An Arbitrary Cross Section, Locking Free Shear-flexible Curved Beam Finite Element

In this paper, a finite element model is proposed for the study of two-dimensional arch structures. Three- and five-node elements are developed irrispective of the shape of the arch and capable of analyzing thick to very thin structures using a modified Mindlin-Reissner theory. A compatibility displacement-based method is used: full integration is introduced to evaluate all energy terms and the convergence pattern is completely independent of the thickness values, even if a coarse mesh is employed. Shear and membrane locking are completely eliminated, shaping shear and membrane strains by means of suitable functions appropriately projected over Gauss integration points. A formulation has been developed which takes into account, in the elastic range, the possibility of working with a more general cross-section conceived as a set of layers. Numerical examples are also given to show the accuracy of the method and comparisons with previous models are made.

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