Otimização topológica verdadeiramente sem malha em estruturas multimateriais elastostáticas: o uso do método de Petrov-Galerkin local sem malha direto

Abstract

This thesis introduces a new method for solving topology optimization problems involving elastic structures with multiple materials, combining the Direct Meshless Local Petrov-Galerkin (DMLPG) and Gradual Bi-Directional Evolutionary Structural Optimization (gBESO) techniques. In recent years, meshless methods have been used in several science and engineering fields due to their potential. The DMLPG method stands out as a truly meshless approach, utilizing low-degree polynomials in numerical integration to achieve accurate and computationally efficient results without the need for complex shape functions. In the proposed methodology, DMLPG is employed to determine smooth nodal displacements, strains and stresses, while gBESO updates the structural geometry based on the sensitivity values of objective function, gradually increasing the Young’s modulus of the material. The objective function of the optimization approach is to minimize the total strain energy under volume constraints. Numerical examples are provided to demonstrate the applicability and validity of the approach.