Interactive buckling in thin-walled beams—I. Theory

Abstract A method is derived for the analysis of mode interaction in thin-walled elastic beams. A nonlinear plate theory is employed for the plate segments of the beam, in which the exact nonlinear expressions are used for the middle surface strain measures, but the bending measures are linearized. The beam is subjected to a combination of axial compression and a constant bending moment, and it is assumed to be simply supported at the ends. In the calculation of the total potential energy, the influence of the prebuckling deformations is neglected. The finite strip method is used with the transverse variation of all three displacement components described by cubic polynomials in the arc length. The nonlinear mode interaction is analysed by means of Koiter's asymptotic theory of stability. Some applications of the method to representative problems are presented in a subsequent paper by the authors. This shows that significant mode interaction and imperfection sensitivity occur in these structures.

[1]  W. T. Koiter.  The Application of the Initial Post-Buckling Analysis to Shells , 1982 .

[2]  Viggo Tvergaard,et al.  Imperfection-sensitivity of a wide integrally stiffened panel under compression , 1973 .

[3]  Srinivasan Sridharan,et al.  An improved interactive buckling analysis of thin-walled columns having doubly symmetric sections , 1986 .

[4]  Gregory J. Hancock,et al.  Interaction Buckling in I-Section Columns , 1981 .

[5]  W. T. Koiter.  THE STABILITY OF ELASTIC EQUILIBRIUM , 1970 .

[6]  Gregory J. Hancock,et al.  Nonlinear Analysis of Thin Sections in Compression , 1979 .

[7]  S. Sridharan,et al.  The Local Collapse of Elastic Thin Walled Columns , 1980 .

[8]  Mark A. Bradford,et al.  INTERACTION OF LOCAL AND LATERAL BUCKLING IN BEAMS , 1982 .

[9]  P. Goltermann,et al.  Interactive buckling in thin-walled beams—II. Applications , 1989 .

[10]  James G.A. Croll,et al.  Interaction between local and overall buckling , 1975 .

[11]  A. van der Neut,et al.  The interaction of local buckling and column failure of thin-walled compression members , 1969 .

[12]  Srinivasan Sridharan,et al.  Doubly symmetric interactive buckling of plate structures , 1983 .

[13]  Srinivasan Sridharan,et al.  Interactive buckling analysis with finite strips , 1985 .

[14]  T. R. Graves Smith,et al.  A finite strip method for the post-locally-buckled analysis of plate structures , 1978 .

[15]  Esben Byskov,et al.  Mode interaction in axially stiffened cylindrical shells , 1977 .

[16]  Srinivasan Sridharan,et al.  Interactive Buckling in Thin‐Walled Beam‐Columns , 1985 .