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Elasticity pp 149-170 | Cite as

Wedge Problems

  • J. R. Barber
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 172)

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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