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 C 0 -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 EulerÀLagrange equations are ordinary second-order differential equations that can be solved in a closedÀform 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.The most common analysis tool for the determination of the mechanical behavior of composite laminates is the so-called classical laminate plate theory (CLPT; see, e.g., [1]). Being in essence a two-dimensional theory, CLPT assumes a plane state of stress in conjunction with the kinematical assumptions of Kirchhoff's classical plate theory and yields reasonably accurate results for the overall response of layered structures like in-plane stresses or buckling and free-vibration modes. However, in the vicinity of free edges of the laminate (e.g., in the presence of discontinuities like interfaces between dissimilar layers within composite laminates), the CLPT state of stress is heavily perturbed. In such areas, the assumptions of CLPT break down and threedimensional stress fields with steep gradients occur. Besides the in-plane stresses, interlaminar or out-of-plane stress components play an important role as well. This phenomenon is most commonly called free-edge effect and involves stress fields that on a theoretical basis are dominated by a mathema...

Semi‐analytical computation of 3D stress singularities in linear elasticity

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