Boundary identification for an elastic solid partly immersed in a liquid

Abstract

The authors consider a long elastic cylinder of constant section Ω partly immersed in a liquid of constant density. It is assumed that the body is in the state of plane strain and that Ω has a boundary consisting of two piecewise smooth arcs assumed to meet each other at two, and only two, points on a horizontal line. The upper arc Γ, which is exposed to air, is assumed known, while the lower arc ϒ, assumed to be totally immersed in a liquid of constant density, is unknown and is to be determined. Under the conditions that the displacements and surface stresses on a subarc of Γ are known and that the lower arc ϒ is subjected to a known constant hydrostatic pressure, the authors prove a uniqueness theorem and in the case of existence of a solution, show the existence of a sequence of regularized solutions converging to the exact solution.