Elasticity pp 149-170 | Cite as

# Wedge Problems

Chapter

First Online:

## Abstract

In this chapter, we shall consider a class of problems for the semi-infinite wedge defined by the lines α<θ<β, illustrated in Figure 11.1.

We first consider the case in which the tractions on the boundaries vary with

*r*^{ n }, in which case equations (8.10, 8.11) suggest that the required stress function will be of the form$$\phi = r^{n + 2} f(\theta ).$$

(11.1)

The function f(θ) can be found by substituting (11.1) into the biharmonic equation (8.16), giving the ordinary differential equation

$$\left( {\frac{{d^2 }}{{d\theta ^2 }} + (n + 2)^2 } \right)\left( {\frac{{d^2 }}{{d\theta ^2 }} + n^2 } \right)f = 0.$$

(11.2)

## Keywords

Stress Intensity Factor Half Plane Stress Function Asymptotic Method Stress Singularity
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## Copyright information

© Springer Science+Business Media B.V. 2010