Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Multiphysics Topology Optimization Using Automatic Differentiation and Adjoint Method

Version 1 : Received: 6 October 2022 / Approved: 7 October 2022 / Online: 7 October 2022 (07:32:06 CEST)

How to cite: He, J.; Abueidda, D. Multiphysics Topology Optimization Using Automatic Differentiation and Adjoint Method. Preprints 2022, 2022100071. https://doi.org/10.20944/preprints202210.0071.v1 He, J.; Abueidda, D. Multiphysics Topology Optimization Using Automatic Differentiation and Adjoint Method. Preprints 2022, 2022100071. https://doi.org/10.20944/preprints202210.0071.v1

Abstract

An essential step in solving any topology optimization problem is determining the sensitivities of the objective function and optimization constraints. Unfortunately, these sensitivities are usually derived and implemented manually. Nontrivial objective functions and constraints, especially with the involvement of material and geometric nonlinearities, need strenuous mathematical derivation, leading to error-prone implementation. Another intriguing approach to finding sensitivities is automatic differentiation. This paper uses the automatic differentiation and adjoint method to find the sensitivities for two multiphysics topology optimization problems: 1) thermoelasticity and 2) piezoelectricity. This approach is not limited to these examples and can be easily extended to other single- or multi-physics topology optimization problems.

Keywords

FEniCS; JAX; Sensitivity analysis; Topology optimization

Subject

Computer Science and Mathematics, Computational Mathematics

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