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Nonconvex problem for crack with nonpenetration
Author(s) -
Kovtunenko V.A.
Publication year - 2005
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.200210176
Subject(s) - minification , correctness , energy minimization , perturbation (astronomy) , nonlinear system , energy functional , planar , boundary value problem , mathematics , total energy , mathematical optimization , mathematical analysis , computer science , algorithm , physics , psychology , computer graphics (images) , quantum mechanics , displacement (psychology) , psychotherapist
The problem with crack under nonlinear boundary conditions is considered as a minimization of the total potential energy functional. The functional is nonconvex by assuming the surface energy at a crack presented in a general form. The correctness properties of the nonconvex minimization problem with constraints are investigated. Applying the shape sensitivity analysis, the problem of shape perturbation is formulated, and the derivative of the total potential energy functional with respect to the perturbation parameter is calculated. Examples on the rectilinear and the planar cracks are presented.