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

초록

An evaluation procedure of exact static stiffness matrices for curved beams with non-symmetric thin-walled 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. Copyright (C) 2004 John Wiley Sons, Ltd.

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