Solution of a homogeneous boundary value problem for the sector of a toroidal shell segment: PMM vol. 40, n≗ 4, 1976, pp. 755–759

Abstract

Membrane forces in the segment of a thin toroidal shell loaded by an edge bending load are determined from the particular solution of the fundamental differential equation. Taking account of the asymptotic approximation of the special function in whose terms the particular solution is expressed, it is shown in [1] that the particular solution for a thin toroidal shell agrees with the membrane solution. In the general case, the tensile forces in a shell not closed in two coordinates are determined by membrane theory ; the membrane state of stress is determined taking the solution obtained into account. The method of characteristics, used in [2] to analyze membrane shells, is used to solve the problem. The fundamental differential equation is solved by means of a special integral transform using Fourier series. Results of a numerical computation on an electronic computer and of an experiment are presented.