Two-dimensional static deformation of an anisotropic medium

Abstract

The problem of two-dimensional static deformation of a monoclinic elastic medium has been studied using the eigenvalue method, following a Fourier transform. We have obtained expressions for displacements and stresses for the medium in the transformed domain. As an application of the above theory, the particular case of a normal line-load acting inside an orthotropic elastic half-space has been considered in detail and closed form expressions for the displacements and stresses are obtained. Further, the results for the displacements for a transversely isotropic as well as for an isotropic medium have also been derived in the closed form. The use of matrix notation is straightforward and avoids unwieldy mathematical expressions. To examine the effect of anisotropy, variations of dimensionless displacements for an orthotropic, transversely isotropic and isotropic elastic medium have been compared numerically and it is found that anisotropy affects the deformation significantly.

Quasi-static Planar Deformation in a Medium Composed of Elastic and Thermoelastic Solid Half Spaces Due to Seismic Sources in an Elastic Solid

“…Many other researchers discussed source problems for different types of sources viz. Kumari et al (1992), Singh et al (1993Singh et al ( , 2003, Garg et al (1996Garg et al ( , 2003, Tomar and Dhiman (2003), Kumar et al (2005), Singh et al (2005), and Madan et al (2005).…”

Effect of Irregularity on Static Deformation of Elastic Half-Space

“…The equilibrium equations (12) are equivalent to the first order vector differential equation. For this situation, we define the process as given by Ross 13 and the equilibrium equation becomes…”

“…As an application, the normal line-load acting inside an irregular isotropic halfspace has been considered. The method of Singh et al, 12 is employed to calculate the displacement and stress fields in the irregular medium. Further, the results for the displacements have been derived in the closed form.…”

Stresses in a monoclinic elastic plate placed upon an irregular monoclinic elastic half space

“…Singh et.al. (6) formulated the problem of two-dimensional static deformation of a monoclinic elastic medium using the Eigen value approach and Fourier transform method. Madan (7) obtained solution to the problem of static deformation in a monoclinic elastic medium with considerations of welded half space in the form of a layer with a base under different kind of interfacing in the antiplane strain state of equilibrium.…”