Energy inequalities and error estimates for torsion of elastic shells of revolution

This paper is concerned with the problem of axisymmetric torsion by terminal loads of elastic shells of revolution. Such shells are considered here to be three-dimensional bodies occupying a region of space which includes all points whose distances from a given surface - the midsurface - do not exceed h/2, where h is the shell thickness. The analysis is based on the classical linear theory of elasticity for homogeneous, isotropic materials, and it may be regarded as an extension of the work described in [1] and [2]. The purpose of the present paper is to assess the quality of an approximate solution of the thin shell problem. The case of axisymmetric torsion of thin shells of revolution is perhaps tile simplest one for this purpose, since simple approximate solutions - constructed from two-dimensional shell theories or otherwise - are known [3]. Our results provide estimates, based on the three-dimensional theory of elasticity, for the error involved in a stress analysis in which the 'exact' solution is replaced by an approximate one