Prediction of interlaminar stresses in laminated plates using globalorthogonal interpolation polynomials

Abstract

A postprocessor for displacement-based finite element solutions of laminated plates under transverse loads is developed to obtain the resulting interlaminar stresses. The postprocessor can be used for the finite element solution that has been obtained using either the classical lamination plate theory or the first-order shear deformation theory. The equilibrium equations of elasticity are integrated directly to obtain interlaminar stresses. These equations include the influence of the products of in-plane stresses and out-of-plane rotations and thus can be used to obtain interlaminar stresses for geometrically nonlinear problems. To obtain accurately the derivatives of in-plane stresses, the finite element nodal displacement data are first interpolated using polynomials with global support (i.e., the interpolating polynomials are defined over the whole domain). Two types of polynomials, Chebyshev and a class of orthogonal polynomials that can be generated for a given location of known data points, are used. A least-squares technique is used to find the undetermined coefficients in the global approximation. For evaluation purposes, the results for interlaminar stresses for a set of examples obtained from the present code are compared with those obtained from exact three-dimensional theory of elasticity. A good agreement is shown. Furthermore, to the best of our knowledge, the present paper is the first to present the results for interlaminar normal stress in a two-layered antisymmetric angle-ply square plate without using the three-dimensional elasticity solution. It is observed that the shape of through-the-t hickness distribution of interlaminar normal stress depends on the side-to-thickness ratio and that the maximum interlaminar normal stress increases rapidly as the side-to-thickness ratio increases.