XXVIII. Dynamical problems regarding elastic spheroidal shells and spheroids of incompressible liquid

Abstract

1. The theory of elastic solids in equilibrium presents the following general problem:— A solid of any shape being given, and displacements being arbitrarily produced or forces arbitrarily applied over its whole bounding surface, it is required to find the displacement of every point of its substance. The chief object of the present communication is to show the solution of this problem for the case of a shell consisting of isotropic elastic material, and bounded by two concentric spherical surfaces, with the natural restriction that the whole alteration of figure is very small. 2. Let the centre of the spherical surfaces be taken as origin, and let x , y , z be the rectangular coordinates of any particle of the solid, in its undisturbed position, and x + α , y + β , z + γ the coordinates of the same particle when the whole is in equilibrium under the given superficial disturbing action. Then, by the known equations of equilibrium of elastic solids, we have