Obtaining Tree Structures through the Method of Topological Optimization

• Grant number: 23/07769-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2023
• End date: June 30, 2025
• Field of knowledge: Engineering - Mechanical Engineering - Mechanics of Solids
• Agreement: BG E&P Brasil (Shell Group)
• Principal Investigator: Emílio Carlos Nelli Silva
• Grantee: Luís Otávio Trotti Martins Guedes de Souza
• Host Institution: Escola Politécnica (EP). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Company: Universidade de São Paulo (USP). Escola Politécnica (EP)
• Associated research grant: 20/15230-5 - Research Centre for Greenhouse Gas Innovation - RCG2I, AP.PCPE

Abstract

Trees have their structure optimized by natural selection, and processes such as inappropriate pruning undo this optimization, contributing to eventual falls. The costs due to the frequent falls of trees in São Paulo, and the lack of study tools to overcome this problem, due to the lack of physical fidelity of the models for generating tree structures currently available, indicate the need for new means of obtaining tree structures digitally. This can be done with Topological Optimization, a methodology capable of optimizing the spatial distribution of material in a domain for a given objective. Through the application of topological optimization, it is possible to create algorithms that obtain tree structures both through the elastic formulation of the optimization problem, which represents vector loads on the tree such as winds or the weight of fruits, and through the diffusion formulation of the optimization problem , which represents the diffusion and transport of material inside the tree. Therefore, the objective of this work is to implement, through the software FEniCS, together with the Dolfin-Adjoint and IPOPT libraries, an algorithm capable of using topological optimization to obtain tree structures that are as close as possible to reality and, by proxy, conduct studies which allow for deeper understanding of trees from a structural and physical point of view, with the potential to offer solutions to the problem of tree falls. This study will be based on the Finite Element Method for the implementation of numerical solutions and on the SIMP material model (Solid Isotropic Material with Penalization) for the optimization. The student, who has previous experience with FEniCS, will carry out this project following the steps laid out in the Work Plan, within the time of the Schedule.