A chain algorithm element is created from pseudo-rigid-body segments and used in a chain calculation that accurately predicts the force deflection relationship of beams with large 3-D deflections. Each chain element is made up of three pseudo-rigid-body models superimposed on each other acting orthogonally in relation to each other. The chain algorithm can predict large displacements and the force-deflection relationship of lateral torsional buckled beams significantly faster than the finite element method. This approach is not intended to compete with finite element analysis, but rather is a supplement tool that may prove particularly useful in the early phases of design when many analysis iterations are required. The 3-D chain algorithm is demonstrated and compared to the finite element analysis for the nonlinear large-deflection, post-buckling path of a flexible beam undergoing lateral-torsional buckling.

Original Publication Citation

Chase, R.P. Jr., Todd, R. H., Howell, L.L., Magleby, S.P., “A 3-D Chain Algorithm with Pseudo-rigid-body Model Elements,” Mechanics Based Design of Structures and Machines, Vol. 39, No. 1, pp 142–156, 2011.

Document Type

Peer-Reviewed Article

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Taylor and Francis




Ira A. Fulton College of Engineering and Technology


Mechanical Engineering

University Standing at Time of Publication

Full Professor