The development of numerical formulations based on the Boundary Element Method and the Level Set Method for probabilistic topology optimization of plane and three-dimensional structures

• Grant number: 25/00921-6
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: June 01, 2025
• End date: May 31, 2029
• Field of knowledge: Engineering - Civil Engineering - Structural Engineering
• Principal Investigator: Edson Denner Leonel
• Grantee: Mário Sérgio Oliveira César Filho
• Host Institution: Escola de Engenharia de São Carlos (EESC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This research proposes the development of numerical formulations based on the coupling between the Isogeometric Boundary Element Method (IGABEM) and the Level Set Method (LSM) for the topology optimization of structural elements. In the proposed formulations, the evolution of the body's boundary is described by the LSM, while the mechanical fields are determined by the IGABEM. As in IGABEM, isogeometric descriptions are also employed in the LSM, which provides accuracy, robustness, solution generality, and direct communication between the two methods. Traditionally, structural design is limited to the study of manufacturing cost subject to deterministic loading constraints, without considering the effective safety level of the structure. This approach proves insufficient in many situations, since, as in many cases, the increased failure rate driven by parameter variability can lead to losses greater than the expected savings. A more rational methodology consists of considering the manufacturing cost based on the probability of occurrence of a given failure scenario. Therefore, this project aims to incorporate constraints based on stress state and the target failure probability of the structural element during the topology analysis, leading to robust probabilistic solutions from a safety perspective. In addition to plane analyses, the formulations are intended to be expanded to the tridimensional context. Both approaches lead to disruptive developments. It is expected that the outcome of this project will result in the development of numerical formulations that contribute to this important scientific field, with the generation of industry-applicable numerical tools being one of the main goals.