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Equilibrium state of the internal crack in the infinite elastic wedge with thin coating
Author(s) -
Sobol Boris Vladimirovich,
Soloviev Arcady Nicolaevich,
Rashidova Elena Victorovna,
Vasiliev Pavel Vladimirovich
Publication year - 2018
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.201700246
Subject(s) - wedge (geometry) , mathematical analysis , integral equation , mellin transform , correctness , mathematics , cauchy distribution , collocation (remote sensing) , boundary value problem , collocation method , geometry , ordinary differential equation , laplace transform , differential equation , computer science , algorithm , machine learning
Abstract We studied the stress concentration in the neighborhood of the vertices of the internal crack located on the bisector of an infinite elastic wedge. Normal forces are applied to the edges of the crack. The edges of the wedge are supported by a thin flexible covering, free from stresses from the outside. The effect of the coating on the stress‐strain state of the wedge is modeled by a special boundary condition. The correctness of which is confirmed by numerical simulations. The integral Mellin transform made it possible to reduce the problem to the solution of a singular integral equation of the first kind with a Cauchy kernel with respect to the derivative of the crack opening function. Solutions of the integral equation are constructed by the collocation method for various combinations of geometric and physical parameters of the problem.