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A Hybrid Variational Model for the Analysis of Free‐Corner Effects in Layered Plates
Author(s) -
Mittelstedt Christian,
Becker Wilfried
Publication year - 2004
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200410157
Subject(s) - discretization , calculus of variations , lagrange polynomial , traction (geology) , mathematical analysis , finite element method , lagrange multiplier , boundary value problem , variational principle , interpolation (computer graphics) , mathematics , structural engineering , mathematical optimization , polynomial , physics , classical mechanics , engineering , mechanical engineering , motion (physics)
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)