A numerical comparison of the uniformly valid asymptotic plate equations with a 3D model: Clamped rectangular incompressible elastic plates

Abstract

In this paper, we derive the weak form for clamped plates composed of incompressible neo-Hookean material from the uniformly valid asymptotic plate theory. By using the finite-element software COMSOL, we study the numerical solutions of the weak form. We show the accuracy and the efficiency of the weak form by comparing the numerical results for the two-dimensional weak form and a three-dimensional model. As a basis for comparison we choose numerical values of the displacement, the second Piola–Kirchhoff stress, and the Green–Lagrange strain at the bottom. The numerical simulations are performed for three different cases of thickness–span ratios, including (1) very thin plate, (2) thin plate, and (3) moderately thick plate. The results show that the uniformly valid plate theory is a reliable and implementable plate theory for even moderately thick plates with large deformations.