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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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