Nonlinear Analysis of Space Frames with Finite Rotations
Publication: Journal of Structural Engineering
Volume 119, Issue 1
Abstract
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.
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Information
Published In
Journal of Structural Engineering
Volume 119 • Issue 1 • January 1993
Pages: 1 - 15
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Dec 9, 1991
Published online: Jan 1, 1993
Published in print: Jan 1993
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