Quasi-Static Deformation of a Uniform Thermoelastic Half –Space Due to Seismic Sources and Heat Source

Subject Areas : Engineering

A.K Vashishth ¹ (Department of Mathematics, Kurukshetra University, Kurukshetra 136119, India)
K Rani ² (Department of Mathematics, CMG Govt. College for Women, Bhodia Khera, Fatehabad 125050, India)

Received: 2018-07-01 Accepted : 2018-09-02 Published : 2018-12-30

Keywords: Thermoelastic, Heat source, Seismic source, Dip-slip dislocation, Plane deformation,

Abstract :

This paper investigates the quasi-static plane deformation of an isotropic thermoelastic half-space due to buried seismic sources and heat source. Governing equations of thermo-elasticity are solved to obtain solutions for seismic sources in a thermoelastic half-space. The general solutions are acquired with the aid of Laplace and Fourier transforms and with the use of boundary conditions. The case of dip-slip line dislocation is studied in detail along with line heat source. Analytical solutions for two limiting cases: adiabatic and isothermal, are obtained. The solutions for displacement, stresses and temperature in space-time domain are obtained by using a numerical inversion procedure. The accuracy of the proposed method is verified through a comparison of the results obtained with the existing solutions for elastic medium. In addition, numerical results for displacements, stresses and temperature function, induced by a vertical dip-slip dislocation and line heat source, are presented graphically to illustrate the effect of inclusion of thermal effect in simulation of the problem.

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