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    Fairness of 2d corotational beam spline as compared with geometrically nonlinear elastic beam
    (КПІ ім. Ігоря Сікорського, 2024) Orynyak, Igor; Yablonskyi, Petro; Koltsov, Dmytro; Chertov, Oleg; Mazuryk, Roman
    The goal of this paper is to further investigate the properties and advan-tages of corotational beam spline, CBS, as suggested recently. Emphasis is placed on the relatively simple task of drawing the spline between two endpoints with pre-scribed tangents. In the capacity of “goodness” of spline, the well-known notion of “fairness” is chosen, which presents itself as the integral from the squared curvature of spline over its length and originates from the elastic beam theory as the minimum of energy of deformation. The comparison is performed with possible variants of the cubic Bezier curve, BC, and geometrically nonlinear beam, GNB, with varying lengths. It was shown that CBS was much more effective than BC, where any at-tempt to provide better fairness of BC by varying the distances from endpoints to two intermediate points generally leads to lower fairness results than CBS. On the other hand, GNB, or in other words, the elastica curve, can give slightly better val-ues of fairness for optimal lengths of the inserted beam. It can be explained by the more sophisticated scientific background of GNB, which employs 6 degrees of free-dom in each section, compared with CBS, which operates only by 4 DoF