Otimização topológica de estruturas contínuas baseada no método de Petrov-Galerkin local sem malha direto acoplado com uma abordagem evolucionária bidirecional

Abstract

Topology optimization is one of the most interesting fields of structural optimization, enabling the conception of efficient and lightweight designs. In recent years, meshless numerical methods have emerged as a significant alternative to mesh-based approaches. Although historically reliant on the Finite Element Method, topology optimization techniques have been associated with several meshless methods. However, most of these numerical approaches using a mesh, either to construct the trial functions or to perform the numerical integration. The Direct Meshless Local Petrov-Galerkin - DMLPG method is characterized as a truly meshless method, as it does not use a mesh throughout its development. This method has been applied to solve various boundary value problems, obtaining results with good precision and computational efficiency, since integration is performed under low-degree polynomials instead of considering complex shape functions. In this work, a new approach to topological optimization is proposed, combining DMLPG with a Bidirectional Evolutionary Structural Optimization - BESO method, in order to show the feasibility of this numerical procedure in this field. DMLPG is used to obtain displacements, strains and stresses, while BESO updates the structural geometry based on sensitivity values. Some examples, considering the minimization of the total deformation energy of linear elastic structures, were carried out, demonstrating the applicability and validity of the technique by comparing the optimal designs obtained with other results found in existing literature.