Simple Force Multipoles in the Theory of Deformable Surfaces

Abstract

This paper is concerned with a nonlinear theory of simple force multipoles for a deformable surface, embedded in a Euclidean 3‐space; the surface is not necessarily elastic. The theory is developed with the use of basic thermodynamical principles, together with invariance conditions under superposed rigid body motions. For simplicity, the basic kinematical ingredients are restricted to be the (ordinary) monopolar velocity of the surface and suitable first‐ and second‐order gradients of the velocity. The theory of an elastic surface and other special cases of the general theory which bear on the foundations of the classical theory of shells are also discussed.