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

Pierre Garambois (1, 2) , Sebastien Besset (1, 2) , Louis Jézéquel (1, 2)

1 ECL - École Centrale de Lyon
2 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes

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. 1. Introduction The goal of this paper is to implement a DM-FEM for plate structure enhanced with a sub-structuring reduction method for MO structural optimizations with thickness repartition parameters and mass/stress criteria. This reduced model provides a fast and efficient analysis of complex plate structures vibrations and facilitates the work of the GA used for the optimization. The optimization of a structure's parameters in order to prevent damages is a major concern in mechanical engineering but can only be achieved at the expense of others essential criteria. Even though often carried out manually, MO-optimization methods also naturally appear in the litterature, such as gradient-based method [1, 7] and MO-GA-based methods [6, 8]. In this study, the optimization is performed with a classical GA-based NSGA-II method [4], as it permits to dispense with any weighting of criteria. This kind of method enables to find a set of Pareto-optimal solutions, which are all optimal compared to each other, for at least one criterion. Nevertheless, an inconvenient lies in the repetitions of the criteria's evaluation, depending on the chosen method and theory. In the literature, some of the previous works on thin structures optimization focus on laminated composites [1, 8] with thickness and orientation layer parameters, as well as

Mots clés: multi-objective optimization; plate structural dynamic; Mixed Finite Element Model; sub-structuring modal methods; stress criteria

Domaines: Mécanique des structures [physics.class-ph]; Vibrations [physics.class-ph]; Génie mécanique [physics.class-ph]

Pierre Garambois, Sebastien Besset, Louis Jézéquel. Multi-objective shape optimization of plate structure under stress criteria based on sub-structured mixed FEM and genetic algorithms. Journal of Physics: Conference Series, 2015, 628, pp.012011. ⟨10.1088/1742-6596/628/1/012011⟩. ⟨hal-01266864⟩