Density evolution topological optimization method for continuum structure with smooth boundary

A smooth boundary and topology optimization technology, applied in design optimization/simulation, special data processing applications, etc., can solve problems that affect the stability of optimization algorithms

Pending Publication Date: 2020-12-18
SOUTH CHINA UNIV OF TECH
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  • Application Information

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Problems solved by technology

In addition, the progressive evolution method has the advantages of simple algorithm and easy connection with the finite element analysis program. The finite element model of the final optimization result has only 0/1 units; the optimization result obtaine

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  • Density evolution topological optimization method for continuum structure with smooth boundary
  • Density evolution topological optimization method for continuum structure with smooth boundary
  • Density evolution topological optimization method for continuum structure with smooth boundary

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Embodiment 1

[0088] A topology optimization method for density evolution of continuum structures with smooth boundaries, such as figure 1 shown, including the following steps:

[0089] S1. Establish the geometric initial design domain of the continuum structure through the drawing modeling module;

[0090] S2. Based on the material interpolation model without penalty function, the finite element model of the initial geometric design domain is established, the structure is divided into several finite element element grids, and the optimization result is determined by the presence or absence of element density;

[0091] S3. Establish a mathematical model for the topology optimization problem of the continuum structure, with the goal of minimizing the structural strain energy and constraining the volume of the material used to establish an optimized mathematical model;

[0092] S4. Calculate the sensitivity of the optimization objective and constraints to the design variables, and filter th...

Embodiment 2

[0154] The BDE optimization method can be easily extended to the three-dimensional case. In another three-dimensional structural example, the BSE method is used to assist in the design of a bridge. Its initial design domain is as Figure 12 As shown, the bridge deck is a non-design domain. The nodal load on the bridge deck is 10000KN, and the bottom surface is hinged at four points. The elastic modulus of the material used is 20Gpa, the Poisson's ratio is 0.2, and the volume constraint is 0.2. The initial structure is calculated according to the symmetrical 1 / 2 model. At this time, the design domain is discretized into 52800 8-node units.

[0155] Calculated on a home-use IntelI5-CPU3.3GHz computer, the final number of iterations is 60 steps, and the calculation takes 2375 seconds. The final optimization result is a strain energy of 36.91, and the goal and constraint convergence curve is as follows Figure 13 shown. The optimized finite element model is as Figure 14 shown....

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Abstract

The invention discloses a density evolution topological optimization method for a continuum structure with a smooth boundary. The method comprises the following steps: establishing a geometric initialdesign domain of the continuum structure; establishing a finite element model of a geometric initial design domain based on a material interpolation model without a penalty function; establishing a continuum structure topological optimization problem mathematical model; calculating the sensitivity of the optimization target and the constraint condition to the design variable, and conducting filtering; updating a design variable according to the sensitivity by adopting an optimization algorithm, and carrying out graded filtering on the density to achieve convergence and constraint conditions so as to obtain a finite element model of an optimized structure; and constructing a node strain energy level set, and processing a boundary unit to obtain a structure topological optimization model ofa smooth boundary displayed based on the node density or the node strain energy level set. According to the method, a penalty-function-free material interpolation model and a density grading filtering method are provided, a structure boundary unit is processed, an optimization result with a smooth boundary is obtained, and the topological optimization problem is efficiently solved.

Description

technical field [0001] The invention relates to the research field of structure optimization, in particular to a topology optimization method for density evolution of continuum structures with smooth boundaries. Background technique [0002] Structural topology optimization is to find a way to reasonably distribute limited materials to the design domain to achieve the optimal performance of the structure. Structural topology optimization design method is a new digital structure design method. By establishing a mathematical model including objective functions and constraint equations, finite element numerical analysis is carried out on the structure, and in the design domain, it is iteratively solved according to optimization criteria or mathematical programming methods to meet the target requirements. material distribution. [0003] The structural topology optimization design method was originally limited to mechanical structural design problems, and now it has been gradual...

Claims

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Application Information

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IPC IPC(8): G06F30/23
CPCG06F30/23
Inventor 李雪平
Owner SOUTH CHINA UNIV OF TECH
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