Semi-inverse solutions in nonlinear theory of elastic shells (Archives of Mechanics - Test, 2001)
The semi-inverse method is applied to the solution of static problems in the nonlinear theory of elastic shells. This method consists in construction of particular solutions in such a way that the initial system of equations is reduced to a system of a smaller number of independent variables. Two nonlinear models, one of the Love type and another of the Cosserat type, are considered. For these models, several two-parameter families of finite deformations are found; then the system of partial differential equations of equilibrium reduces to a system of nonlinear ordinary differential equations. The semi-inverse solutions found are valid for prismatic and toroidal shells, as well as for shells of revolution. These solutions are of practical significance. They describe torsion of a prismatic shell under large angles of twist, strong flexure of a thin-walled cylinder of arbitrary cross-section, spatial bending of a shell having the shape of a sector of a surface of revolution, straightening of a toroidal shell to a cylindrical surface, and some other types of large deformations.