Elastic Analysis of Spherical Domes

Part I of this report is concerned with the development of a numerical procedure for the computation of the dynamic response of an elastic spherical shell when subjected to transient uniform pressure. This procedure is based upon the development of a discrete mechanism which replaces the continuous shell, said mechanism containing both bending and membrane resistance and large deformation effects. A numerical procedure is developed for obtaining the dynamic response of the mechanism and a code programmed which makes the analysis on a digital computer. This program for an electronic digital computer is presented in flow diagram form enabling an experienced programmer to convert the order code to any type of computing facility. Using the program for the digital computer certain parameters were investigated and the significant results and conclusions presented. Part II of this report is concerned with the analysis of a membrane spherical shell by a discrete framework approximation. Equivalent areas of bars are derived on the basis of equivalent stiffness under identical loading. The framework is analyzed for natural modes and frequencies and the response of the framework to triangular blast loading is obtained by linear superposition of normal modes. Time histories of displacements are converted to time histories of bar forces which are combined to yield the shell stresses. A short digital computer program is written to superpose modes and to compute shell stresses. Using the program for the digital computer certain parameters were investigated and the significant results and conclusions presented. Another digital computer program is independently developed in Appendix C as appended to Part II to compute the dynamic response of the same framework model. The flow diagram for this digital computer program is also presented, enabling a programmer to convert the order code to any type of computing facility.Research Directorate, Air Force Special Weapons Center. Kirtland Air Force Base.Contract AF 29(601)-464Project 108