A Simplified Theory of Thin Cylindrical Shells

A new simplified theory is derived for the nonaxisymmetrical deformation of thin circular cylinders by assuming that the circumferential strain is negligible. Two equations of equilibrium along with three boundary conditions at each end of the shell are obtained by means of the virtual work theorem. The order of the characteristic equation of the governing equations is reduced from eight to six and the boundary conditions at each end from four to three. The present theory is simpler than Donnell's approximate theory yet when applied to boundary value problems, in one case it appears to be significantly more accurate than Donnell's theory and gives the same results as Flugge's theory; and in another case it gives results as accurate as does Novozhilov's theory. Conditions under which the present theory is applicable are examined.