Mathematics and Mechanics of Solids · 2014 · 239 citations · 39 references
EngineeringComputational EngineeringMechanical EngineeringComputational MechanicsFinite Element AnalysisFinite Element MethodsBeam AnalysisBeam TheoryBending Of BeamsIsogeometric AnalysisNurbs ModelingStructural Finite Element AnalysisAnalytical Beam SolutionsAnalytical SolutionsBeam ElementsBeam Finite Element AnalysisIsogeometric ModelingNon-uniform Rational B-splinesTimoshenko Beam ModelingTimoshenko Beam Theory
A curved beam element based on the Timoshenko model and non-uniform rational B-splines (NURBS) interpolation both for geometry and displacements is presented. Such an element can be used to suitably analyse plane-curved beams and arches. Some numerical results will explore the effectiveness and accuracy of this novel method by comparing its performance with those of some accurate finite elements proposed in the technical literature, and also with analytical solutions: for the cases where such closed-form solutions were not available in the literature, they have been computed by exact integration of the governing differential equations. It is shown that the presented element is almost insensitive to both membrane- and shear-locking, and that such phenomena can be easily controlled by properly choosing the number of elements or the NURBS degree.
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