Recursive Patterns Research Articles

A Method of Solution for the Elastic Quarter-Plane

It is shown in this paper that for given loads on the elastic quarter-plane the prescribed boundary conditions can be fulfilled by repeated superposition of known solutions for the elastic half-plane. This leads to a sequence of infinite integrals of a simple recursion pattern. The solution is exact, since the sequence may be continued to obtain any required accuracy. Solutions are derived in this manner for three types of boundary loads: (a) concentrated normal force, (b) concentrated tangential force, and (c) partially distributed uniform loading.