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 Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 9, Pages 1546–1565 (Mi zvmmf11133)

Dynamics of an elastic punch on an elastic half-plane with crack formation

L. A. Alexeyevaab, T. B. Duishenalievc, B. T. Sarsenovbd

a Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science, Republic of Kazakhstan, Almaty
b Institute of Mechanics and Machine Science named by academician U.A. Dzholdasbekov
c National Research University "Moscow Power Engineering Institute"
d Kh. Yasavi International Kazakh-Turkish University

Abstract: The dynamics of buildings and structures in an earthquake zone is studied relying on a model boundary value problem describing the dynamics of an elastic punch on an elastic half-plane under diffraction and refraction of waves generated by stress release on a crack. The problem is solved by applying an explicit difference scheme constructed using the method of bicharacteristics combined with dimensional splitting. The problems of wave diffraction and refraction by an elastic inclusion in the release of vertical and shear stresses on a horizontal crack in an elastic half-plane are considered, which model the dynamics of seismic processes in the formation of mode I and II cracks. Computer experiments are performed for media with various elastic parameters and various punch–crack distances. Their results are presented in the form of oscillograms on the ground surface and the punch, as well as diffraction displacement velocity fields and stress tensor invariants in the medium and the punch.

Key words: contact boundary value problem, elastic half-plane, elastic body, unsteady elastic waves, diffraction, refraction, stress-strain state.

 Funding Agency Grant Number Ministry of Education and Science of the Republic of Kazakhstan 0253-ÃÔ3AP05135494 This work was supported by the Committee of Science of the Ministry of Education and Science of the Republic of Kazakhstan, grants 0253-GF3, AP05135494.

DOI: https://doi.org/10.31857/S0044466920090045

English version:
Computational Mathematics and Mathematical Physics, 2020, 60:9, 1499–1517

Bibliographic databases:

UDC: 539.3
Revised: 03.02.2020
Accepted:09.04.2020

Citation: L. A. Alexeyeva, T. B. Duishenaliev, B. T. Sarsenov, “Dynamics of an elastic punch on an elastic half-plane with crack formation”, Zh. Vychisl. Mat. Mat. Fiz., 60:9 (2020), 1546–1565; Comput. Math. Math. Phys., 60:9 (2020), 1499–1517

Citation in format AMSBIB
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