An Investigation on Axisymmetric Concentrated Load Problems of Elasticity : Applications of solutions with singularities

Abstract

The principal object of this paper is to investigate the fundamental properties of solutions with singularities in the theory of elasticity in order to consider its meaning as a concentrated load and possibility of applying it to practical problems, using the stress functions with singularities. The principal results are as follows: (1) The so-called force of a center of dilatation plays an important role in many problems of elasticity. If we appropriately distribute problems are obtained, and it is possible to make clear the meaning of a solution. (2) A hollow elastic sphere with two rigid taper pins inserted is analysed. (3) An exact solution to the problem of a center of dilatation acting at a point inside an elastic half-space is shown. (4) An exact solution to a problem of an indefinitely extended elastic solid subjected to radial forces acting on a finite straight line (a segment of crack subjected to an inner pressure) is shown, and it is compared with the result for an elastic half-space.