Effect of warping in geometric nonlinear analysis of spatial beams

Geometric nonlinear analysis of three-dimensional beams with thin-walled op en sections is performed. Using the total Lagrangian formulation, the displ acement field is described, and the warping degree of freedom is taken into consideration to simulate the structural behaviors of slender or curved be ams with an arbitrary shape. The element stiffness constructed with the ass umption 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 free dom from the global stiffness matrix, the improved are-length method in con nection with the proposed algorithm is adopted to overcome the numerical in stability in the snap-through buckling analysis. Finally, correlation studi es between analytical results and other previous numerical studies are cond ucted to establish the validity of the proposed numerical approach. (C) 200 1 Elsevier Science Ltd. All rights reserved.