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Shape equilibrium constraint: a strategy for stress-constrained structural topology optimization

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Abstract

In topology optimization of a continuum, it is important to consider stress-related objective or constraints, from both theoretical and application perspectives. It is known that the problem is challenging. Although remarkable achievements have been made with the SIMP (Solid Isotropic Material with Penalization) framework, a number of critical issues are yet to be fully resolved. In the paper, we present an approach of a shape equilibrium constraint strategy with the level-set/X-FEM framework. We formulate the topology optimization problem under (spatially-distributed) stress constraints into a shape equilibrium problem of active stress constraint. This formulation allows us to effectively handle the stress constraint, and the intrinsic non-differentiability introduced by local stress constraints is removed. The optimization problem is made into one of continuous shape-sensitivity and it is solved by evolving a coherent interface of the shape equilibrium concurrently with shape variation in the structural boundary during a level-set evolution process. Several numerical examples in two dimensions are provided as a benchmark test of the proposed shape equilibrium constraint strategy for minimum-weight and fully-stressed designs and for designs with stress constraint satisfaction.

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Acknowledgments

The financial support from the Research Grants Council of Hong Kong S.A.R. (project No. CUHK417309) is gratefully acknowledged. The author would like to thank Drs. Qi Xia and Zhen Luo for their valuable discussions on the related topics.

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Authors and Affiliations

  1. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, NT, Hong Kong

    Michael Yu Wang & Li Li

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  1. Michael Yu Wang
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  2. Li Li
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Correspondence to Michael Yu Wang.

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Wang, M.Y., Li, L. Shape equilibrium constraint: a strategy for stress-constrained structural topology optimization. Struct Multidisc Optim 47, 335–352 (2013). https://doi.org/10.1007/s00158-012-0846-9

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