Effect of warping in geometric nonlinear analysis of spatial beams

Abstract

Geometric nonlinear analysis of three-dimensional beams with thin-walled open sections is performed. Using the total Lagrangian formulation, the displacement field is described, and the warping degree of freedom is taken into consideration to simulate the structural behaviors of slender or curved beams with an arbitrary shape. The element stiffness constructed with the assumption of the Euler-Bernoulli theory which neglects the shear deformation is transformed into a global coordinate system by using the Eulerian angles. After taking the static condensation to reduce the warping degree of freedom from the global stiffness matrix, the improved are-length method in connection with the proposed algorithm is adopted to overcome the numerical instability in the snap-through buckling analysis. Finally, correlation studies between analytical results and other previous numerical studies are conducted to establish the validity of the proposed numerical approach. (C) 2001 Elsevier Science Ltd. All rights reserved.