Solving Three-Dimensional Stress Analysis Problems by a Surface Representation Alone

A numerical procedure is devised for the solution of three-dimensional static problems in an homogeneous linear elastic medium by means of a surface distribution of potential functions. Once the surface distribution is known, the solution in the interior is found by integration of the distribution over the surface. The procedure involves division of only the surface into discrete areas which is an advantage over the volume divisions of the finite element method. The procedure has the benefits in initially conceiving the problem, in formalizing the data, in reduced size of matrices to solve and in ease of handling discontinuous boundary conditions. The potential function approach is extended to bodies of more than one medium and to multi-seam mining where the horizons may be differing linear elastic properties and the seam may be nonelastic and even time dependent. It is shown that the case of axisymmetry cannot be reduced to two potential functions in two dimensions.