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**A complex variable solution for a deforming buoyant tunnel in a heavy elastic half-plane.**
*(English)*
Zbl 1032.74038

Summary: An analytical solution is presented for a buoyant tunnel in an elastic half-plane. The tunnel undergoes a prescribed displacement along its boundary, and the surface of the half-plane is stress-free. The solution uses the complex variable method and consists of conformally mapping the hole and half-plane to an annular region. The complex potentials each contain two logarithmic terms due to the resultant buoyancy force acting on the tunnel, and, as a result, the displacements at infinity are unbounded. An example is presented for the case of a rigid buoyant tunnel in a half-plane with gravity loading. Even though the tunnel does not deform, the buoyancy effect can be clearly seen in the contours of displacements and stresses.

### MSC:

74L10 | Soil and rock mechanics |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

30C20 | Conformal mappings of special domains |

74G05 | Explicit solutions of equilibrium problems in solid mechanics |

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\textit{O. E. Strack} and \textit{A. Verruijt}, Int. J. Numer. Anal. Methods Geomech. 26, No. 12, 1235--1252 (2002; Zbl 1032.74038)

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