe respectively the center of circle and the radius of τ the large envelope circle in Approximate Design zone;

Above-mentioned equation of constraint is integrated with a KS function constraint equation:

$C_{\mathrm{KS}}=\frac{1}{p}\ln [\underset{i=1}{\overset{n-1}{\mathrm{\Σ}}}\underset{j=i+1}{\overset{n}{\mathrm{\Σ}}}\underset{k=1}{\overset{N_i}{\mathrm{\Σ}}}\underset{l=1}{\overset{N_j}{\mathrm{\Σ}}}{e}^{p{C}_{\mathrm{ij}}^{\mathrm{kl}}}+\underset{\mathrm{\ϵ}=1}{\overset{n}{\mathrm{\Σ}}}\underset{\mathrm{\τ}=1}{\overset{N_{\mathrm{\ϵ}}}{\mathrm{\Σ}}}\underset{\mathrm{\ζ}=1}{\overset{M}{\mathrm{\Σ}}}{e}^{p{C}_{\mathrm{\ϵ}}^{\mathrm{\τ\ζ}}}]\≥1$

In formula, p is the parameter of KS function;

Step 3, set up Topological optimization model and be:

Find η=(η ₁, η ₂..., η _Enum); S=(s ₁, s ₂... s _n), s wherein _i=(x _i, y _i, θ _i)

min?φ(η,S)

s.t.KU＝F

$G_j(\mathrm{\η},S)\≤{\stackrel{\‾}{G}}_j,j=1,2,...,J$

C _KS≥1

In formula, η is the pseudo-intensity vector in the unit on design domain; Enum is design domain grid number; S is the Position Design variable of assembly, wherein s _i=(x _i, y _i, θ _i) represent respectively x coordinate, y coordinate and the direction coordinate of i assembly barycenter; N is component count; φ (η, S) is the objective function of topology optimization problem; K is finite element model global stiffness matrix; F is the node equivalent load vectors; U is node global displacement vector; G _j(η, S) is j constraint function;

It is the upper limit of j constraint function; J is the number of constraint; C _KSEquation of constraint for the KS construction of function;

Step 4, model is carried out to a finite element analysis: respectively how much variablees and pseudo-density variables are carried out to sensitivity analysis, try to achieve the sensitivity of objective function and constraint condition, choose gradient optimal method GCMMA and be optimized design, result is optimized.

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