Geometrically Nonlinear 3D Topological Optimization: An Efficient MATLAB Code for the SESO Method

Resumo

The study of Topological Optimization (TO) in three-dimensional structures with geometrically nonlinear formulation is scarce. This work aims to apply TO in elasticity problems extended to consider geometric nonlinearity, using the total Lagrangian formulation. To achieve this goal, we developed a numerical model in MATLAB, employing the finite element method with hexahedral elements. We used the TO method Smoothing Evolutionary Structural Optimization (SESO) in conjunction with the Method of Moving Asymptotes to accelerate the optimization procedure, especially in the calculation of sensitivity factors. SESO is based on a bidirectional heuristic, systematically removing and adding elements with lower compliance compared to the maximum compliance of the structure. The results show that Smoothing - Evolutionary Structural Optimization Geometrically Non-Linear (SESO-GNL) is robust and efficient in solving classic problems from the literature.