CN103425830B - Structural topological optimization method based on multi-point displacement coordination constraint - Google Patents

Abstract

The invention discloses a structural topological optimization method based on multi-point displacement coordination constraint, and the structural topological optimization method based on multi-point displacement coordination constraint is used for solving the technical problem that an existing continuous body structural topological coordination optimization method cannot achieve displacement coordination constraint so that practicality is poor. According to the technical scheme, a finite element model is built, certain displacement constraint controlling points are selected, and a layer of auxiliary units cover the geometrical area defined by the displacement controlling points; a topological optimization model is built, sensitivity of the objective function and the constraint conditions is obtained through the optimization of sensitivity analysis, a step optimization algorithm is adopted to carry out optimization design, and the optimization result is obtained. Due to the fact that the auxiliary units are connected with each controlling point, the purpose of controlling the relative displacement between nodes is achieved through constraining the overall soft and smooth degree of the auxiliary units, therefore, the purpose of achieving multi-point displacement coordination constraint is achieved, and the practicality is strong.

Description

Structure topology optimization method based on multi-point displacement coordination constraint

Technical Field

The invention relates to a structural topology optimization method. In particular to a structural topology optimization method based on multi-point displacement coordination constraint.

Background

Reference is made to fig. 1-3. In the fields of aerospace, automobile manufacturing and the like, a large number of parts such as aircraft windows, assembly trusses and the like are subjected to external loads (concentrated force, thermal stress and the like) or self-gravity, and relative displacement occurs between members connected with the parts or local related control points. If the relative deformation is too large, the geometrical configuration formed by the control points is distorted or warped, and the like. The displacement coordination means that the displacements of the control points are coordinated and changed, so that severe deformation in the control structure cannot be caused. The spatial multi-node displacement coordination constraint aims to constrain the relevant control points to generate rigid displacement in space as a whole geometric configuration. If the undeformed aircraft porthole 2 on the aircraft fuselage 1 rotates integrally, the aircraft porthole 4 after the integral rotation has large displacement of the displacement control points 3, but because the relative displacement between the displacement control points 3 is small, the aircraft porthole cannot be damaged; although the absolute displacement of each displacement control point 3 is small, the relative displacement between the displacement control points 3 is large, and the aircraft porthole 5 is damaged.

Refer to fig. 4. Document 1 "topology optimization of continuum structure under constraint of stress and displacement, applied mathematics and mechanics, suyun kang, liu zheng, sun shines, and 2000" discloses a topology optimization method of continuum structure under constraint of displacement. The method establishes a continuum structure topology optimization model taking weight as a target and considering stress and displacement constraints, and deduces an explicit relational expression between the stress and displacement constraints and topology design variables. And (3) utilizing a dual planning simplified model, and further completing the inversion from dispersion to continuity by adopting a threshold value for a topological coordination solution through the comprehensive coordination of the stress topological solution and the displacement-stress topological solution.

Although the method disclosed in document 1 can constrain the displacement of a given node, in a multi-displacement constraint, the displacement of each node is independent, and this method cannot conform: the optimized configuration can not constrain the original relative displacement of the nodes, i.e. the method can not realize the coordinated constraint of multipoint displacement. Under the action of loads P1-P3, the method independently restricts the displacement of the point A, B, C, and the positions of the three points after loading become A ', B ' and C ', although the method can independently restrict the displacement of the three points, the method cannot restrict the relative displacement of the three points, so the method does not have a multi-point displacement coordination function and has poor practicability.

Disclosure of Invention

In order to overcome the defect that the prior continuum structure topology optimization method cannot realize displacement coordination constraint and is poor in practicability, the invention provides a structure topology optimization method based on multipoint displacement coordination constraint. The method comprises the steps of establishing a finite element model, selecting certain displacement constraint control points, and covering a layer of auxiliary units on a geometric area defined by the displacement constraint control points; and establishing a topological optimization model, obtaining the sensitivity of the objective function and the constraint condition through optimizing sensitivity analysis, and performing optimization design by adopting a gradient optimization algorithm to obtain an optimization result. Because the auxiliary unit is connected with each control point, the aim of controlling the relative displacement between each node is achieved by constraining the whole flexibility of the auxiliary unit, so that the aim of coordinated constraint of multi-point displacement is achieved, and the practicability is high.

