Multi-objective structural robust optimization under stress criteria based on mixed plate super-elements and genetic algorithms

Abstract

This paper presents a methodology for the multi-objective (MO) robust optimization of plate structures under stress criteria, based on Mixed Super-Elements (MSEs). The optimization is performed with a classical Genetic Algorithm (GA) method based on Pareto-optimal solutions. It considers antagonist objectives among them stress criteria and thickness parameters distributed along the plate. This work aims at providing fast and efficient objective calculations. Our method is based on the implementation of MSEs for each zone of the plate featured by its own thickness. They are constructed with a Mixed Finite Element Model (MFEM) based on a displacement-stress mechanical formulation, and is enhanced with a sub-structuring modal reduction method in order to reduce the size of each constant thickness MSE. Those methods combined enable a fast and stress-wise efficient structure analysis, which improves the performance of the repetitive GA. A few cases minimizing the mass and the maximum Von Mises stress within a plate structure under dynamic loads put forward the relevance of our method with promising results. For the sake of robustness, both discrete frequencies and frequency bands are studied. The MO optimization is able to satisfy multiple damage criteria with different thickness distributions. It brings simplicity, saves computational time and the Pareto-front presentation with stress objective provides a good overview of the possibilities for the designers.