| Abstract: | A set of governing equations for nonlinear theory of spatially curved elastic beams of thin-walled open cross section composed of straight rectangular elements is presented explicitly in the Lagrangian form. It is shown that local deformations, i.e. in-plane distortion of the cross section may easily be taken into account by the use of the analytical model proposed by Epstein and Murray. The essential feature which distinguishes the present work from Epstein and Murray's is the use of an auxiliary element when the axial curve of beams is not located on the cross section. This enables us to select arbitrarily the axial curve of rods. For the engineering theory of rods, the simplified governing equations for the nonlinear and linear theories with and without local deformations are derived from the rigorous nonlinear theory by employing the thinness assumption. It is also shown that the reduced linear theory without local deformations agrees with the Vlasov theory. |
