NONLINEAR ANALYSIS OF SPACE FRAMES WITH FINITE ROTATIONS

In nonlinear analysis of rigid-jointed space frames, the assumption that rotations of a body are additive has been widely adopted by researchers in updating the end rotations of frame elements at each incremental step. Such an assumption remains valid only for incremental steps with small rotations. For cases with finite rotations, it is necessary to consider the noncommutative nature of rotations in three dimensions. Based on Euler’s finite rotation formula, unique, analytical expressions that are valid for updating the geometry of the frame element involving finite rotations are derived in the present paper. With these expressions, the displacement increments solved from the structure equations of equilibrium at each incremental step can be decomposed into the rigid-body modes and member deformations, thereby providing the basis for recovering and updating the element forces. The validity of the present procedure is demonstrated in the postbuckling analysis of a circular arch, involving large rotations in a three-dimensional space.