Elasticity pp 149-170 | Cite as

Wedge Problems

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


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
$$\phi = r^{n + 2} f(\theta ).$$
The function f(θ) can be found by substituting (11.1) into the biharmonic equation (8.16), giving the ordinary differential equation
$$\left( {\frac{{d^2 }}{{d\theta ^2 }} + (n + 2)^2 } \right)\left( {\frac{{d^2 }}{{d\theta ^2 }} + n^2 } \right)f = 0.$$


Stress Intensity Factor Half Plane Stress Function Asymptotic Method Stress Singularity 
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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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