Analytical and numerical investigations of the flexure of isotropic plates using the novel first-order shear deformation theory

Abstract

A variant of the first-order shear deformation theory is presented for the flexure of shear deformable linear isotropic plates undergoing small deformations. The principle of stationary potential energy is utilized to obtain governing differential equations and variationally consistent boundary conditions. Unlike the Mindlin’s plate theory, the presented variant involves two coupled governing partial differential equations involving two unknown functions. This reduction will result in saving of the computational time involved for the plate boundary value problem, especially when external forces acting on the plate are variable/non-linear in nature. Solutions for the flexure of shear deformable isotropic plates by utilizing Lévy’s method are obtained using analytical and numerical techniques. The fourth-order Runge–Kutta technique is utilized for obtaining numerical solutions. The effect of the plate thickness-to-length ratio on the flexure of shear deformable isotropic plates with two opposite edges simply-supported and remaining two edges having different combinations of boundary conditions are presented. These results are compared with corresponding results available in the literature.