Multiphysics shape and topology optimization with perimeter constraints

• Grant number: 24/02939-7
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: October 01, 2024
• End date: March 28, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Pedro Tavares Paes Lopes
• Grantee: Giovanna Castello de Andrade
• Supervisor: Alex Ferrer
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: International Center For Numerical Methods In Engineering, Spain
• Associated to the scholarship: 21/14604-1 - Multiphysics shape and topology optimization with perimeter constraints, BP.DR

Abstract

The goal of this ongoing PhD research project is to perform a thorough analysis of multiphysics shape and topology optimization problems with perimeter constraints. Up to now, in the shape sensitivity analysis framework, a transient semi-coupled thermo-mechanical model has been considered. Also, in the topological sensitivity analysis framework, temperature constraints were investigated, considering heat sink design as a model problem. Computational experiments are being carried in Python using the FEniCSx package and applications to thermal management devices and the design of electric vehicles are serving as guidelines for numerical experiments. During the proposed internship, theoretical and computational aspects of approximate perimeter functionals will be studied. Furthermore, algorithms for coupling shape and topological derivatives will be investigated.