Fairness of 2D corotational beam spline as compared with geometrically nonlinear elastic beam

Abstract

The goal of this paper is to further investigate the properties and advantages of corotational beam spline, CBS, as suggested recently. Emphasis is placed on the relatively simple task of drawing the spline between two endpoints with prescribed 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 attempt 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 values 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 freedom in each section, compared with CBS, which operates only by 4 DoF.