Interlaminar Stress Concentrations in Layered Structures: Part II - Closed-Form Analysis of Stresses at Laminated Rectangular Wedges with Arbitrary Non-Orthotropic Layup

Abstract

In the second of a series of two papers, a refined closed-form analysis method for the calculation of interlaminar stress concentrations in the vicinity of rectangular wedges of thermally loaded composite laminates with arbitrary layup is presented. Based on adequate layerwise shape assumptions for the in-plane components of Cauchy’s stress tensor that automatically fulfill the conditions of traction free edges, the interlaminar stresses are derived from the three-dimensional equilibrium conditions in combination with the exact fulfillment of the given homogeneous boundary conditions of traction-free laminate facings and the requirement of continuity of the interlaminar stresses at the ply interfaces. The far field conditions of recovery of the stress results by classical laminate plate theory in the inner laminate regions with increasing distance from the laminate corner are accounted for. Free constants in the stress shape functions are determined by the minimization of the laminate’s complementary potential energy which can be accomplished in an iterative manner. The stress shape functions are assumed as simple exponential terms with respect to the in-plane coordinates, whereas polynomials are applied as thickness functions. The present analysis methodology is found to be in good agreement with finite-element computations and yields reasonably accurate results with little computational effort.