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Stress-based topology optimization using spatial gradient stabilized XFEM

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Abstract

This paper presents an immersed boundary approach for level set topology optimization considering stress constraints. A constraint agglomeration technique is used to combine the local stress constraints into one global constraint. The structural response is predicted by the eXtended Finite Element Method. A Heaviside enrichment strategy is used to model strong and weak discontinuities with great ease of implementation. This work focuses on low-order finite elements, which given their simplicity are the most popular choice of interpolation for topology optimization problems. The predicted stresses strongly depend on the intersection configuration of the elements and are prone to significant errors. Robust computation of stresses, regardless of the interface position, is essential for reliable stress constraint prediction and sensitivities. This study adopts a recently proposed fictitious domain approach for penalization of displacement gradients across element faces surrounding the material interface. In addition, a novel XFEM informed stabilization scheme is proposed for robust computation of stresses. Through numerical studies the penalized spatial gradients combined with the stabilization scheme is shown to improve prediction of stresses along the material interface. The proposed approach is applied to the benchmark topology optimization problem of an L-shaped beam in two and three dimensions using material-void and material-material problem setups. Linear and hyperelastic materials are considered. The stress constraints are shown to be efficient in eliminating regions with high stress concentration in all scenarios considered.

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Acknowledgements

The authors acknowledge the support of the National Science Foundation under Grant EFRI-ODISSEI 1240374 and of the US Air Force of Scientific Research under Grant FA9550-16-1-0169. The second author also acknowledges the support of the National Science Foundation under Grant CMMI 1463287. The opinions and conclusions presented in this paper are those the authors and do not necessarily reflect the views of the sponsoring organizations.

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  1. Department of Aerospace Engineering Sciences, University of Colorado at Boulder, Boulder, CO, 427 UCB, USA

    Ashesh Sharma & Kurt Maute

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  1. Ashesh Sharma
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  2. Kurt Maute
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Correspondence to Kurt Maute.

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Sharma, A., Maute, K. Stress-based topology optimization using spatial gradient stabilized XFEM. Struct Multidisc Optim 57, 17–38 (2018). https://doi.org/10.1007/s00158-017-1833-y

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