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Mathematical Modeling of Rock Massif Dynamics Under Explosive Sources of Disturbances

  • G. K. Zakir’yanovaEmail author
Conference paper
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Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 123)

Abstract

Mathematical models are developed for the dynamics of the rock mass during wave propagation using the model of anisotropic elastic media. For such media by use of the apparatus of generalized functions theory Green’s tensor are received. Based on the constructed Green’s tensor the fundamental stress tensor are obtained. For action any mass forces distributed in the medium the generalized solutions are also obtained. The influence of the degree of anisotropy of the medium on the character of the stress-strain state of the rock mass in the vicinity of various types of disturbance sources is studied. Some results of numerical calculations of the fundamental solutions, the fundamental stress tensor for various anisotropic elastic media are given. As acting loads, sources of perturbations of various types are considered, including impulse ones.

Keywords

Elastic medium Anisotropy Green’s tensor Stress-strain state Generalized functions 

Notes

Acknowledgments

This research is financially supported by a grant from the Ministry of Science and Education of the Republic of Kazakhstan (Grant No. AP05135494).

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute of Mechanics and Mechanical EngineeringAlmatyKazakhstan

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