Abstract
The equilibrium problem solved by Valentino Cerruti (1850-1909) concerns a linearly elastic isotropic half-space acted upon by a concentrated load, tangent to the boundary plane. We take up the version of the Cerruti Problem, where a diffused tangent load is applied, with constant magnitude per unit length and infinitely long support.
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Notes
- 1.
Recall that
$$\begin{aligned} u_\rho&={\mathbf{{\textit{e}} }}\cdot (u_\alpha \mathbf{e }_\alpha )=u_1\cos \vartheta +u_2\sin \vartheta ,\\ u_\vartheta&={\mathbf{{\textit{e}} }}^\prime \cdot (u_\alpha \mathbf{e }_\alpha )=-u_1\sin \vartheta +u_2cos\vartheta , \end{aligned}$$ - 2.
A plane Cerruti stress field can be constructed also by an ad hoc use of the Airy method (see Sect. A.3.2).
References
Cerruti V (1882) Ricerche intorno all’equilibrio de’ corpi elastici isotropi. Rend Accad Lincei 3(13):81–122
Podio-Guidugli P (2004) Examples of concentrated contact interactions in simple bodies. J Elast 75:167–186
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Podio-Guidugli, P., Favata, A. (2014). The Cerruti Problem. In: Elasticity for Geotechnicians. Solid Mechanics and Its Applications, vol 204. Springer, Cham. https://doi.org/10.1007/978-3-319-01258-2_8
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DOI: https://doi.org/10.1007/978-3-319-01258-2_8
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