Response of an elastic half-space with power-law nonhomogeneity to static loads |
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Authors: | G B Muravskii |
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Institution: | (1) Faculty of Civil Engineering, Technion – Israel Institute of Technology, Haifa, 32000, Israel |
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Abstract: | In this paper a series of problems for an isotropic elastic half-space with power-law nonhomogeneity are considered. The action
of surface vertical and horizontal forces applied to the half-space is studied. A part of the paper deals with the case of
zero-valued surface shear modulus (for positive values of the power determining the nonhomogeneity). This condition leads
to simple solutions for two-dimensional (2D) case when radial distribution of stresses exists for surface loads concentrated
along an infinite line. Corresponding results for the three-dimensional (3D) case are constructed on the basis of the relationships
between 2D and 3D solutions developed in the paper. A more complicated case, in which the shear modulus at the surface of
the half-space differs from zero, is treated using fundamental solutions of the differential equations for Fourier–Bessel
transformations of displacements. In the paper the fundamental solutions are built in the following two forms: (a) a combination
of functions expressing displacements of the half-space under the action of vertical and horizontal forces in the case of
zero surface shear modulus, and (b) a representation of the fundamental solutions using confluent hypergeometric functions.
The results of numerical calculation given in the paper relate to Green functions for the surface vertical and horizontal
point forces. |
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Keywords: | Nonhomogeneous half-space Power-law inhomogeneity Fundamental solutions Green function |
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