An efficient isogeometric beam formulation for analysis of 2D non-prismatic beams

This study presents an efficient beam formulation for static and vibration analysis of 2D non-prismatic beams with the kinematic assumptions of the Timoshenko beam theory. Beams having complex configurations can be straightforwardly constructed by using B-spline basis functions, which are used for descriptions of the beam axis and the sectional height. This feature enables analysis of free-form non-prismatic beams with strong curvatures to be performed conveniently and accurately, and is not virtually found in any existing formulations that are related to non-prismatic beams. The concept of isogeometric analysis is adopted by discretizing the kinematic unknowns, i.e., the translational displacements of the beam axis and the sectional rotation, using B-spline basis functions. A procedure for the recovery of stress components is also presented. The accuracy and performance of the developed approach are assessed through several numerical examples which cover several types of beam, e.g., sinusoidal beam, tapered beam and Tschirnhausen's beam representing free-form beams. Furthermore, convergence tests are also performed to demonstrate convergence properties of the proposed formulation.