A consistent dynamic finite-strain plate theory for incompressible hyperelastic materials

Abstract

In this chapter, a dynamic finite-strain plate theory for incompressible hyperelastic materials is deduced. Starting from nonlinear elasticity, we present the three-dimensional (3D) governing system through a variational approach. By series expansion of the independent variables about the bottom surface, we deduce a 2D vector dynamic plate system, which preserves the local momentum-balance structure. Then we propose appropriate position and traction boundary conditions. The 2D plate equation guarantees that each term in the variation of the generalized potential energy functional attains the required asymptotic order. We also consider the associated weak formulations of the plate model, which can be applied to different types of practical edge conditions.