• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.10a
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• pp.239-246
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• 1997

The general formulation of free vibration and stability analysis of unsymmetric thin-walled space frames and beam-columns is presented. The kinetic and total potential energy is derived by applying the extended virtual work principle, introducing displacement parameters defined at the arbitrarily chosen axis and including second order terms of finite semitangential rotations. In formulating the finite element procedure, cubic Hermitian polynomials are utilized as shape functions of the two node space frame element. Mass, elastic stiffness, and geometric stiffness matrices for the unsymmetric thin-walled section are evaluated. In order to illustrate the accuracy and practical usefulness of this formulation, finite element solutions for the free vibration and stability problems of thin-walled beam-columns and space frames are presented and compared with available solutions.

• Computational Structural Engineering
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• v.11 no.1
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• pp.191-204
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• 1998

The general formulation for free vibration and stability analysis of unsymmetric thin-wared space frames is presented in case where the shear deformation effects are neglected. The kinetic and total potential energies are derived by applying the extended virtual work principle, introducing displacement parameters defined at the arbitrarily chosen axis and including warping deformation and second order terms of finite semitangential rotations. In formulating the finite element procedure, cubic Hermitian polynomials are utilized as shape functions of the two node space frame element. Mass, elastic stiffness, and geometric stiffness matrices for the unsymmetric thin-walled section are evaluated, and load-correction stiffness matrices for off-axis distributed loadings are considered. In order to illustrate the accuracy and practical usefulness of this formulation, finite element solutions for the free vibration and stability problems of thin-walled beam-columns and space frames are presented and compared with available solutions.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.1
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• pp.13-24
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• 1993

The tangent stiffness matrices of the plane frame and the thin-walled space frame are derived by using the principle of virtual displacement. In case of the plane frame, the shape function and stiffness matrices are presented for the rigid-hinged condition. For the unsymmetric thin-walled space frame, the elastic and geometric stiffness matrices in three cases of the unrestrained torsion, the restrained torsion, and the restrained anti unrestrained torsion are evaluated by using the various Hermitian polynomials as the shape function. Numerical examples for the lateral buckling analysis of the space frames and the circular arch illustrate the accuracy and convergence characteristics of the derived formulations.