Multiphysics shape and topology optimization with perimeter constraints

• Grant number: 21/14604-1
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: March 01, 2022
• End date: August 28, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Pedro Tavares Paes Lopes
• Grantee: Giovanna Castello de Andrade
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated scholarship(s): 24/02939-7 - Multiphysics shape and topology optimization with perimeter constraints, BE.EP.DR

Abstract

The goal of this research project is to perform a thorough analysis of multiphysics shape and topology optimization problems with perimeter constraints, and to develop softwares for the numerical approximation of these problems based on this analysis. Existence of solutions in the continuous settings will be shown. In the discrete setting, the dependence of the design on the perimeter constraint will be investigated. Shape and topological derivatives will be employed for the sensitivity analysis of the problem, and level set methods based on radial basis funcions will be employed in the numerics. (AU)