FINITE DISPLACEMENT THEORY OF CURVED AND TWISTED THIN-WALLED BEAMS.

The emphasis of this paper is on the derivation of finite displacement fields in which warping displacement is fully examined. The resulting displacement fields are considered to be accurate in the sense that all the second-order terms with respect to displacements are taken into account. The principle of virtual work is used to derive equilibrium equations and associated boundary conditions. The validity of the governing equilibrium equations is verified by comparison with currently accepted equilibrium equations for typical cases. Numerical analysis is restricted primarily to procedures embodying the finite element method, where nonlinear problems can be formulated using Hellinger-Reissner's Principle with the help of mixed finite elements. Governing nonlinear equations are solved by Newton-Raphson's method. The validity of the formulation is illustrated through numerical solutions for nonlinear behavior of a curved and twisted thin-walled beam, and a comparison of these solutions with experimental results.