A single-layer theory approach to stress concentration phenomena in layered plates

An approximate closed-form higher-order plate theory approach to displacements, strains and stresses in the vicinity of free rectangular corners of thermally loaded layered plates is presented. For simplicity the analysis is restricted to the technically important situation of symmetric cross-ply laminates with an arbitrary number of layers. The method is based on the concept of a single-layer formulation for the displacement field, i.e. the overall behaviour of the layered plate is represented by effective properties and continuous displacement terms through the thickness which are assumed to consist of simple trigonometric functions. The inplane components of the displacement representations are determined by formulating equilibrium in an integrated form and fulfilling the given boundary conditions, which can also be done in an integral sense. The resultant strains and stresses then can be easily calculated in a straightforward manner. As the present analytical approach is completely closed-form the required computational effort is negligible.