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Topology optimization in contact, plasticity, and fracture mechanics using a level-set method

Abstract : The main contribution of this thesis is the theoretical and the numerical study shape and topology optimization for nonlinear phenomena, like contact, plasticity, and fracture using the level-set method. One application of the contact boundary condition for an idealized-bolt model is also proposed. The governing equations of the three physics dealt with in this thesis: contact, plasticity and damage, are theoretically not shape-differentiable. In each case, we construct an approximation by penalization, regularization or a combination of the two. The approximations for contact and plasticity are shown to be well-posed and to admit solutions that converge to the exact solution. For each physics, the shape sensitivity analysis is performed on the approximate model and the resultant adjoint problem is shown to be well-posed under technical assumptions. The shape optimization is implemented numerically using a level-set method with body-fitted remeshing, which captures the boundary of the shapes while allowing for topology changes. Numerical results are presented in 2D and 3D. We also discuss high-performance computing for linear elasticity and for fracture model, and present a few 3D results.
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https://hal.archives-ouvertes.fr/tel-03465162
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Submitted on : Friday, December 3, 2021 - 4:49:27 PM
Last modification on : Tuesday, October 18, 2022 - 8:34:05 AM
Long-term archiving on: : Friday, March 4, 2022 - 7:28:38 PM

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  • HAL Id : tel-03465162, version 1

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Jeet Desai. Topology optimization in contact, plasticity, and fracture mechanics using a level-set method. Optimization and Control [math.OC]. Universite Paris Diderot-Paris VII; Ecole polytechnique X; IRT systemX, 2021. English. ⟨NNT : ⟩. ⟨tel-03465162⟩

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