CN104765922A - Method for topological optimization design of cantilever beam structure based on shape-preserved constraints - Google Patents

Abstract

The invention discloses a method for topological optimization design of a cantilever beam structure based on shape-preserved constraints and aims at solves the technical problem of poor precision in the present method for topological optimization design of a cantilever beam structure. The technical scheme comprises the steps: adopting a structural strain energy physics function and quantizing buckling deformation in a local area of the cantilever beam structure; utilizing a quantized strain energy numeric value as a constraint during optimization, giving an upper bound of the constraint and solving the flexibility of the strain energy constraint function in an accompanying method; meanwhile, introducing a constraint of material quantity, utilizing the whole rigidness of the cantilever beam structure as a target function, performing topological optimization, thereby obtaining a design result. By adopting the method, the deformation of the cantilever beam structure is effectively inhibited after the local area is stressed with load; meanwhile, the displacement form of the rigid body in the area is maintained and the shape-preserved design effect is realized. The optimization design result shows that the deformation capacity of the local area of the cantilever beam structure with the shape-preserved constraints is reduced to be 0.2% of the background art when the usage quantity of the same material is 40%.

Description

Based on the cantilever beam structure method of topological optimization design of conformal constraint

Technical field

The present invention relates to a kind of cantilever beam structure method of topological optimization design, particularly relate to a kind of cantilever beam structure method of topological optimization design based on conformal constraint.

Background technology

Document " Evolutionary topology optimization of continuum structures with a globaldisplacement control; Computer-Aided Design; 2014; Vol56, p58-67 " discloses a kind of Structural Topology Optimization Design method retrained based on overall maximum displacement.The method, for cantilever beam structure, by the maximum displacement value of restraining structure under distributed load effect and material usage, achieves structure maximum displacement and is less than set-point, and meets certain rigidity requirement design.

Method described in document is that the maximum displacement point of restraining structure is less than set-point, realizes the shape to structure and Deformation control.Rigid body displacement and warp displacement are constrained its size and Orientation by this nodal Displacement Constraint simultaneously, and result will make project organization rigid body, and any position and change of shape do not occur.In engineering reality, need all warp displacement of localized region to suppress, ensure that planform is stablized and form accuracy.Method described in document is only for single maximum displacement point, and applicability is not strong, cannot retain rigid body displacement yet.

Summary of the invention

In order to overcome the deficiency of existing cantilever beam structure method of topological optimization design low precision, the invention provides a kind of cantilever beam structure method of topological optimization design based on conformal constraint.The method adopts structural strain energy physical function, the buckling deformation of regional area in cantilever beam structure is quantized.Optimize process in the strain energy numerical value of this quantification for constraint, the given constraint upper bound, tries to achieve the sensitivity of this strain energy constraint function by adjoint method, introduce material usage constraint simultaneously, with cantilever beam structure integral rigidity for objective function, carry out structural Topology Optimization and obtain design result.The method effectively can suppress the self-deformation in cantilever beam structure after regional area stand under load, maintains the rigid body displacement form in this region simultaneously, realizes conformal design effect.

The technical solution adopted for the present invention to solve the technical problems is: a kind of cantilever beam structure method of topological optimization design based on conformal constraint, is characterized in adopting following steps:

Step one, set up the Topological optimization model of cantilever beam structure, the central rectangular of cantilever beam structure is divided into the conformal region of local.Fixed constraint is applied to cantilever beam structure left end, and in lower right corner effect one concentrated force load straight down.

Step 2, definition conformal regional structure Ω _sfor the non-design domain of semi-girder topological optimization.By the design domain Ω in semi-girder topological optimization _ddiscrete is n finite elements, x _ifor the pseudo-density that unit is corresponding, F is load vectors, and U is global displacement vector, and K is structure global stiffness matrix, for conformal regional structure stiffness matrix, for the motion vector in conformal region, for the strain energy function in conformal region.

