A refined finite element formulation for flexural and torsional buckling of beam-columns with finite rotations

Abstract This paper describes a consistent formulation of a tangent stiffness matrix for the geometrically nonlinear analysis of the space beam–column elements allowing for axial–flexural, lateral–torsional and axial–torsional buckling. In the proposed formulation, three deformation matrices are derived for moderately large rotations in practical three-dimensional space frames subjected to axial force and moments. These matrices are functions of the element deformations and include the coupling among axial, lateral and torsional deformations. The proposed matrices are used together with linear and geometric stiffness matrices for beam elements to study the large deflection behavior of space frames which comprise members with negligible warping effects. Numerical examples show that the proposed element formulation is accurate and efficient in predicting the nonlinear behavior of space frames even when only a few elements are used to model a member.

[1]  Nicholas S. Trahair,et al.  Inelastic Torsion of Steel I-Beams , 1993 .

[2]  Faris Albermani,et al.  Nonlinear Analysis of Thin‐Walled Structures Using Least Element/Member , 1990 .

[3]  Yeong-Bin Yang,et al.  Stiffness Matrix for Geometric Nonlinear Analysis , 1986 .

[4]  H. Ziegler Principles of structural stability , 1968 .

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

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

[7]  J. L. Meek,et al.  Geometrically nonlinear analysis of space frames by an incremental iterative technique , 1984 .

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

[9]  Sung-Pil Chang,et al.  Spatial Postbuckling Analysis of Nonsymmetric Thin-Walled Frames. I: Theoretical Considerations Based on Semitangential Property , 2001 .

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

[11]  Siu Lai Chan,et al.  Large deflection kinematic formulations for three-dimensional framed structures , 1992 .

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

[13]  John F. Abel,et al.  Equilibrium considerations of the updated Lagrangian formulation of beam‐columns with natural concepts , 1987 .

[14]  K. Bathe,et al.  Large displacement analysis of three‐dimensional beam structures , 1979 .

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

[16]  C. Oran Tangent Stiffness in Plane Frames , 1973 .

[17]  Manolis Papadrakakis,et al.  Conjugate gradient algorithms in nonlinear structural analysis problems , 1986 .

[18]  Yeong-Bin Yang,et al.  Force recovery procedures in nonlinear analysis , 1991 .

[19]  Amr S. Elnashai,et al.  Eulerian formulation for large-displacement analysis of space frames , 1993 .

[20]  Richard H. Gallagher,et al.  Finite element analysis of torsional and torsional–flexural stability problems , 1970 .

[21]  Siu-Lai Chan Geometric and material non‐linear analysis of beam‐columns and frames using the minimum residual displacement method , 1988 .

[22]  K. Hsiao Corotational total Lagrangian formulation for three-dimensional beamelement , 1992 .

[23]  M. Crisfield A consistent co-rotational formulation for non-linear, three-dimensional, beam-elements , 1990 .

[24]  Yong-Lin Pi,et al.  Nonlinear Inelastic Analysis of Steel Beam‐Columns. I: Theory , 1994 .

[25]  Kuo Mo Hsiao,et al.  A co-rotational finite element formulation for buckling and postbuckling analyses of spatial beams , 2000 .

[26]  W. F. Chen,et al.  Improved nonlinear plastic hinge analysis of space frame structures , 2000 .

[27]  Sritawat Kitipornchai,et al.  Geometric nonlinear analysis of asymmetric thin-walled beam-columns , 1987 .

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

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

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

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

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

[33]  S. Timoshenko Theory of Elastic Stability , 1936 .

[34]  John F. Abel,et al.  Convected systems for curved structural elements , 1987 .

[35]  Shyh-Rong Kuo,et al.  Theory & analysis of nonlinear framed structures , 1994 .

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