On the design of three-ply nonlinearly elastic composite plates with optimal resistance to buckling

Abstract

The optimal design of symmetric three-ply sandwich plates is studied in the context of finite deformation incompressible nonlinear elasticity. The overall shape of the plate is dictated, fixed amounts of two materials are at our disposal, and performance is defined solely in terms of resistance to buckling. The problem is characterized by three parameters: the volume ratio of the two materials, the stiffness ratio of the two (neo-Hookean) materials, and one of the aspect ratios of the plate. Two competing constructions are considered: one in which the stiffer material is used in the outer plies and the other in which the stiffer material is used for the central ply. It is found that if the material volume ratio and the material stiffness ratio are fixed, then there is a single aspect ratio dependent transition in the optimal design. The configuration with the stiffer material used for the central ply is the optimal design for plates that are sufficiently short in the direction of thrust, while the configuration with the stiffer material used for the outer plies is the optimal design for plates that are sufficiently long in the direction of thrust.