A comparative study of shell equations by three-dimensional FEM analysis

Abstract

An analysis of the accuracy of thin shell equations is made for both classical and refined equations. The comparison is based on an exact reference obtained by a three-dimensional procedure using a finite element method (FEM). The classical equations are here represented by those of Flügge and Morley-Koiter. A higher approximation of the constitutive shell equations is used in the refined equations. The investigation is done by means of natural frequencies for free undamped vibrations of axisymmetric shells, especially circular cylindrical shells. In order to investigate the a priori estimate of the intrinsic errors of the thin shell equations an error expansion is employed, i.e. the error is written in powers of the thickness to principal curvature ratio h/R and thickness to characteristic wavelength ratio h/L. The results hereby obtained indicate that the error estimate agrees with the true error. Furthermore, the classical equations yield remarkably good results compared with the refined equations. The natural frequencies of shells in the shape of a spherical zone with two boundaries obtained by classical thin shell equations and FEM are briefly compared. These results also indicate agreement between the error estimate and the true error.