Numerical formulations for the topology optimization of structures considering hyperelastic materials and associated uncertainties

• Grant number: 25/10388-3
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: September 01, 2025
• End date: February 28, 2029
• Field of knowledge: Engineering - Civil Engineering - Structural Engineering
• Principal Investigator: Edson Denner Leonel
• Grantee: Gabriel Neves Queiroz
• Host Institution: Escola de Engenharia de São Carlos (EESC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This research project aims the development of numerical formulations based on the Finite Element Method (FEM) for the topology optimization (TO) of two- and three-dimensional homogeneous hyperelastic solids reinforced by fibers. The TO enables the determination of optimized material distributions in structures for solid mechanics problems, becoming an important tool for promoting sustainability and the rational use of materials. Moreover, hyperelastic materials have huge potential for application in special structures, such as energy dissipators and prostheses, for example. In such applications, geometrically nonlinear approaches are essential, along with the incorporation of uncertainties into the analysis. In this context, it becomes rational to quantify the cost of the structure based on the probability of a given failure scenario occurrence. Thus, constraints based on the stress state and the target failure probability of the structural element during the topological analysis lead to robust solutions from a safety perspective. In this proposal, formulations based on the RBDO, RBTO, and RTO approaches will be developed considering fiber-reinforced hyperelastic materials. Applications in the civil, mechanical, aerospace, and biomechanical domains are the targets, as these areas are where such formulations have the potential to generate disruptive solutions.