Exact Static Element Stiffness Matrix of Non-Symmetric Thin-Walled Curved Beams
An evaluation procedure of exact static stiffness matrix for curved beams with non-symmetric thin-walled cross section is rigorously presented for the static analysis. Higher order differential equations for a uniform curved beam element are first transformed into a set of the first order simultaneous ordinary differential equations by introducing 14 displacement parameters where displacement modes corresponding to zero eigenvalues are suitably taken into account. This numerical technique is then accomplished via a generalized linear eigenvalue problem with non-symmetric matrices. Next the displacement functions of displacement parameters are exactly calculated by determining general solutions of simultaneous non-homogeneous differential equations. Finally an exact stiffness matrix is evaluated using force-deformation relationships. In order to demonstrate the validity and effectiveness of this method, displacements and normal stresses of cantilever thin-walled curved beams subjected to tip loads are evaluated and compared with those by thin-walled curved beam elements as well as shell elements.