A Simplified Method of Elastic-Stability Analysis for Thin Cylindrical Shells

This paper develops a new method for determining the buckling stresses of cylindrical shells under various loading conditions. For convenience of exposition, it is divided into two parts.

In part I , the equation for the equilibrium of cylindrical shells introduced by Donnell in NAOA Report No. 479 to find the critical stresses of cylinders in torsion is applied to find critical stresses for cylinders with simply supported edges under other loading conditions. It is shown that by this method solutions may be obtained very easily and the results in each case may be expressed in terms of two nondimensional parameters, one dependent on the critical stress and the other essentially determined by the geometry of the cylinder. The influence of boundary conditions related to edge displacements in the shell median surface is discussed. The accuracy of the solutions found is established by comparing them with previous theoretical solutions and with test results. The solutions to a number of problems concerned with buckling of cylinders with simply supported edges on the basis of a unified viewpoint are presented in a convenient form for practical use.

In part II, a modified form of Donnell's equation for the equilibrium of thin cylindrical shells is derived which is equivalent to Donnell's equation but has certain advantages in physical interpretation and in ease of solution, particularly in the case of shells having clamped edges. The solution of this modified equation by means of trigonometric series and its application to a number of problems concerned with the shear buckling stresses of cylindrical hells are discussed. The question of implicit boundary conditions also is considered.