Abstract: In CAD system, Bézier, B-spline representations are widely used to describe complex geometry, while traditional finite element analysis uses totally different method to describe the geometry of model. Such an incompatibility makes it difficult to transfer geometry created in CAD systems into CAA model, and leads to difference geometry between these two systems. The method of conversion from the Bézier and B-spline curve to absolute nodal coordinate formulation (ANCF) elements is focused on. The linear relationship between Bézier, B-spline and ANCF cable elements is established in order to facilitate the automatic transformation to each other. That makes it a possible way for integration of the CAD and CAA system. It shows that ANCF description has the character of Bézier description, and Bézier description is actuary a special case of ANCF description. Bézier and B-spline curve can be represented by ANCF elements exactly. The continuity of B-spline and ANCF elements are studied then. The concept of knot multiplicity is used to control the continuity of B-spline, while ANCF description can automatically ensure C1 continuity because it uses the position and gradient vectors as nodal coordinates. Linear algebraic constraint equations based on equal curvature will eliminate gradient coordinate, leading to C 2 continuity. For cubic curve, C 3 continuity will convert two elements to a single bigger element, even though the two elements are different. It shows also that ANCF elements with different continuity can be created directly by B-spline representation during conversion and analysis, no constraint equation is actuary used. The dynamic respond of a cantilever under the acting of impact force is taken as an example to demonstrate the effect of continuity on finite element analysis.

Key words: Absolute nodal coordinate formulation, Bézier curve, B-spline curve, Computer aided design, Finite element analysis