Flexibility-Corotational Formulation of Space Frames with Large Elastic Deformations and Buckling

While the joints of a frame move in the space with large displacements and rotations, the deformations of the frame member with respect to the imaginary line connecting end joints, known as the chord, remain relatively small but still affect the stress field along the member length. A separation, known also as the corotational formulation, is simple for small displacements and rotations, and for small deformations, while in presence of large geometric changes the kinematic and dynamic interaction between the two systems (rigid and deformational) requires enhanced treatment. An enhanced corotational formulation, based on the flexibility modeling of elastic space frames with large deformations and rotations, expanding the prior developments by the authors, is presented in this article. The enhancements with respect to previous formulations cover: (1) rigid translations and expanded rotations of the chord; (2) a combination of axial and flexural deformations expanded to include torsional and shear influences; (3) a consistent formulation of geometric stiffness matrix; and (4) a rederivation of the formulation in time-independent incremental form. The entire reformulation enables the application of flexibility-based solutions to space frames addressing flexural and torsional buckling or postbuckling problems and allows for further integration of material nonlinearity.