A unified approach for topology optimization with local stress constraints considering various failure criteria: Von Mises, Drucker-Prager, Tresca, Mohr-Coulomb, Bresler- Pister and Willam-Warnke

被引：60
作者：
Giraldo-Londoño O. [1 ]
Paulino G.H. [1 ]
机构：
[1] School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, 30332, GA
来源：
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences | 2020年 / 476卷 / 2238期
基金：
美国国家科学基金会;
关键词：
augmented Lagrangian; material failure; stress constraints; topology optimization; yield surface;
D O I：
10.1098/rspa.2019.0861
中图分类号：
学科分类号：
摘要：
An interesting, yet challenging problem in topology optimization consists of finding the lightest structure that is able to withstand a given set of applied loads without experiencing local material failure. Most studies consider material failure via the von Mises criterion, which is designed for ductile materials. To extend the range of applications to structures made of a variety of different materials, we introduce a unified yield function that is able to represent several classical failure criteria including von Mises, Drucker-Prager, Tresca, Mohr-Coulomb, Bresler-Pister and Willam-Warnke, and use it to solve topology optimization problems with local stress constraints. The unified yield function not only represents the classical criteria, but also provides a smooth representation of the Tresca and the Mohr-Coulomb criteria - an attribute that is desired when using gradient-based optimization algorithms. The present framework has been built so that it can be extended to failure criteria other than the ones addressed in this investigation. We present numerical examples to illustrate how the unified yield function can be used to obtain different designs, under prescribed loading or design-dependent loading (e.g. self-weight), depending on the chosen failure criterion. © 2020 The Author(s).
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