On Boundary Integral Equations for Circular Cylindrical Shells

Abstract

The so-called direct approach establishes boundary integral equations with the aid of Somigliana’s boundary identity. This identity is based on the Betti’s reciprocal work theorem and the so-called fundamental solutions of the basic equations. For elasticity problems in general these singular solutions are due to point loads.

In this work for the linear theory of thin shells a new reciprocal theorem is deduced. There the interaction energy of two elastic states is expressed by derivatives of the displacements and the stress functions.

The knowledge of stress functions, which solve the equilibrium equations for the cases of point loads directed along the three coordinate lines (Antes 1980), gives the possibility to derive from this new reciprocal theorem boundary integral formulations for the solution as well of the geometrical as of the statical boundary value problem. Here this derivation is realized for the case of circular cylindrical shells.