A simple higher-order non-linear shear deformation plate theory

Abstract

A recently proposed higher-order theory is shown to be reducible to a simple form with a reduction in the number of variables by one by assuming that the in-plane rotation tensor does not vary with the thickness coordinate. The resulting theory accounts for a parabolic variation of the transverse shear stresses with zero values at the free surfaces. The von Karman extension of the theory is found to be remarkably simple for obtaining approximate solutions. Approximate solutions are derived for the non-linear bending and vibration of thick isotropic and transversely isotropic plates and the results are compared with Reissner-Mindlin theories where available. © 1989.