We consider an elastic half-space subject to constant body forces acting perpendicular to its surface. Assume that the medium is perforated by a parabolic cylindrical cavity whose plane of symmetry is perpendicular to the surface. We characterize the state of stress in the medium; in particular, we compute the hoop stresses along the boundary of the cavity. Our solution is obtained by applying the complex variable method in plane elasticity, extending the technique to stress states which do not necessarily vanish at infinity.
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Marshall J. Leitman, Piero Villaggio, Parabolic tunnels in a heavy elastic medium. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 24 (2013), no. 1, pp. 1–10DOI 10.4171/RLM/642