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The Quarterly Journal of Mechanics and Applied Mathematics 1990 43(1):1-14; doi:10.1093/qjmam/43.1.1
© 1990 by Oxford University Press
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A VERTICAL LOAD IN THE INTERIOR OF A NON-HOMOGENEOUS INCOMPRESSIBLE ELASTIC HALF-SPACE

R. K. N. D. RAJAPAKSE

( Department of Civil Engineering, University of Manitoba Winnipeg, Canada R3T 2N2 )

Governing equations for torsionless axisymmetric deformations of a nonhomogeneous incompressible elastic medium are established. The shear modulus of the elastic medium is assumed to vary linearly with depth. General solutions for stresses and displacements are derived by solving the governing equations through the application of Hankel integral transforms. Explicit solutions for displacements and stresses corresponding to an arbitrary axisymmetric vertical load acting in the interior of the half-space are derived by treating the loaded half-space as a two-domain boundary-value problem. Hankel transforms corresponding to some common loading configurations are presented. Selected numerical results for displacements and stresses are presented to portray the influence of the degree of non-homogeneity, depth of loading and configuration of loading on the response of the non-homogeneous half-space.


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