Abstract
In the previous chapter we saw how the solutions of two-dimensional approximations in isotropic Linear Elasticity can be obtained from the Airy stress potential \(\varPhi \) that satisfies a bi-harmonic equation (either homogeneous or inhomogeneous). When the region occupied by the elastic material is unbounded (see Fig. 9.1), integral transforms provide a robust analytical framework for solving the various boundary-value problems satisfied by \(\varPhi \).
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Notes
- 1.
In this chapter we do not use \(\varvec{X}_\perp \) for the position vector of points in \(\mathbb {E}^2\) as most of the work will be done in components.
- 2.
These are still Cartesian-coordinate stresses, but expressed in terms of the polar coordinates defined in Fig. 9.4, \(X_1=r\cos \theta \) and \(X_2=r\sin \theta \).
- 3.
Compare this with (9.43).
- 4.
Recall the notations N and T introduced in Sect. 3.7.
- 5.
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Coman, C.D. (2020). Special Two-Dimensional Problems: Unbounded Domains. In: Continuum Mechanics and Linear Elasticity. Solid Mechanics and Its Applications, vol 238. Springer, Dordrecht. https://doi.org/10.1007/978-94-024-1771-5_9
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