2023/07/07 by Stefano Almi, Almi, Stefano, Ulisse Stefanelli +1
Computer Science · Engineering · #49J20 #49K20 #49Q10 #74P10 #74Q05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Structure Analysis and Optimization #FOS: Mathematics #Optimization and Control (math.OC) #Topology Optimization in Engineering
paper · pdf · doi:10.48550/arxiv.2307.03471
openalex publication_date 2023/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealth of innovative applications, calling for the combined design of the macroscopic mechanical piece and its underlying microstructure. In this context, we investigate a topology optimization problem for an elastic medium featuring a periodic microstructure. The optimization problem is variationally formulated as a bilevel minimization of phase-field type. By resorting to Gamma-convergence techniques, we characterize the homogenized problem and investigate the corresponding sharp-interface limit. First-order optimality conditions are derived, both at the homogenized phase-field and at the sharp-interface level.