New Finite Element for Analysis of Thin-Walled Structures

The analysis of thin-walled structures has been discussed by many theoreticians who produced seminal works. Unfortunately, these studies are based on mathematical formulations which are not easy to understand by the majority of engineers because the background provided by the undergraduate schools does not cover the solution of complex differential equations or the use of area coordinates in the calculation of cross-section properties. Accordingly, practicing engineers are often at a loss in problems involving nonlinear differential equations or the meaning of an elusive mechanical action called bimoment in the evaluation of longitudinal stresses caused by warping torsion. On the other hand, present day formulations should take advantage of the availability of computers that can easily handle the matrix relations on which the finite element analysis is based. This work presents a new finite element that allows the evasion of the aforementioned complexities. The main novelty is the discussion of a nonnodal degree of freedom that efficiently captures the possible shear flow along the longitudinal edges of a beam-column element. DOI: 10.1061/(ASCE)ST.1943-541X.0000372. (C) 2011 American Society of Civil Engineers.