Linear and nonlinear bending of shear-deformable plates

Abstract

A high-order shear-deformation theory of plates is developed. By assuming a constant in-plane rotation tensor through the thickness in Reddy's higher-order theory (J, appl. Mech. 51, 745-752, 1984), it is shown that the number of variables can be reduced by one. The theory incorporates a quadratic transverse shear-strain distribution through the plate thickness with zero values at the two free surfaces. Exact closed-form solutions of the resulting governing equations for square isotropic plates are obtained for two different boundary conditions. There is close agreement between the present results and those from theories developed by other workers. Extension of the present theory to nonlinear analyses yields governing equations which are remarkably simple to obtain approximate solutions to large-deflection behaviour of shear-deformable plates. Approximate solutions are detained for the large-deflection isotropic and transversely isotropic rectangular plates for the simply-supported and clamped boundary conditions under uniformly distributed load. © 1988.