Topology optimization with local stress constraint based on level set evolution via reaction-diffusion

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• 作者：Hé ; lio Emmendoerfer Jr. ^{helio.e.j@posgrad.ufsc.br" class="auth_mail" title="E-mail the corresponding author} ; Eduardo Alberto Fancello ; ^{eduardo.fancello@ufsc.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Topology optimization ; Level sets ; Stress constraints ; Augmented Lagrangian ; Reaction&ndash ; diffusion equation
• 刊名：Computer Methods in Applied Mechanics and Engineering
• 出版年：2016
• 出版时间：15 June 2016
• 年：2016
• 卷：305
• 期：Complete
• 页码：62-88
• 全文大小：1891 K

文摘

This work focuses the structural topology optimization problem of mass minimization subject to local stress constraints. To this aim, two related issues are addressed. The first one is the successful strategy used to define local stress constraints by means of an Augmented Lagrangian approach. The second, and main contribution of the present paper, is the use of a reaction–diffusion equation to guide, via evolution of a level set, the design optimization sequence. The advantages of this strategy are twofold: firstly, it allows the creation of new holes during the optimization process, a significant feature for a true topological optimization method. Secondly, reinitialization steps usually found in classical Hamilton–Jacobi based evolution are eliminated with a significant improvement in convergence ease. A set of benchmark examples in two dimensions are presented. Numerical results show the efficiency of the algorithm to create new holes, identify stress concentrations and to provide stable optimization sequences converging to local minima defined by stress saturated designs.