Concentrated Force at a Point in an Infinite Solid Medium

2 Concentrated Force at a Point in an Infinite Solid Medium 

Consider the case of a concentrated force applied to a point in an infinite solid medium. To find the relationships between the point force and the resulting stresses, Love s stress function may be selected, from sets of solutions of Eq. (2.25), as [Timoshenko and Goodier, 1970] 

Note that all the stresses in Eq. (2.27) become singular at the origin where the point force is applied. To avoid this singularity, consider a small spherical cavity whose center is located at the origin of the coordinates as shown in Fig. 2.4. The coordinates are arranged such that the force is in the z-direction and is applied at the origin of the coordinates. Thus, the summation of the surface forces from the stresses in the direction of the z-axis balances the point force inside the solid medium. 

Consider the ring-shaped element shown in Fig. 2.4. The z-component of the summation of surface stresses on the element, Tz, is given by 

the total surface force Fz is found by integrating the surface stresses over the entire 

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