Static, stability, and dynamic analysis of shells of revolution by numerical integration — A comparison

Abstract

The use of numerical integration for the analysis of practical shell-of-revolution structures was documented almost simultaneously in the United States by three independent groups of researchers (Cohen, Kalnins, Mason et al.). These early efforts have been refined, reformulated, and increased in scope and applicability to become major program systems (SRA, Kalnins, STARS). While all three programs utilize basically the same mathematical formulation for integrating the shell differential equations, the matrix solution procedures from this point are basically different. The purpose of this paper is twofold, as follows: (1) to present the differences in solution procedures of the largest system (the Grumman — NASA STARS) from the other two, and point out the inherent advantages of this approach; and (2) compare the numerical integration procedure, as utilized in the STARS, with finite difference and finite element procedures, noting the relative advantages of each in the analysis of shells of revolution for static, buckling, and dynamic loadings. To fulfill the above purpose, a brief review of the numerical integration procedure for the analysis of shells of revolution is presented, and the matrix solution procedures of the SRA, Kalnins, and STARS programs are contrasted. The limitations imposed by the relative procedures are discussed. The unique formulation utilized by STARS for the solution of stability and vibration problems, and its advantages, are discussed in detail. The STARS program's analytical capabilities, capacity, and user options are compared with those of other major systems utilizing either finite differences or finite elements for the analysis of shells of revolution. Comparisons are made in terms of program size, program accuracy, number of degrees of freedom required for analysis, ease of idealization and user inputs, limitations imposed on analysis capability or output, running time, and so forth. All advantages and differences are demonstrated by use of solutions for realistic shell problems in the areas of statics, stability (including dead and live load distributions), vibrations, and dynamic response of shells subjected to time-dependent loadings.