Buoyancy-induced deformations in a compressible elastic solid

Given a rectangular slab of a purely elastic material (neo-Hookean) with different temperatures imposed on the lateral surfaces, it is shown, within the context of a linearized theory, that the resulting deformation field is, under suitable boundary conditions, virtually identical to its fluid-mechanical counterpart given by a rectangular trench filled with a Newtonian liquid. A second, more general analogy between problems involving buoyancy induced deformations and the classical theory of thin plates is also presented.