Regularities of distribution of displacements in the isotropic half-space, lying on the elastic basis, at the concentrating action in the border (Q2901785)

Boussinesq problem is the base model in the study of applied problems. It regular occurrence in the press of the scientific works devoted to its generalizations speaks. Regularities in the distribution of displacements inside and on the half-space boundary at action on it of the concentrated force enclosed to a boundary plane, are investigated in the given work. The normal stresses and displacements are proportional, the shear stresses are absent at the boundary of the half-space. The solution is obtained using the Hankel integral transformation. Analysis of the distribution of vertical and radial displacements, depending on the coefficient of proportionality of stress and displacement is shown in the graphs. Zones, where the radial displacements are tensile and compressive, are found. Curves of displacement s have both a positive maximum, and negative. The larger the coefficient of proportionality, the smaller the absolute values of the radial displacements. Vertical displacements are more than radial ones. Influence of coefficient of proportionality is considerable with large values the displacement decreases. Convergence of integrals on half-space border is deteriorated. Preliminary researches of integrals included in the solution are necessary for carrying out of calculations.