Spatial Postbuckling Analysis of Nonsymmetric Thin-Walled Frames. I: Theoretical Considerations Based on Semitangential Property

To present the spatial postbuckling analysis procedures of shear deformable thin-walled space frames with nonsymmetric cross sections, theoretical considerations based on the semitangential rotation and the semitangential moment are presented. First, similarity and difference between Rodriguez' rotations and semitangential rotations are addressed. Next, the improved displacement field is introduced using the second-order terms of semitangential rotations and rotational properties of off-axis loads and conservative moments are discussed based on the proposed displacement field. Finally, it is deduced that the resulting potential energy due to stress resultants corresponds to semitangential bending and torsional moments. In a companion paper, the elastic strain energy including bending-torsion coupled terms and shear deformation effects is newly derived and a clearly consistent finite-element procedure is presented based on the updated Lagrangian corotational formulation. Tangent stiffness matrices of the t...

[1]  D. W. Scharpf,et al.  Finite element method — the natural approach , 1979 .

[2]  Moon-Young Kim,et al.  Improved formulation for spatial stability and free vibration of thin-walled tapered beams and space frames , 2000 .

[3]  D. W. Scharpf,et al.  On the geometrical stiffness of a beam in space—a consistent V.W. approach , 1979 .

[4]  M. Géradin,et al.  A beam finite element non‐linear theory with finite rotations , 1988 .

[5]  M. J. Clarke,et al.  Co-rotational and Lagrangian formulations for elastic three-dimensional beam finite elements , 1998 .

[6]  Yeong-Bin Yang,et al.  Joint Rotation and Geometric Nonlinear Analysis , 1986 .

[7]  Sung-Pil Chang,et al.  Spatial postbuckling analysis of nonsymmetric thin-walled frames. II : Geometrically nonlinear Fe procedures , 2001 .

[8]  Sung-Pil Chang,et al.  SPATIAL STABILITY ANALYSIS OF THIN-WALLED SPACE FRAMES , 1996 .

[9]  J. C. Simo,et al.  A Geometrically-exact rod model incorporating shear and torsion-warping deformation , 1991 .

[10]  J. Argyris.  An excursion into large rotations , 1982 .

[11]  Atef F. Saleeb,et al.  Effective modelling of spatial buckling of beam assemblages, accounting for warping constraints and rotation-dependency of moments , 1992 .

[12]  Shyh-Rong Kuo,et al.  NONLINEAR ANALYSIS OF SPACE FRAMES WITH FINITE ROTATIONS , 1993 .

[13]  Aura Conci,et al.  Natural approach for geometric non‐linear analysis of thin‐walled frames , 1990 .

[14]  Ziad M. Elias.  Theory and methods of structural analysis , 1986 .

[15]  D. W. Scharpf,et al.  On large displacement-small strain analysis of structures with rotational degrees of freedom , 1978 .

[16]  Shyh-Rong Kuo,et al.  Frame Buckling Analysis with Full Consideration of Joint Compatibilities , 1992 .

[17]  Sung-Pil Chang,et al.  Stability of Shear Deformable Thin-Walled Space Frames and Circular Arches , 1996 .

[18]  George E. Blandford,et al.  Closure of "Thin-Walled Space Frames. I: Large-Deformation Analysis Theory" , 1991 .

[19]  Markku Tuomala,et al.  Static and dynamic analysis of space frames using simple Timoshenko type elements , 1993 .

[20]  M. J. Clarke,et al.  New Definition of Conservative Internal Moments in Space Frames , 1999 .

[21]  M. J. Clarke,et al.  Symmetry of Tangent Stiffness Matrices of 3D Elastic Frame , 2000 .

[22]  George E. Blandford,et al.  Thin-Walled Space Frames. II: Algorithmic Details and Applications , 1991 .