Accession Number : AD0603692

Title :   TOROIDAL SHELLS UNDER INTERNAL PRESSURE IN THE TRANSITION RANGE.

Descriptive Note : Technical rept. no. 19,

Corporate Author : HARVARD UNIV CAMBRIDGE MASS DIV OF ENGINEERING AND APPLIED PHYSICS

Personal Author(s) : Rossettos,John N. ; Sanders,J. Lyell ,Jr.

Report Date : JUN 1964

Pagination or Media Count : 75

Abstract : For the circular toroidal shell under internal pressure, the solution of the linear membrane equations does not yield continuous displacements. This difficulty can be resolved by the use of either linear bending or nonlinear membrane theory when they apply. An analytic solution is found in a transition range where both bending and nonlinear membrane action must be considered simultaneously. The governing equations are reduced to two simultaneous equations each containing a large parameter. Methods of asymptotic integration are then used, and the problem is finally reduced to solving four sets of two simultaneous, second order, linear differential equations whose solution depends on a transition parameter. These equations are solved numerically for various values of the transition parameter, and the resulting functions can be used to solve the problem for practical values of parameters in the transition range without the further need of a computer. (Author)

Descriptors :   (*SHELLS(STRUCTURAL FORMS), DEFORMATION), PRESSURE, MEMBRANES, NONLINEAR SYSTEMS, NUMERICAL INTEGRATION, DIFFERENTIAL EQUATIONS, NUMERICAL ANALYSIS, FUNCTIONS(MATHEMATICS)

Distribution Statement : APPROVED FOR PUBLIC RELEASE