A Refined Shear Deformation Theory of Bending of Isotropic Plates*

ABSTRACT

A nonlinear, in-plane displacement assumption is proposed, based on an undetermined variation df/dz of transverse shear strains through the plate thickness. A second-order ordinary differential equation for f(z) and two surface conditions, as well as a set of eighth-order partial differential equations and four associated boundary conditions, are derived from the principle of minimum potential energy. Coupling exists between the partial and ordinary differential equations. In the homogeneous solutions for the former, in addition to an interior solution contribution, there exist two edge-zone solution contributions, one of which induces self-equilibrated (in the thickness direction) boundary stresses. Three examples are calculated using the present theory. The last gives the stress couple and maximum-stress concentration factors at the free edge of a circular hole in a large bent plate. Numerical results for the examples are compared with those given by three-dimensional elasticity theory and several two-dimensional theories. It is found that the present theory can accurately predict nonlinear variations of in-plane stresses through the thickness of a plate.