Abstract
The aims of this paper are to make a full disscussion of the following two points. The first point is to formulate the governing equation in the reference state, which is applicable to the large displacements and large rotations for a uniform thin-walled open section whose axial curve forms a space curve, in the brief general equation which is graspable the main deformation behaviours under the deformation of the cross section and the transverse deformation. The second one is to present the unific formulation, which can treat similarly thin-walled open sections as the problem of rods with full sections, in order to full up a gap on the theory between a full section and a thin-walled open section and for applying to the thin-walled member with relative thick wall. The governing equation is obtained by regarding the thin-walled open section as the three-dimensional body and by reducing the body to the one-dimensional one through the modified Hellinger-Reissner's variational theorem. From a viewpoint to treating the main deformation behavior, it is assumed that the displacement is composed of the plane deformation of the cross section for stretching, bending, the transverse deformation, the rotation of twisting (distorsion) and the deformation of the cross section without the local deformation mode and of warping and furthermore that warping adds to the plane deformation. Warping is generally expressed in the power series expansion into the transverse coordinate axes. This paper consists of two parts and in the part 1 we present the rigorous formulation of the general equation independent of the engineering theory of the bending and torsion.
