Stability of thin-walled members having arbitrary flange shape and flexible web

A finite element method is presented for analysing thin-walled structural members comprising a flexible web connected to one or two rigid flanges of arbitrary shape. A general thin-walled beam-column element is used to model the flanges while a thin plate element is used to model the web. Based on the derived total potential energy functional, explicit linear and geometric stiffness matrices for the two types of element are obtained. Using static condensation and appropriate transformations, the beam-column element and the plate element are combined to yield a super element with 22 degrees of freedom capable of modelling the flexural, torsional, web distortional and coupled web and flange local buckling modes of a general thin-walled member. The technique may be used to predict the elastic buckling load of members under any loading and boundary conditions. Several numerical examples are presented to demonstrate the accuracy, efficiency and versatility of the method.

[1]  K. Washizu.  Variational Methods in Elasticity and Plasticity , 1982 .

[2]  F. W. Williams,et al.  Buckling curves for elastically supported columns with varying axial force, to predict lateral buckling of beams , 1987 .

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

[4]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

[5]  Gregory J. Hancock.  LOCAL DISTORTIONAL AND LATERAL BUCKLING OF I-BEAMS , 1978 .

[6]  Mark A. Bradford,et al.  Lateral stability of beams on seats , 1983 .

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

[8]  Mark A. Bradford,et al.  Distortional instability of fabricated monosymmetric I-beams , 1988 .

[9]  Teoman Peköz,et al.  Torsional-Flexural Buckling of Thin-Walled Sections Under Eccentric Load , 1969 .

[10]  P. Goltermann,et al.  Lateral Distortional Buckling: Predicting Elastic Critical Stress , 1988 .

[11]  Mark A. Bradford,et al.  Distortional Buckling of I-Beams , 1979 .

[12]  N. S Trahair,et al.  ELASTIC STABILITY OF CONTINUOUS BEAMS , 1969 .

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

[14]  V. Vlasov.  Thin-walled elastic beams , 1961 .

[15]  Mark A. Bradford,et al.  Web distortion and flexural torsional buckling , 1979 .

[16]  R. J. Plank,et al.  Buckling under combined loading of thin, flat‐walled structures by a complex finite strip method , 1974 .

[17]  Kenneth M. Will,et al.  Beam Buckling by Finite Element Procedure , 1974 .

[18]  van Gm Gerard Erp.  Advanced buckling analyses of beams with arbitrary cross sections , 1989 .

[19]  William C. Schnobrich,et al.  FINITE ELEMENT ANALYSIS OF TRANSLATIONAL SHELLS , 1972 .

[20]  Mark A. Bradford,et al.  Distortional buckling of thin-web beam-columns , 1982 .

[21]  F. W. Williams,et al.  Buckling and vibration of anisotropic or isotropic plate assemblies under combined loadings , 1974 .

[22]  Edward L. Wilson,et al.  Numerical methods in finite element analysis , 1976 .

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

[24]  T. M. Roberts,et al.  Lateral, local and distortional buckling of I-beams , 1983 .

[25]  Robert E. Miller.  Reduction of the error in eccentric beam modelling , 1980 .

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

[27]  Y. K. Cheung,et al.  FINITE STRIP METHOD IN STRUCTURAL ANALYSIS , 1976 .