Interaction of plane nonstationary waves with a thin elastic inclusion under smooth contact conditions |
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Authors: | A P Moiseenok V G Popov |
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Institution: | 1.Mechnikov Odessa National University,Odessa,Ukraine;2.Odessa National Maritime Academy,Odessa,Ukraine |
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Abstract: | We solve the problem of determining the stress state near a thin elastic inclusion in the form of a strip of finite width
in an unbounded elastic body (matrix) with plane nonstationary waves propagating through it and with the forces exerted by
the ambient medium taken into account. We assume that the matrix is in the plane strain state, and the smooth contact conditions
are realized on both sides of the inclusion. The method for solving this problem consists in using the integral Laplace transform
with respect to time and in representing the stress and displacement images in terms of the discontinuous solution of Lamé
equations in the case of plane strain. As a result, the initial problem is reduced to a system of singular integral equations
for the transforms of the unknown stress and displacement jumps. To invert the Laplace transform, we use a numerical method
based on replacing the Mellin integral by the Fourier series. As a result, we obtain approximate formulas for calculating
the stress intensity factors (SIF) for the inclusion, which are used to study the SIF time-dependence and its influence on
the values of the inclusion rigidity. We also studied the possibility of considering the inclusions of higher rigidity as
absolutely rigid inclusions. |
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Keywords: | |
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