A VARIATIONAL FINITE LAYER TECHNIQUE FOR THE INVESTIGATION OF THERMALLY INDUCED STRESS CONCENTRATIONS IN COMPOSITE STRUCTURES

Abstract

The technical relevance of stress fields near free laminate edges under mechanical and/or hygrothermal loads (“free-edge effect”) has long been recognized. However, the state of stress near free laminate corners (i.e., at corners that are generated by two merging straight free laminate edges) has gone nearly unnoticed in the open literature. To gain further insight into the mechanics of free-corner stress fields (“free-corner effect”), the present contribution is devoted to the closed-form analysis of displacements, strains and stresses in the vicinity of free rectangular corners of symmetric crossply laminates under uniform thermal load by means of a layerwise C0-continuous displacement approach. The laminate is discretized into an arbitrary number of mathematical layers through the thickness. However, concerning the two in-plane directions, no discretization is employed, but on the contrary, unknown in-plane functions are assumed that are then determined by application of the principle of minimum potential energy of the laminate. Due to some simplifying prerequisite assumptions concerning the utilized displacement approach and performing a separation of the in-plane variables, the resultant governing Euler–Lagrange equations are ordinary second-order differential equations that can be solved in a closed–form way. Hence, all state variables of the given thermoelastic free-corner problem can be written in a closed-form manner, which makes the present method easily applicable and allows a good insight into the underlying mechanics. Given boundary conditions of traction-free laminate edges are satisfied in an average sense. The present method is easily applicable, requires little computational effort, and is in excellent conformity with accompanying finite element computations. Because the presented approach enables a closed-form analytic formulation with respect to the in-plane coordinates, it is appropriate to designate the methodology as a finite layer technique.