Step 3, definition conformal optimization problem: Φ (X) is optimization object function, is taken as the compliance function that cantilever beam structure is overall in conformal optimization problem, and constraint condition is that materials'use amount is less than the strain energy change upper limit of conformal regional structure is ε >0:

$\begin{array}{cc}\mathrm{find}& X=(x_1,x_2,...,x_n)\\ \min & \mathrm{\Φ}\left(X\right)\\ s.t.& \mathrm{KU}=F\\ & V\left(X\right)-\stackrel{\‾}{V}\≤0\\ & C_{{\mathrm{\Ω}}_s}=\frac{1}{2}{U}_{{\mathrm{\Ω}}_s}^T{K}_{{\mathrm{\Ω}}_s}{U}_{{\mathrm{\Ω}}_s}\≤\mathrm{\ϵ}\end{array}$

The dynamic respond U of step 4, finite element analysis computation cantilever beam structure.The dynamic respond in conformal region is calculated according to U and calculate the strain energy in conformal region

Step without, calculate conformal Regional strain energy function for the pseudo-density x of unit in design domain _isensitivity.

Step 6, be optimized according to above-mentioned sensitivity of trying to achieve, choose gradient optimal method, Optimized Iterative obtains result.

The invention has the beneficial effects as follows: the method adopts structural strain energy physical function, the buckling deformation of regional area in cantilever beam structure is quantized.Optimize process in the strain energy numerical value of this quantification for constraint, the given constraint upper bound, tries to achieve the sensitivity of this strain energy constraint function by adjoint method, introduce material usage constraint simultaneously, with cantilever beam structure integral rigidity for objective function, carry out structural Topology Optimization and obtain design result.The method effectively can suppress the self-deformation in cantilever beam structure after regional area stand under load, maintains the rigid body displacement form in this region simultaneously, realizes conformal design effect.Optimum Design Results shows, in 40% identical materials'use consumption situation, larger buckling deformation occurs the cantilever beam structure regional area of background technology method conformal constraint.The deformation energy of the cantilever beam structure regional area of the inventive method conformal constraint declines to a great extent as original 0.2%, and buckling deformation is obviously suppressed, and construction profile is well ensured.

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

Accompanying drawing explanation

Fig. 1 is cantilever beam structure involved by the inventive method and scale diagrams, and cantilever beam structure center is with the conformal region of rectangle.

Fig. 2 is load and the boundary condition schematic diagram of semi-girder topological optimization structure involved by the inventive method.

Fig. 3 is background technology method cantilever beam structure topology optimization design result schematic diagram.

Fig. 4 is the inventive method cantilever beam structure topology optimization design result schematic diagram.

Fig. 5 is after background technology method cantilever beam structure topology optimization design, the enlarged drawing of conformal region and distortion thereof.

Fig. 6 is after the inventive method cantilever beam structure topology optimization design, the enlarged drawing of conformal region and distortion thereof.

In figure: 1-cantilever beam structure; 2-conformal region; 3-concentrated force load; 4-fixed boundary; The node configuration of 5-topological optimization result; Distortion after 7-optimal design.

Embodiment

With reference to Fig. 1-6.The cantilever beam structure method of topological optimization design concrete steps that the present invention is based on conformal constraint are as follows:

A () sets up semi-girder Topological optimization model, cantilever beam structure 1 length 100mm, height 70mm; Center is the conformal region 2, rectangle length 20mm, width 20mm of a rectangle.Thickness is 10mm.Cantilever beam structure 1 lower right corner applies concentrated force load 3, and size is F=100N, and direction straight down; Left end is fixed boundary 4.

B () definition cantilever beam structure 1 is the design domain Ω of topological optimization _d, the Young modulus of design domain material is 100GP; Definition conformal region 2 is non-design domain, and the Young modulus of non-design domain material is 10GPa.Poisson ratio is μ=0.3.By design domain Ω _ddiscrete is 7000 2 dimension unit, x _ifor the pseudo-density that unit is corresponding, F is load vectors, and U is global displacement vector, and K is structure global stiffness matrix, and C (X) is structure compliance function, for the structural stiffness matrix in conformal region, for the motion vector in conformal region, for the strain energy function in conformal region.

