Three-Dimensional Nonlinearly Varying Rectangular Loads on a Transversely Isotropic Half-Space

In engineering situations, loads applied to the four corners of a rectangle might have different values and might not be uniformly or linearly distributed. A configuration of linearly or nonlinearly varying loads with different contact pressures at each corner can be represented as a superposition of various loading types. The loading types include uniform, linearly varying in the $x$ direction, linearly varying in the $y$ direction, nonlinearly varying in the $x$ direction, and nonlinearly varying in the $y$ direction. This work newly presents the first and second loading solutions, and derives the others therefrom. These solutions are directly obtained by integrating the point load solutions in a transversely isotropic half-space. The presented solutions are concise and easy to use; they specify that the type and degree of material anisotropy, the dimensions of the loaded region, and the loading types decisively affect the displacements and stresses in a transversely isotropic half-space. The proposed solutions can simulate realistically the actual loading problem in many engineering situations.