Through-the-thickness stress distributions near edges of composite laminates using stress recovery scheme and third order shear and normal deformable theory

Abstract

The reliable prediction of failure in laminated plates using stress based failure theories requires accurate evaluation of stresses. Noting that stresses are likely to be singular near laminate edges, we explore here whether or not a third order shear and normal deformable plate theory (TSNDT) and the commonly used stress recovery scheme (SRS) enables one to accurately compute stresses near edges of a composite laminate deformed statically with surface tractions applied on its major surfaces. In the TSNDT the three displacement components at a point are expressed as complete polynomials of degree three in the thickness coordinate. For laminated plates, we use a single layer TSNDT and the SRS to compute through-the-thickness distribution of transverse normal and transverse shear stresses. However, for monolithic plates stresses are obtained directly from the constitutive relations. Using in-house developed software based on the finite element (FE) formulation of the problem, we study seven example problems for plates subjected to different boundary conditions at the edges and various loads such as combined normal and tangential tractions uniformly distributed on the major surfaces, non-uniform pressure acting on a part of the major surface, and sinusoidal normal tractions. For each problem studied stresses computed using the TSNDT are compared with those obtained by analyzing 3-dimensional (3-D) linear elastic deformations with either the FE commercial software, ABAQUS, or the analytical solution reported in the literature. The significance of the present work is in investigating whether or not the TSNDT and the SRS give accurate values of stresses near edges laminates. It is found that for some thick laminates (span/thickness=5), stress distributions near an edge predicted by the TSNDT coupled with the SRS differ by 40% from those computed by analyzing the 3-D deformations.