Displacements under linearly distributed pressures by extended Mindlin’s equations

Analytical elasticity solutions provide an efficient means of performing a first approximate analysis in foundation engineering. One of the well-known solutions is Mindlin’s solution to the stress and displacement induced by a point load at an embedment depth in a half-space. This solution is more superior but less widely used than Boussinesq’s solution. To promote this situation, Mindlin’s displacement equations are integrated to obtain a complete set of explicit formulae for calculating the displacements at an arbitrary point. The displacements are induced by uniformly and triangularly distributed horizontal or vertical pressures, which are exerted over a horizontal or vertical rectangular area in the interior of a homogeneous, isotropic, elastic half-space. These formulae facilitate the future development of computer programs for the analysis of related practical problems in foundation engineering.