The stress state in an elastic body with a rigid inclusion of the shape of three segments broken line under the action of the harmonic oscillation of the longitudinal shift
DOI:
https://doi.org/10.17721/1812-5409.2019/1.36Abstract
There is a thin absolutely rigid inclusion that in a cross-section represents three segments broken line in an infinite elastic medium (matrix) that is in the conditions of antiplane strain. The inclusion is under the action of harmonic shear force Pe^{iwt} along the axis Oz. Under the conditions of the antiplane strain the only one different from 0 z-component of displacement vector W (x; y) satisfies the Helmholtz equation. The inclusion is fully couple with the matrix. The tangential stresses are discontinuous on the inclusion with unknown jumps.
The method of the solution is based on the representation of displacement W (x; y) by discontinuous solutions of the Helmholtz equation. After the satisfaction of the conditions on the inclusion the system of integral equations relatively unknown jumps is obtained. One of the main results is a numerical method for solving the obtained system, which takes into account the singularity of the solution and is based on the use of the special quadrature formulas for singular integrals.
Key words: inclusion, shear force, fixed singularities.
Pages of the article in the issue: 158-161
Language of the article: Ukrainian
References
PASTERNAK Y.M., SULIM G.T. (2011) Plane problems of elasticity of anisotropic bodies with thin elastic branching inclusions. Bulletin TNTU. 16(4). p. 23-31.
POPOV V.G. (2013) Stress state near two cracks emanating from one point during harmonic oscillation of the longitudinal shear. Bulletin of Kiev Shevchenko nat. Univ. Ser: Phys. – math. Sciences. 3. p. 205-208.
POPOV V.G. (2015 The crack in the form of a three-unit broken under the action of wave of longitudinal shear. Mat. methods and physical and fur. field. 50(1). p. 112-120.
LITVIN О. V., POPOV V.G. (2017) Interaction the harmonic wave of the longitudinal shift with V-similar inclusion. Mat. methods and physical and fur. field. 60(1). p. 1-11.
POPOV V. G. (1992) Investigation of the fields of stresses and displacements in the case of diffraction of elastic shear waves on a thin rigid exfoliated inclusion. Moscow: Izv. RAS, Mechanics of Solid State. 3. p.139–146.
ANDREEV A.V. (2005) A direct numerical method for solving singular integral equations of the first kind with generalized kernels. Izv. RAS. Mechanics of a solid. № 1. p. 126-146.
KRYLOV V.I. (1967) The approximate calculation of integrals. Moscow: Science.
SZEGO G. (1962) Orthogonal polynomials. Moscow: Fizmatgiz.
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