Elastic buckling analysis of 3D trusses and frames with thinwalled members
Abstract
A finite element method is presented for the determination of the elastic buckling load of threedimensional trusses and frames with rigid joints. The beam element stiffness matrix is constructed on the basis of the exact solution of the governing equations describing the coupled flexuraltorsional buckling behaviour of a threedimensional beam with an open thinwalled section in the framework of a small deformation theory. Large deformation effects are taken into account approximately through consideration of P∆ effects. The structural stiffness matrix is obtained by an appropriate superposition of the various element stiffness matrices. The axial force distribution in the members is obtained iteratively for every value of the externally applied loading and the vanishing of the determinant of the structural stiffness matrix is the criterion used to numerically determine the elastic buckling load of the structure. The effect of initial member imperfections is also included in the formulation. Comparisons of accuracy and efficiency of the present exact finite element method against the conventional approximate finite element method are made. Cases where the axial force distribution determination can be done without iterations are also identified. The effect of neglecting the warping stiffness of some monosymmetric sections is also investigated. Numerical examples involving simple and complex threedimensional trusses and frames are presented to illustrate the method and demonstrate its merits.
 Publication:

Computational Mechanics
 Pub Date:
 2002
 DOI:
 10.1007/s0046600203556
 Bibcode:
 2002CompM..29..459B