The technical scheme adopted by the invention for solving the technical problems is as follows: a structural topology optimization method based on multipoint displacement coordination constraint is characterized by comprising the following steps:

step one, establishing a finite element model, and applying constraint and boundary load to the model.

And secondly, selecting displacement constraint control points, covering a layer of auxiliary units on a geometric area defined by the control points, wherein the Young modulus of the auxiliary units is at least five orders of magnitude lower than that of the structure.

Step three, defining a topology optimization model:

find X=(x₁，x₂，...，x_n)

min Φ(X)

s.t. KU＝F

C_a≤

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

in the formula, X is a topological optimization variable vector on a design domain; n is the number of shape design variables; phi (X) is an objective function of topology optimization; k is a finite element model overall stiffness matrix; f is a node equivalent load vector; u is a node overall displacement vector; c_aIs the compliance of the auxiliary unit; the upper limit of the flexibility of the auxiliary unit is extremely small positive number; g_j(X) is the jth constraint function;is the upper limit of the jth constraint function; j is the number of constraints.

Step four, carrying out primary finite element analysis on the model; and obtaining the sensitivity of the target function and the constraint condition by optimizing sensitivity analysis, and selecting a gradient optimization algorithm to carry out optimization design to obtain an optimization result.

The invention has the beneficial effects that: the method comprises the steps of establishing a finite element model, selecting certain displacement constraint control points, and covering a layer of auxiliary units on a geometric area defined by the displacement constraint control points; and establishing a topological optimization model, obtaining the sensitivity of the objective function and the constraint condition through optimizing sensitivity analysis, and performing optimization design by adopting a gradient optimization algorithm to obtain an optimization result. Because the auxiliary unit is connected with each control point, the aim of controlling the relative displacement between each node is achieved by constraining the whole flexibility of the auxiliary unit, so that the aim of coordinated constraint of multi-point displacement is achieved, and the practicability is high.

The present invention will be described in detail below with reference to the accompanying drawings and examples.

Drawings

FIG. 1 is a schematic view of a background art aircraft porthole.

FIG. 2 is a schematic diagram of displacement-coordinated deformation of a porthole of a prior art aircraft.

FIG. 3 is a schematic diagram of non-displacement coordination of a background art aircraft porthole.

Fig. 4 is a schematic diagram of solving the multipoint displacement constraint problem in the background art document 1.

FIG. 5 is a schematic diagram of a model and auxiliary units of a particular embodiment.

FIG. 6 is a schematic illustration of the attachment of the auxiliary unit to the form in an embodiment.

FIG. 7 is a schematic diagram of a final design using the method of the present invention.

Fig. 8 is a schematic diagram of the final design of the method disclosed in the background art document 1.

In the figure, 1 — the fuselage of the aircraft; 2-undeformed aircraft porthole; 3-displacement control point; 4-airplane porthole after integral rotation; 5-the deformed aircraft porthole; 6-rectangular design domain; 7-a pendant structure; 8-an auxiliary unit; 9-control point; 10-a support structure; 11-comparative support structure.

Detailed Description

Reference is made to fig. 5-7. The structural topology optimization method based on the multipoint displacement coordination constraint specifically comprises the following steps.

The invention is illustrated below by way of a planar rectangular design area.

