Second-order elasticity with axial symmetry—I General theory

Abstract

The equations of second-order elasticity are developed for axially symmetric deformations of incompressible isotropic elastic materials. It is shown that by introducing a ‘displacement function’ the second-order problem can be reduced to the solution of an equation of the form E 4ψ = ƒ(R, Z) where E 2 is Stokes' differential operator, R, Z are cylindrical polar coordinates, and ƒ(R, Z) depends only on the first-order solution. The problem is formulated in terms of both cylindrical polar and spherical polar coordinates.