A General Method of Improving the Accuracy of Approximate Solutions of Circular Cylindrical Shells

Abstract

Although Flugge’s differential equations have been known for many years, very few problems have been solved with them due to the high complexity of these equations. Hence a set of simplified differential equations (Donnell’s equations) were developed and have gained wide usage. However, it has been found that the solutions of the simplified equations may be in error by 25% for point load problems, and even more for very long finite shells. This paper introduces a general method of improving the accuracy of the approximate solutions without substantially increasing the amount of labor, by employing only the simplest set of differential equations. Through the introduction of corrector functions and application of an iterative procedure, the improved solutions are expressed in a general form consisting of the solution of Donnell’s equations plus a series of correction terms. It is shown through examples that the improved solutions are very close to those of Flugge’s equations, and that they may be obtained i...