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Journal of Applied Mathematics
Volume 2012, Article ID 516290, 11 pages
Review Article

Displacement Field Approximations for Force-Based Elements in Large Displacement Analyses

School of Civil Engineering, College of Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran

Received 10 August 2011; Revised 24 February 2012; Accepted 15 March 2012

Academic Editor: Hester Bijl

Copyright © 2012 M. Vahidi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper investigates different approximation techniques for planar beam column elements in force-based methods. The three fields, introduced in this review, are: curvature-based displacement interpolation (CBDI) used in matrix-based flexibility formulations, linear displacement approximation applied in state space, and higher-order displacement approximation utilized again in state space. Using these three approximation fields, the responses and their accuracies in some systems are compared in examples. Finally, focusing on the accuracy and regarding the performed analyses, it seems that the computational cost is reduced and accuracy of responses is elevated in many engineering problems using the higher-order approximation field in state space.