Multicriteria optimization of variable thickness plates using adaptive weighted sum method

Abstract

In this paper, a multicriteria design framework for variable thickness isotropic plates using the adaptive weighted sum method is developed. The design objectives are the minimization of weight and static displacement and the design variables are the elemental thicknesses of plates modelled using finite elements. Here, the multicriteria optimization framework is constructed by integrating the finite element method, analytical sensitivity technique along with optimization algorithms. The first-order shear deformation theory is used in the static and dynamic analyses of plates. Both single and multiobjective optimization studies are conducted to study the optimal thickness distributions of variable thickness plates under static and dynamic constraints. To study multicriteria optimization of plates, the weighted sum method is first applied which gives sparsely distributed Pareto optimal solutions. Then, the adaptive weighted sum method is employed where a coarser representation of Pareto optimal solutions is generated using the weighted sum method and less populated regions are identified for further refinement. The suboptimization problems are solved in these regions to determine a new set of Pareto optimal solutions. The Pareto optimal curves obtained using the adaptive weighted sum method are also compared with the conventional weighted sum method under different constraints. The effect of boundary conditions on the Pareto optimal solutions and thickness distributions of plates is also investigated.