The two ends of the bottom of the rectangular design domain 6 are fixed and are connected with a pendant structure 7 with certain quality through control points 9. The auxiliary unit 8 controls the deformation of the suspension structure 7 itself, and the material properties of each structure are as follows:

rectangular design area 6: elastic modulus E =210KPa, density ρ =7900kg/m3, poisson ratio ν = 0.3;

the hanging part structure 7: elastic modulus E =210KPa, density ρ =10000kg/m3, Poisson ratio ν = 0.3;

the overall structure is subjected to a vertical downward 9.8m/s2 gravitational acceleration, and the rectangular design field 6 is given a 50% upper limit on material usage with the design goal being maximum overall structural stiffness.

The method comprises the following specific steps:

step one, establishing a finite element model, and applying constraint and boundary load to the model.

And step two, selecting displacement constraint control points. The geometry of the pendant structure 7 enclosing these control points 9 is covered by a layer of auxiliary units 8, the material properties of the auxiliary units 8 are as follows:

the auxiliary unit 8: elastic modulus E =2.1Pa, density ρ =0kg/m3, poisson ratio ν = 0.3.

Step three, defining a topology optimization model:

find x＝(x₁，x₂，...，x_n)

min C(X)

s.t. KU＝F

C_a≤1.5E-14

V(X)-0.5≤0

wherein,x is a topological optimization design variable vector on a design domain; n is the number of shape design variables; c (X) is the flexibility of the structure; k is a finite element model overall stiffness matrix; f is a node equivalent load vector; u is a node overall displacement vector; c_aCompliance of the auxiliary unit 8; v (X) is the volume fraction of the structure.

Step four, carrying out primary finite element analysis on the model by using finite element software Ansys; and performing optimization sensitivity analysis through a structure optimization platform Boss-Quattro to obtain the sensitivity of the objective function and the constraint condition, and performing optimization design by selecting a gradient optimization algorithm GCMMA (Global Convergent Method of Moving asymptes) optimization algorithm to obtain an optimization result.

As can be seen from the optimization results, compared with the comparative support structure 11 optimized by the method disclosed in document 1, the support structures 10 after coordinated optimization of displacement are communicated with each other by the method of the present invention, so that the relative displacement of the control points 9 connected to the pendant structures 7 is reduced, and the flexibility of the auxiliary units 8 connected to the control points 9 is 1.5E to 14J. The method disclosed in the document 1 can only control the displacement of a single node, and cannot apply displacement coordination constraint among a plurality of nodes, an auxiliary unit is connected to a control point of a model established by applying the method disclosed in the document 1, and after the optimization is finished, the compliance of the auxiliary unit is 1.1E-12J, which is much greater than that of the auxiliary unit of the method disclosed by the invention. The method disclosed by the invention is used for optimizing and implementing the multipoint displacement coordination constraint of the pendant structure 7, and is high in practicability, while the method disclosed by the document 1 cannot implement the multipoint displacement coordination constraint and only can implement the independent node displacement constraint, and is poor in practicability.

Claims (1)

1. A structural topology optimization method based on multipoint displacement coordination constraint is characterized by comprising the following steps:

step one, establishing a finite element model, and applying constraint and boundary load to the model;

selecting displacement constraint control points, covering a layer of auxiliary units on a geometric area defined by the control points, wherein the Young modulus of the auxiliary units is at least five orders of magnitude lower than that of the structure;

step three, defining a topology optimization model:

find X＝(x₁，x₂，...，x_n)

min Φ(X)

s.t. KU＝F

C_a≤

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

in the formula, X is a topological optimization variable vector on a design domain; n is the number of shape design variables; phi (X) is an objective function of topology optimization; k is a finite element model overall stiffness matrix; f is a node equivalent load vector; u is a node overall displacement vector; c_aIs the compliance of the auxiliary unit; the upper limit of the flexibility of the auxiliary unit is extremely small positive number; g_j(X) is the jth constraint function;is the upper limit of the jth constraint function; j is the number of constraints;

step four, carrying out primary finite element analysis on the model; and obtaining the sensitivity of the target function and the constraint condition by optimizing sensitivity analysis, and selecting a gradient optimization algorithm to carry out optimization design to obtain an optimization result.