Nonlinear pure bending of toroidal shells of arbitrary cross-section

Abstract

The geometrically nonlinear problem of in-plane pure bending of a toroidal shell of arbitrary cross-section (both closed and open) is considered. A finite element algorithm for solution of the problem is proposed. The equilibrium states of the discrete system are determined by an iterative method based on calculation of the coefficients of the first and second variations of the total potential energy. Nonlinear deformation of cylindrical and toroidal shells of closed cross-section is considered. As an example of open cross-sectional contour, a solution for the problem of pure bending of a thin plate is given. The resultant solutions are compared with those of the other authors.