Topology optimization of multi-material for the heat conduction problem based on the level set method

2010 ◽  
Vol 42 (9) ◽  
pp. 811-831 ◽  
Author(s):  
Chungang Zhuang ◽  
Zhenhua Xiong ◽  
Han Ding
Keyword(s):  
Topology Optimization ◽  
Heat Conduction ◽  
Level Set Method ◽  
Level Set ◽  
Heat Conduction Problem

Minimizing the quadratic mean temperature gradient for the heat-conduction problem using the level-set method

2007 ◽  
Vol 221 (2) ◽  
pp. 235-248 ◽  
Author(s):  
C G Zhuang ◽  
Z H Xiong ◽  
H Ding
Keyword(s):  
Heat Conduction ◽  
Temperature Gradient ◽  
Objective Function ◽  
Level Set Method ◽  
Level Set ◽  
Heat Conduction Problem ◽  
Shape Sensitivity ◽  
Material Derivative ◽  
Quadratic Mean ◽  
Mean Temperature

This paper presents a numerical algorithm for minimizing the quadratic mean temperature gradient for the heat-conduction problem on the basis of the shape derivative for an elliptical system and the level-set method for a propagating surface. The level-set method as an implicit boundary model is employed to represent the optimal boundaries of heat transfer material. The objective function of the optimization problem is the quadratic mean temperature gradient. The shape of physical domain is treated as the design variable. The material derivative theory of the continuum mechanics and the adjoint method are used to implement the shape sensitivity analysis of the objective function. Since the level-set approach itself cannot generate new holes in the material region, as a remedy, the topological derivative of the elliptic equations that generates new holes to suppress the topological dependence of initialization is introduced. Numerical examples demonstrate that the proposed method is an effective technique for the optimal design of the heat-conduction problem.

Topology optimization of hyperelastic structures using a level set method

2017 ◽  
Vol 351 ◽  
pp. 437-454 ◽  
Author(s):  
Feifei Chen ◽  
Yiqiang Wang ◽  
Michael Yu Wang ◽  
Y.F. Zhang
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set

scholarly journals Efficient Local Level Set Method without Reinitialization and Its Appliance to Topology Optimization

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Wenhui Zhang ◽  
Yaoting Zhang
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Computational Efficiency ◽  
Numerical Stability ◽  
Local Level ◽  
Band Model ◽  
Numerical Process ◽  
Local Level Set ◽  
Narrow Band Model

The local level set method (LLSM) is higher than the LSMs with global models in computational efficiency, because of the use of narrow-band model. The computational efficiency of the LLSM can be further increased by avoiding the reinitialization procedure by introducing a distance regularized equation (DRE). The numerical stability of the DRE can be ensured by a proposed conditionally stable difference scheme under reverse diffusion constraints. Nevertheless, the proposed method possesses no mechanism to nucleate new holes in the material domain for two-dimensional structures, so that a bidirectional evolutionary algorithm based on discrete level set functions is combined with the LLSM to replace the numerical process of hole nucleation. Numerical examples are given to show high computational efficiency and numerical stability of this algorithm for topology optimization.

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