• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.4
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• pp.39-49
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• 1993

In order to present the geometrically nonlinear F.E. formulation of space frames, two beam/column elements including the effects of transverse shear deformation and bending stretching coupling are developed. In the case of the first element (Finite segment method), the tangent stiffness matrices are derived by directly integrating the equilibrium equations, whereas in the case of the second element (Finite element method) elastic and geometric stiffness matrices are calculated by using the hermitian polynomials including shear deformation effect as the shape function. Both elements possess the usual twelve degrees of freedom. Also, the bowing function including shear deformation effects is obtained in order to account for the effect of shortening of member chord length due to the bending and torsional behavior. Numerical results are presented for the selected test problems which demonstrate that both elements represent reliable and highly accurate tools.

• Journal of Korean Society of Steel Construction
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• v.18 no.6
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• pp.727-735
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• 2006

In this paper, a geometric nonlinear analysis procedure of the beam-column element including multi-noded cable element in extension of companion paper (Kim et al., 2005) is presented. First, a stiffness matrix was derived about the beam-column element that considers the second effect of the initial force supposing the curved shape at each time-step, with Hermitian polynomials as the shape function. Second, the multi-noded cable element was also subjected to the tangent stiffness matrix. To verify the geometric nonlinearity of this newly developed multi-noded cable-truss element, the Innovative Prestressed Support (IPS) system using this theory was analysed by geometric nonlinear method and the results were compared with those produced by linear analysis.

• Journal of Korean Society of Steel Construction
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• v.11 no.2 s.39
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• pp.153-165
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• 1999

In order to trace the lateral-torsional post-bucking behaviors of thin-walled space frames with non-symmetric cross sections, a geometrically non-linear finite element formulation is presented by applying incremental equilibrium equations based on the updated Lagrangian formulation and introducing Vlasov's assumption. The improved displacement field for non-symmetric thin-walled cross sections is introduced based on inclusion of second order terms of finite rotations, and the potential energy corresponding to the semitangential rotations and moments is consistently derived. For finite element analysis, tangent stiffness matrices of thin-walled space frame element are derived by using the Hermition polynomials as shape functions. A co-rotational formulation in order to evaluate the unbalanced loads is presented by separating the rigid body rotations and pure deformations from incremental displacements and evaluating the updated direction cosines and incremental member forces.

• Computational Structural Engineering
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• v.10 no.4
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• pp.205-216
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• 1997

In order to trace the lateral post-buckling behaviors of thin-wafled space frames, a geometrically nonlinear finite element formulation is presented by applying incremental equilibrium equations based on the updated Lagrangian formulation and introducing Vlasov's assumption. The improved displacement field for symmetric thin-walled cross sections is introduced based on inclusion of second order terms of finite rotations, and the potential energy corresponding to the semitangential rotations and moments is consistently derived. For finite element analysis, tangent stiffness matrices of the thinwalled space frame element with 7 degrees of freedom including the restrained warping for each node are derived by using the Hermition polynomials as shape functions. A co-rotational formulation in order to evaluate the unbalanced loads is presented by separating the rigid body rotations and pure deformations from incremental displacements and evaluating the updated direction cosines of the frame element due to rigid body rotations and incremental member forces from pure deformations. Finite element solutions for the spatial buckling and post-buckling analysis of thin-walled space frames are presented and compared with available solutions and other researcher's results.