Three-dimensional analysis of large strain of spatially bent curvilinear bar

Abstract

The problem of bending and twisting of an elastic body in the form of a ring sector with an arbitrary cross-section is considered on the base of precise three-dimensional equations of the non-linear elasticity theory. The initial spatial nonlinear elastostatics problem is reduced to the two-dimensional boundary-value problem for the plane domain in the form of the ring cross-section. Boundary conditions on the bar ends are developed in the integral Saint-Venan terms. Various variation definitions of non-linear two-dimensional problem are given on the bar cross-section.