EXACT GEOMETRICALLY NONLINEAR MATHEMATICAL FORMULATION AND NUMERICAL SIMULATION OF CURVED ELASTIC BEAMS

Based on the assumption of straight normal line of beams and by employing geometrically nonlinear theory for axially extensible beams, governing equations of large static deformations of curved elastic beams subjected to arbitrarily distributed loads(conservative or non-conservative)are derived. The equations contain seven independent unknown functions such as the arc length, the displacements of the central line, the rotational angle and the resultant internal forces at a cross section. By introducing the deformed arc length as one of the unknown functions, it makes the range of the spatial variables of the problem still within the undeformed length of the beam. In the mathematical model, not only the effects of the axial elongation and the initial curvature of the curved beam on the deformation are accurately taken into account but also the coupling between elongation and bending is considered. As a numerical example, the nonlinear plane bending of a cantilever semicircle beam subjected to tangentially distributed follower force along the axial line is analyzed by a shooting method. The equilibrium paths and configurations of the deformed beams, varying with the load parameter in a large range, are presented.