Three-Dimensional Topology Optimization Considering Geometric Nonlinearity: A Comparative Study between SESO and BESO with MATLAB Code

Resumo

The study of Topological Optimization (TO) in three-dimensional structures with geometrically nonlinear formulation is scarce. This paper aims to apply three-dimensional TO in elasticity problems considering geometric nonlinearity, using the total Lagrangian formulation and comparing the SESO and BESO optimization methods whose heuristics are bidirectional, that is, they allow the removal and addition of inefficient elements during the iterative process. To achieve this goal, a numerical model was developed via finite elements, in MATLAB, for both methods with the objective of minimizing compliance, using hexahedral elements. The Moving Asymptotes Method was adopted to accelerate the optimization procedure, especially in the calculation of sensitivity factors. The results show that the Geometrically Nonlinear Smoothing Evolutionary Structural Optimization (SESO-GNL) and Bi-directional Evolutionary Structural Optimization (BESO) are robust and efficient in solving classical problems in the literature.