A bifurcation analysis of space structures by using 3D beam-column element considering finite deformations and bowing effect

The present paper describes the space frame element and the fundamental strategies in computational elastic bifurcation theory of geometrically nonlinear, single load parameter conservative elastic spatial structures. A method for large deformation (rotation) analysis of space frame is based on an Eulerian formulation, which takes into consideration the effects of large joint rotations with finite deformation(rotation). The local member force-deformation relationships are based on the beam-column approach, and the change in member chord lengths caused by axial strain and flexural bowing are taken into account. And the derived geometric stiffness matrix is asymmetric because of the fact that finite rotations are not commutative under addition. To detect the singular point such as bifurcation point, an iterative pin-pointing algorithm is proposed. And the path switching mode for bifurcation path is based on the non-negative eigen-value and its corresponding eigen-vector. Some numerical examples for bifurcation analysis for a plane frame, plane circular arch and space dome structures are described.