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Laminated Orthotropic Plates under Subdifferential Boundary Conditions. A Variational‐Hemivariational Inequality Approach
Author(s) -
Stavroulakis G. E.,
Panagiotopoulos P. D.
Publication year - 1988
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19880680610
Subject(s) - subderivative , mathematics , superpotential , orthotropic material , monotonic function , boundary value problem , mathematical analysis , monotone polygon , boundary (topology) , regular polygon , convex optimization , geometry , physics , mathematical physics , thermodynamics , supersymmetry , finite element method
This paper deals with an orthotropic laminated plate concerning the delamination problem. A nonmonotone multivalued law simulates the mechanical behaviour of the binding material. This law is written in terms of a generalized gradient (in the sense of F. H. Clarke) of an appropriately defined nonconvex superpotential. Moreover, monotone, e.g. frictional slipallowing boundary conditions of subdifferential type are assumed to hold, which are obtained from a convex superpotential through subdifferentiation. The problem is formulated as a variational‐hemivariational inequality which physically expresses the principle of virtual work in inequality form. The existence and the approximation of the solution of this inequality is discussed by an appropriate combination of compactness, monotonicity and average value arguments.