2020/12/07 by Stefano Almi, Almi, Stefano, Ulisse Stefanelli +1
Computer Science · Engineering · #49J20 #49K20 #49Q10 #74C05 #74P10 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Topology Optimization in Engineering
paper · pdf · doi:10.48550/arxiv.2012.03764
openalex publication_date 2020/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic medium under kinematic hardening. We adopt a phase-field approach and argue by subsequent approximations, first by discretizing time and then by regularizing the flow rule. Existence of optimal shapes is proved both at the time-discrete and time-continous level, independently of the regularization. First order optimality conditions are firstly obtained in the regularized time-discrete setting and then proved to pass to the nonregularized time-continuous limit. The phase-field approximation is shown to pass to its sharp-interface limit via an evolutive variational convergence argument.