Abstract
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.
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