A Hybrid Variational Model for the Analysis of Free-Corner Effects in Layered Plates

Abstract

A variational model for the assessment of free-edge and free-corner effects [1-3] in thermally loaded rectangular cross-ply laminate plates is presented. The physical layers of the plate are discretized by an arbitrary number of mathematical layers through the laminate thickness. A layerwise displacement field with unknown interface functions which depend on the inplane coordinates is formulated wherein an a priori assumed layerwise linear thickness interpolation scheme is employed. The application of the principle of minimum elastic potential yields a set of governing Euler-Lagrange differential equations for the unknown inplane functions which for the special free-corner problem in rectangular cross-ply plates can be solved in a closed-form analytical manner. Boundary conditions of traction free laminate edges are fulfilled in an average sense. Since the approach utilizes a discretization through the plate thickness yet allows for closed-form solutions within the layer planes for all state variables it is appropriate to speak of a hybrid analysis approach. The presented method allows easy application, can be run on every standard personal computer and is in favourable agreement with comparative finite element calculations. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)