Abstract
This chapter presents the theoretical and the numerical study of shape and topology optimization for linear elasticity, plasticity and fracture using the level-set method. The governing equation of linear elasticity is theoretically shape-differentiable, while that of plasticity and damage is not shape-differentiable. To overcome the non-differentiability issue for the latter, we construct an approximation by penalization and regularization. For the three physics, the shape sensitivity analysis is performed using Céa’s technique. 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.
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