Exact dynamic and static stiffness matrices of shear deformable thin-walled beam-columns |
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Authors: | Kim Moon-Young Kim Nam II |
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Institution: | a Department of Civil-Environmental Engineering, SungKyunKwan University, Cheoncheon Dong Jangan-Ku, Kyoungki-Do, Suwon 440-746, South Koreab Civil-Electric Research and Development Department, Korea Railroad Research Institute, Woulam-Dong, Kyonggi-Do, Uiwang-city 437-050, South Korea |
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Abstract: | Total potential energy of non-symmetric thin-walled beam-columns in the general form is presented by introducing the displacement field based on semitangential rotations and deriving transformation equations between displacement and force parameters defined at the arbitrary axis and the centroid-shear center axis, respectively. Next, governing equations and force-deformation relations are derived from the total potential energy for a shear-deformable, uniform beam element and a system of linear eigenproblem with non-symmetric matrices is constructed based on 14 displacement parameters. And then explicit expressions for displacement parameters are derived and exact dynamic stiffness matrices are determined using force-deformatin relationships. In addition, the modified numerical method to eliminate multiple zero eigenvalues and to evaluate the exact static stiffness matrix is developed for spatial stability analysis. Finally, in order to demonstrate the validity and the accuracy of this study, the spatially coupled natural frequencies and buckling loads are evaluated and compared with analytical solutions or results analyzed by thin-walled beam elements and ABAQUS's shell elements. |
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