Reliability of the finite element method for calculating free edge stresses in composite laminates

Abstract

The edge-stress problem for a [±45] s graphite/epoxy laminate was examined in detail. A review of the literature on this problem showed that the interlaminar normal stress σ z distributions along the interface between the +45° and -45° plies, obtained by various investigators, disagreed in magnitude and sign. In particular, a finite difference solution and a perturbation solution predicted a tensile σ z , whereas the finite element methods predicted a compressive stress. Since a stress singularity exists at the intersection of the interface and the free edge, the differences in magnitude of the peak stress were expected, but not the difference in the sign. This paper investigates the reliability of the displacement-formulated finite element method in analyzing the edge-stress problem. Analyses of two well-known elasticity problems, one involving a stress discontinuity and one a singularity, showed that the finite element analysis yields accurate stress distributions everywhere except in two elements closest to the stress discontinuity or singularity. Stress distributions for a [±45] s laminate showed the same behavior near the singularity as found in the well-known problems with exact solutions. The displacementformulated finite element method, therefore, appears to be a highly accurate technique for calculating interlaminar stresses in composite laminates. The disagreement among the numerical methods was attributed to the unsymmetric stress tensor at the singularity.