3-DIMENSIONAL STRESS-FIELD ANALYSIS IN UNIFORMLY LOADED, SIMPLY SUPPORTED COMPOSITE PLATES

A three-dimensional bending analysis of uniformly loaded, simply supported single-ply and laminated rectangular plates is addressed. The sub-layer/spline approximation method is applied. According to the method, each physical layer is divided into a number of sub-layers, and local approximations of displacements in terms of deficient spline functions are used to satisfy internal stress continuity conditions at the interfaces and prescribed boundary conditions at the facing surfaces with the requisite accuracy. In-plane division of the plate into rectangular elements and approximation of displacements with respect to the in-plane coordinates in terms of continuously differentiable spline functions is used to satisfy a prescribed set of 'global' edge boundary conditions. Three solution examples for simply supported plates under uniformly distributed load show excellent agreement with the finite element solution of Ozaksa et al. and the series solution of Srinivas and Rao (particularly, with their results for sandwich-type orthotropic plates). A number of peculiarities in the 3-D stress distributions near the interaction of a simply supported edge with the loaded face surface are discussed. It is shown that the traditional formulation of boundary conditions at a simply supported edge implies an inherent contradiction in the case of a uniformly distributed load. To avoid the contradiction, a 'local' formulation of boundary conditions is proposed, and the corresponding solution approach is outlined.