Exact static element stiffness matrices of non-symmetric thin-walled curved beams

An evaluation procedure of exact static stiffness matrices for curved beams with non-symmetric thinwalled cross section are 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.