Multi-objective optimization in dynamics of the structures with nonlinear behavior: Contributions of the metamodels
Multi-objective optimization is a tool for help of making decision in structural design in a pre-project or project phase. The procedures frequently employed in optimization require several reanalyses which are essential to calculate the generalized cost functions. But, the complexity of the especially nonlinear models and associated modeling makes these reanalyses long and sometimes impossible for reasons of calculation cost. To overcome these difficulties, in this paper we propose a strategy of multi-objective optimization where the parameters of design are deterministic. The objective of this strategy is to treat complex structures whose finite element model (FEM) is of large size in the presence of localised nonlinearities. It is based mainly on two steps, which are the calculation of the functions objectives and the search for the optimal design solutions. In the first step, we proposed two levels of FEM model reduction. The first level consists in reducing the modified model by a robust dynamic condensation method followed by an iterative procedure allowing to approach the stationary solution of the systems with several degrees of freedom (dof) subjected to harmonic excitations. It can lead to a fast prediction of the nonlinear responses in time or frequency domain. The second level of reduction consists in exploiting an original metamodel named adaptive response surface method (ARSM) or by modified response surface method (RSM). The second step of optimization consists in seeking the optimal solutions by an evolutionary algorithm of type nondominated sorting genetic algorithm (NSGA). This multi-objective optimization strategy enables us to find the full set of the optimal solutions at lower cost. The interest of methodology suggested and its performances are highlighted through examples of numerical simulation.
multi-objective optimization metamodel genetic algorithm karhunenlove method robust condensation localized nonlinearities