Discrete material optimization with sandwich failure constraints

Abstract

Discrete material optimization (DMO) is a method, which was originally developed for designing composite structures via multi-material topology optimization principles. Current study applies DMO to sandwich structures with variable thickness in the core and face sheets. Each layer contains design variables for available materials. Materials are combined through interpolation schemes to define properties of the layer. The objective function (mass of the structure) and the failure constraints are interpolated via Rational Approximation of Material Properties (RAMP) in order to calculate with smooth variables, but achieve discrete results. This enables gradient optimization via Interior Point Optimizer (IPOPT) with constraints on maximum stress, wrinkling, and crimping. Structure is modeled by the finite element method, which calculates element forces and moments repeatedly as the stiffness of the structure changes during optimization. Element loads are used by the first-order shear deformation theory to evaluate the stresses in the layers to obtain failure constraints requested in each iteration by the gradient optimizer. Solution is demonstrated on the plate examples showing material distribution and discreteness level. In addition, constraint aggregation by Kreisselmeier-Steinhauser (KS) function was utilized to decrease the number of constraints in the optimization.Discrete material optimization (DMO) is a method, which was originally developed for designing composite structures via multi-material topology optimization principles. Current study applies DMO to sandwich structures with variable thickness in the core and face sheets. Each layer contains design variables for available materials. Materials are combined through interpolation schemes to define properties of the layer. The objective function (mass of the structure) and the failure constraints are interpolated via Rational Approximation of Material Properties (RAMP) in order to calculate with smooth variables, but achieve discrete results. This enables gradient optimization via Interior Point Optimizer (IPOPT) with constraints on maximum stress, wrinkling, and crimping. Structure is modeled by the finite element method, which calculates element forces and moments repeatedly as the stiffness of the structure changes during optimization. Element loads are used by the first-order shear deformation theory to evaluate the stresses in the layers to obtain failure constraints requested in each iteration by the gradient optimizer. Solution is demonstrated on the plate examples showing material distribution and discreteness level. In addition, constraint aggregation by Kreisselmeier-Steinhauser (KS) function was utilized to decrease the number of constraints in the optimization.