(c) definition conformal optimization problem: optimization object function is that structure collectivity compliance function is minimum, and constraint material uses volume fraction to be less than 40%, and the conformal regional structure strain energy upper limit is less than 10 ^-4j:

$\begin{array}{cc}\mathrm{find}& X=(x_1,x_2,...,x_{6600})\\ \min & C\left(X\right)=\frac{1}{2}{U}^T\mathrm{KU}\\ s.t.& \mathrm{KU}=F\\ & V\left(X\right)-0.4\≤0\\ & C_{{\mathrm{\Ω}}_s}=\frac{1}{2}{U}_{{\mathrm{\Ω}}_s}^T{K}_{{\mathrm{\Ω}}_s}{U}_{{\mathrm{\Ω}}_s}\≤{10}^{-4}\end{array}$

D () uses the dynamic respond U of finite element analysis software Ansys computing structure model.The dynamic respond in conformal region is calculated according to U and calculate the initial strain energy in conformal region

E () calculates conformal about intrafascicular, and conformal Regional strain energy is for the pseudo-density x of unit in design domain _isensitivity; And the sensitivity of calculating target function.

F () introduces the strain energy constraint in conformal region in optimizing process, choose gradient optimal method GCMMA (Globally Convergent Method of Moving Asymptotes) according to above-mentioned sensitivity of trying to achieve and be optimized iteration, be finally optimized result.

Contrasted as can be seen from the node configuration 5 of different topological optimization results, adopt the inventive method, after considering conformal constrained optimization, material surrounds and is distributed in around conformal region.Traditional without conformal constrained optimization result, the original shape in conformal region 2 is compared in the distortion 7 after the optimal design of its rectangular area, and larger buckling deformation occurs; And after the inventive method adds conformal constraint, the distortion 7 after its rectangular area optimal design maintains the original shape in conformal region 2 well, and significantly reduces the strain energy numerical value in this region.

The method applied in the present invention solves the buckling deformation problem of regional area in cantilever beam structure well.Compared with background technology optimum results, the optimum results performance of the inventive method is better.

Table 1

Claims (1)

1., based on a cantilever beam structure method of topological optimization design for conformal constraint, it is characterized in that comprising the following steps:

Step one, set up the Topological optimization model of cantilever beam structure, the central rectangular of cantilever beam structure is divided into the conformal region of local; Fixed constraint is applied to cantilever beam structure left end, and in lower right corner effect one concentrated force load straight down;

Step 2, definition conformal regional structure Ω _sfor the non-design domain of semi-girder topological optimization; By the design domain Ω in semi-girder topological optimization _ddiscrete is n finite elements, x _ifor the pseudo-density that unit is corresponding, F is load vectors, and U is global displacement vector, and K is structure global stiffness matrix, for conformal regional structure stiffness matrix, for the motion vector in conformal region, for the strain energy function in conformal region;

Step 3, definition conformal optimization problem: Φ (X) is optimization object function, is taken as the compliance function that cantilever beam structure is overall in conformal optimization problem, and constraint condition is that materials'use amount is less than the strain energy change upper limit of conformal regional structure is ε >0:

find X＝(x ₁,x ₂,...,x _n)

min Φ(X)

s.t.KU＝F

$V\left(X\right)-\stackrel{\‾}{V}\≤0$

${C_{\mathrm{\Ω}}}_s=\frac{1}{2}{U_{\mathrm{\Ω}}^T}_s{K_{\mathrm{\Ω}}}_s{U_{\mathrm{\Ω}}}_s\≤\mathrm{\ϵ}$

The dynamic respond U of step 4, finite element analysis computation cantilever beam structure; The dynamic respond in conformal region is calculated according to U and calculate the strain energy in conformal region

Step 5, calculating conformal Regional strain energy function are for the pseudo-density x of unit in design domain _isensitivity;

Step 6, be optimized according to above-mentioned sensitivity of trying to achieve, choose gradient optimal method, Optimized Iterative obtains result.