Multi-objective shape optimization of plate structure under stress criteria based on sub-structured mixed FEM and genetic algorithms

Abstract

This paper presents a methodology for the multi-objective (MO) shape optimization of plate structure under stress criteria, based on a mixed Finite Element Model (FEM) enhanced with a sub-structuring method. The optimization is performed with a classical Genetic Algorithm (GA) method based on Pareto-optimal solutions and considers thickness distributions parameters and antagonist objectives among them stress criteria. We implement a displacement-stress Dynamic Mixed FEM (DM-FEM) for plate structure vibrations analysis. Such a model gives a privileged access to the stress within the plate structure compared to primal classical FEM, and features a linear dependence to the thickness parameters. A sub-structuring reduction method is also computed in order to reduce the size of the mixed FEM and split the given structure into smaller ones with their own thickness parameters. Those methods combined enable a fast and stress-wise efficient structure analysis, and improve the performance of the repetitive GA. A few cases of minimizing the mass and the maximum Von Mises stress within a plate structure under a dynamic load put forward the relevance of our method with promising results. It is able to satisfy multiple damage criteria with different thickness distributions, and use a smaller FEM.