Binary Discrete Method of Topology Optimization

MEI Yu-lin; WANG Xiao-ming; CHENG Geng-dong

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Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(6): 631-642

MEI Yu-lin, WANG Xiao-ming, CHENG Geng-dong. Binary Discrete Method of Topology Optimization[J]. Applied Mathematics and Mechanics, 2007, 28(6): 631-642.

Citation:

MEI Yu-lin, WANG Xiao-ming, CHENG Geng-dong. Binary Discrete Method of Topology Optimization[J]. Applied Mathematics and Mechanics, 2007, 28(6): 631-642.

Citation:

MEI Yu-lin, WANG Xiao-ming, CHENG Geng-dong. Binary Discrete Method of Topology Optimization[J]. Applied Mathematics and Mechanics, 2007, 28(6): 631-642.

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Binary Discrete Method of Topology Optimization

1.
Mechanical Engineering Department, Dalian University of Technology, Dalian 116024, P. R. China;

Received Date: 2006-07-13
Rev Recd Date: 2007-04-11
Publish Date: 2007-06-15

Abstract

Abstract

The numerical non-stability of a discrete algorithm of topology optimization can result from the inaccurate evaluation of element sensitivities,especially,when material is added to elements.The estimation of element sensitivities is very inaccurate.Even their sign are also estimated wrongly.In order to overcome the problem,a new incremental sensitivity analysis formula was constructed based on the perturbation analysis of the elastic equilibrium increment equation,which can provide us with a good estimate of the change of the objective function whether material is removed from or added to elements.Meanwhile it can also be considered as the conventional sensitivity formula modified by a non-local element stiffness matrix.As a consequence,a binary discrete method of topology optimization was established,in which each element is assigned either a stiffness value of solid material or a small value indicating no material.And the optimization process can remove material from elements or add material to elements so as to make the objective function decrease.And a main advantage of the method is simplicity,no need of much mathematics,and particularly engineering application.
- discrete variable,
- topology optimization,
- sensitivity analysis,
- matrix perturbation

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References(8)

References

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