A Complex Potential-Variational Method for Stress Analysis of Unsymmetric Laminates With an Elliptical Cutout

Abstract

A combined complex potential-variational solution method is developed for the analysis of unsymmetrically laminated plates with finite planform geometry, subjected to arbitrary edge loads, and with an inclined elliptical cutout. This method uses complex potentials and their Laurent series expansions to reduce the potential energy of a plate to a contour integral that is evaluated numerically by the trapezoidal rule. A variational statement of equilibrium is applied to the potential energy to obtain a linear system of equations in terms of the unknown coefficients of the Laurent series, whose solutions yield the stress and displacement fields for a given problem. This approach represents a computationally efficient alternative to boundary collocation procedures that are typically used to solve problems based on complex potential theory. Comparisons are made with corresponding results obtained from finite element analysis for a square unsymmetrically laminated plate with a central inclined elliptical cutout and subjected to biaxial tension. The results confirm the validity of the solution method.