Inelastic post-buckling analysis of tubular beam-columns and frames

Abstract A numerical procedure for tracing the load-deflection path of tubular beam-columns and frames is presented. Nonlinearities arising from both the change of geometry and material yielding are included, incorporating the effects of arbitrarily large rotations and strain unloading. This numerical scheme is based on a compatible relationship between the incremental and the total equilibrium equations, as opposed to the generally available methods. An updated Lagrangian formulation, coupled with the numerical minimum residual displacement method, is employed for the solution of the nonlinear simultaneous equations. The proposed scheme is validated against a number of examples of which the results by other methods are available. The present method is capable of tracing the equilibrium paths of tubular struts with complex loading and boundary conditions using the incremental-iterative method throughout; suppression of iterations as required in other methods is not needed. This leads to a significant improvement in efficiency and accuracy because of the non-existence of the drift-off numerical error.

[1]  Gouri Dhatt,et al.  Incremental displacement algorithms for nonlinear problems , 1979 .

[2]  Manolis Papadrakakis,et al.  Post-buckling analysis of spatial structures by vector iteration methods , 1981 .

[3]  R. Wen,et al.  Nonlinear Elastic Frame Analysis by Finite Element , 1983 .

[4]  W. F. Chen,et al.  Analysis of tubular beam-columns and frames under reversed loading , 1987 .

[5]  S. Vinnakota,et al.  Inelastic behaviour of rotationally restrained columns under biaxial bending , 1974 .

[6]  M A Crisfield.  LARGE-DEFLECTION ELASTO-PLASTIC BUCKLING ANALYSIS OF PLATES USING FINITE ELEMENTS , 1973 .

[7]  S. Remseth,et al.  Nonlinear static and dynamic analysis of framed structures , 1979 .

[8]  M. Crisfield.  A FAST INCREMENTAL/ITERATIVE SOLUTION PROCEDURE THAT HANDLES "SNAP-THROUGH" , 1981 .

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

[10]  Jerome J. Connor,et al.  Nonlinear Analysis of Elastic Framed Structures , 1968 .

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

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

[13]  S. L. Chan,et al.  Geometric and material nonlinear analysis of structures comprising rectangular hollow sections , 1987 .

[14]  G. Powell,et al.  Improved iteration strategy for nonlinear structures , 1981 .

[15]  P. Bergan,et al.  Solution techniques for non−linear finite element problems , 1978 .

[16]  S. L. Chan,et al.  INELASTIC POST-BUCKLING BEHAVIOUR OF TUBULAR STRUTS , 1986 .

[17]  Ekkehard Ramm,et al.  Strategies for Tracing the Nonlinear Response Near Limit Points , 1981 .

[18]  W. J. Supple,et al.  Post-critical behaviour of tubular struts , 1980 .

[19]  Sritawat Kitipornchai,et al.  Nonlinear Finite Element Analysis of Angle and Tee Beam‐Columns , 1987 .

[20]  W. F. Chen,et al.  Behaviour of portal and strut types of beam-columns , 1983 .

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

[22]  Manolis Papadrakakis.  Inelastic Post-Buckling Analysis of Trusses , 1983 .

[23]  Semih S. Tezcan,et al.  Tangent Stiffness Matrix for Space Frame Members , 1969 .

[24]  Wai‐Fah Chen,et al.  Inelastic Post‐Buckling Behavior of Tubular Members , 1985 .

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

[26]  Charles Birnstiel,et al.  Inelastic H-Columns Under Biaxial Bending , 1968 .