A Variational Model for Boundary Layer Effects in Cross-ply Laminates based on a C0-Continuous Layerwise Displacement Formulation

Abstract

A variational approach to free-edge and free-corner effects in cross-ply laminates under thermal load is presented. Based on the discretization of the laminate into mathematical layers with respect to the thickness coordinate and the postulation of a C⁰-continuous layerwise displacement formulation with unknown in-plane functions and a linear interpolation through the layer thickness, the application of the principle of minimum potential yields a set of coupled ordinary differential equations, which govern the unknown in-plane functions. Due to some simplifying assumptions in the assumed displacement fields, the resultant Euler-Lagrange equations can be decomposed with respect to the two in-plane coordinates which eventually enables a closed-form solution. After fulfilling the given boundary conditions of traction-free laminate edges in an integral sense, the complete stress field in the cross-ply laminate is obtained in a closed-form manner. The approach allows for an easy application, requires very little computational effort, and is in excellent agreement with comparative finite element calculations.

Keywords

laminates free-edge effects free-corner effects closed-form analysis variational model layerwise displacement formulation

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