Abstract
We consider a nonhomogeneous isotropic medium, whose shear modulus is a power of a linear binomial in the Cartesian coordinates while Poisson's ratio is constant. The conditions are found under which the general solution of the plane and three-dimensional problems of the theory of elasticity can be expressed in terms of harmonic functions. Also some special cases of the variation of the shear modulus for a variable Poisson's ratio are considered. The obtained results are used for solving the problem of the stress-strain state of a nonhomogeneous half-space under the action of concentrated forces, applied normally and tangentially to the boundary surface.
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