Construction method for circular arc elements in rational absolute nodal coordinate formulation

The Rational Absolute Nodal Coordinate Formulation (RANCF) element nodal coordinates and weights can be obtained through a rational Bézier description, which is relatively cumbersome for engineering applications. In this paper, a method for directly defining RANCF elements is proposed for circular arc geometric configurations. In this method the nodal coordinates and weights can be expressed directly by the position coordinates of geometric configurations. By utilizing position coordinates in defining RANCF elements for a geometric configuration, it becomes easier to adjust continuity conditions between elements and apply constraint equations during the preprocessing phase before simulation initiation. As a result, there is no longer a need to use knot multiplicity in NURBS representation to adjust continuity conditions. To address the arbitrary and diverse definitions of RANCF elements, a parameterization method for RANCF elements is proposed, along with an assessment criterion and an optimal parameterization method for RANCF circular arc elements. Numerical examples are presented to compare the performance of various parametric RANCF circular arc elements. The results demonstrate that convergence can be achieved by using fewer optimal parametric elements.