Analytical Solution of the Cerruti Problem Under Linearly Distributed Horizontal Loads over Polygonal Domains

Abstract

The classical Cerruti problem of an isotropic homogeneous half-space subject to a concentrated load tangential to its surface is extended to cope with linear distributions of loads acting over a polygonal domain. The approach is based upon a generalized version of the Gauss theorem and recent results of potential theory which consistently take into account the singularities affecting the expressions of the fields of interest. This issue, which has been recently dealt within the literature by exploiting generalized constitutive theories, is successfully addressed in the paper within classical elasticity theory by proving that uneliminable singularities can be experienced only at the vertices of the loading region and only for a single component of stress. Analytical expressions of displacements, strains and stresses are derived at an arbitrary point of the half-space as a function of the loading function, assumed to be linear, and of the position vectors which define the boundary of the loaded region. The proposed approach is validated by numerical examples.