An analysis procedure for cylindrical and spherical shells subjected to multi-harmonic loads

• Main Author: Purdy, D. M.
• Other Authors: Engineering Mechanics
• Format: Others
• Language: en
• Published: Virginia Polytechnic Institute 2017
• Subjects: LD5655.V856 1967.P873
• Online Access: http://hdl.handle.net/10919/76604

The analysis of shells of revolution subjected to complicated multi-harmonic surface loads is a very complex problem. Although several techniques exist for the solution of complex shell problems, all of these techniques present certain difficulties which make them impractical for use with complex surface loads. In an attempt to avoid these difficulties, an analysis procedure is developed to analyze cylindrical and spherical shells of this type. The surface loads of particular interest are the wind loads obtained from model tests in the stability wind tunnel at Virginia Polytechnic Institute. Although designed for use with wind loads the procedure could be applied equally well to any surface load which could be effectively represented by a Fourier series with variable coefficients. The surface loads are expanded into a Fourier series with polynomial coefficients for the cylindrical shell and into spherical harmonics for the spherical shell. The series are truncated after ten terms and give results which fit the wind loads within about 3% for all but a few points. Exact solutions are obtained for the series loadings from the complex shell equations developed by Novozhilov. Novozhilov's equations are developed using a complex substitution which reduces the order of the governing equations from eighth to fourth order. This substitution simplifies the equations in such a manner that it becomes possible to obtain solutions for isotropic, uniform thickness shells without resorting to approximate techniques such as finite differences, finite elements, or numerical integration. The solutions are obtained in series form for single-layered, isotropic, uniform thickness shells with arbitrary boundary conditions. The solutions are as accurate as the load representation and the theory allows. A computer program was written in Fortran IV to develop the loading series and to obtain numerical answers from the solution series. The program although cumbersome in size gives solutions without excessive use of computer time. The input of the program is not difficult to develop and does not require any knowledge of shell theory or of the solution technique. === Ph. D.