Determine the stress field solution (8.4.47) for the problem of a half-space under a concentrated surface moment

Question:

Determine the stress field solution (8.4.47) for the problem of a half-space under a concentrated surface moment as shown in Fig. 8.23. It is recommended to use the superposition and limiting process as illustrated in the figure. This solution can be formally developed using either Cartesian or polar coordinate stress components. However, a simple and elegant solution can be found by noting that the superposition and limiting process yields the stress function solution where ∅ is the solution to the Flamant problem shown in Fig. 8.21.