Abstract
This article aims to develop a novel approach to non-probabilistic reliability-based multi-material topology optimization with stress constraints to address the optimization design problem considering external loading uncertainties. To be specific, the ordered solid isotropic material with penalization multi-material interpolation model is introduced into the non-probabilistic reliability-based topology optimization considering structural volume minimization under stress constraints, the multidimensional ellipsoidal model describes the non-probabilistic uncertainty. By utilizing the first-order reliability method, the failure probability can be estimated, and a non-probabilistic reliability index can be obtained. The global maximum stress is measured by adopting the normalized p-norm function method in combination with relaxation stress. The sensitivity analysis of the stress constraints is derived by the adjoint variable method, and the method of moving asymptote is employed to solve the design variables. Through several numerical examples, the effectiveness and feasibility of the presented method are verified to consider multi-material topology optimization with stress constraints in the absence of accurate probability distribution information of uncertain variables.
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Data availability
All simulations are performed using an in-house MATLAB implementation. All the datasets generated in this work and the MATLAB codes are available upon reasonable request to the corresponding author.
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Acknowledgements
The authors are thankful for Professor Krister Svanberg for the MMA program made freely available for research purposes and the anonymous reviewers for their helpful and constructive comments.
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The funding was provided by National Natural Science Foundation of China, (Grand Number 52175236), Qinghai Zhao.
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Cheng, F., Zhao, Q. & Zhang, L. Non-probabilistic reliability-based multi-material topology optimization with stress constraint. Int J Mech Mater Des 20, 171–193 (2024). https://doi.org/10.1007/s10999-023-09669-2
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DOI: https://doi.org/10.1007/s10999-023-09669-2