Elasticity pp 363-376 | Cite as

Singular Solutions

Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 172)

Abstract

Singular solutions have a special place in the historical development of potential theory in general and of Elasticity in particular. Many of the important early solutions were obtained by appropriate superposition of singular potentials, noting that any form of singularity is permitted provided that the singular point is not a point of the body1.

The generalization of this technique to allow continuous distributions of singularities in space (either at the boundary of the body or in a region of space not occupied by it) is still one of the most widely used methods of treating three-dimensional problems.

In this chapter, we shall consider some elementary forms of singular solution and examine the problems that they solve when used in the various displacement function representations of Chapter 21. The solutions will be developed in a rather ad hoc way, starting with those that are mathematically most straightforward and progressing to more complex forms. However, once appropriate forms have been introduced, a systematic way of developing them from first principles will be discussed in the next chapter.

Keywords

Half Space Maximum Shear Stress Singular Solution Concentrate Force Singular Potential 
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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Mechanical Engineering and Applied MechanicsUniversity of MichiganAnn ArborUSA

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