A critical comparative assessment of differential equation-driven methods for structural topology optimization

In recent years, differential equation-driven methods have emerged as an alternate approach for structural topology optimization. In such methods, the design is evolved using special differential equations. Implicit level-set methods are one such set of approaches in which the design domain is repre...

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Bibliographic Details
Published in:Structural and multidisciplinary optimization 2013-10, Vol.48 (4), p.685-710
Main Authors: Gain, Arun L., Paulino, Glaucio H.
Format: Article
Language:English
Subjects:
Computational Mathematics and Numerical Analysis
Design optimization
Differential equations
Engineering
Engineering Design
Evolution
Hamilton-Jacobi equation
Reaction-diffusion equations
Review Article
Theoretical and Applied Mechanics
Topology optimization
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Summary:In recent years, differential equation-driven methods have emerged as an alternate approach for structural topology optimization. In such methods, the design is evolved using special differential equations. Implicit level-set methods are one such set of approaches in which the design domain is represented in terms of implicit functions and generally (but not necessarily) use the Hamilton-Jacobi equation as the evolution equation. Another set of approaches are referred to as phase-field methods; which generally use a reaction-diffusion equation, such as the Allen-Cahn equation, for topology evolution. In this work, we exhaustively analyze four level-set methods and one phase-field method, which are representative of the literature. In order to evaluate performance, all the methods are implemented in MATLAB and studied using two-dimensional compliance minimization problems.
ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-013-0935-4