Pierre Garambois

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

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.

MULTI-OBJECTIVE STRUCTURAL OPTIMIZATION UNDER STRESS CRITERIA BASED ON MIXED PLATE FEM AND GENETIC ALGORITHMS

The purpose of this study is to implement a powerful multi-objective (MO) genetic algorithm(GA)-based optimization technique for structural problems, based on the use of displacement-generalized stress Dynamic Mixed plate Finite Element Model (DM- plate-FEM). The idea is to optimize different thickness parameters of a plate structure in order to minimize antagonist objectives among these stress criteria under dynamic loads. In this article, the optimization is performed with a GA-based iterative method and propose a set of Pareto-optimal solutions, leaving the final choice to the user. The repetitions of the calculations in this method is offset by the use of the displacement-stress mixed plate FEM. Such a model discretizes both displacements and generalized stresses in the same model, in order to get the latter directly and increase the efficiency of the method. The implementation of the Kirchoff-Love (KL) plate theory also improve the work of the GA as it allows a quick change of the thickness structure parameters without rebuilding the whole assembly. The number and complexity of calculations needed by the GA is thus smaller and the speed of the method highly improved. A few numerical investigations are made with both simple and complex test examples in order to validate the methods and show its relevance. This work shows efficient and promising results that may turn out to be interesting regarding industrial optimization cases with plate structures.