General Conversion between ANCF and B-spline Surfaces

Abstract: In this paper, general conversion equations are derived between Absolute Nodal Coordinates Formulation (ANCF) finite surface elements and B-spline surfaces, an extension of our previous work on the conversion between ANCF cable elements and B-spline curves. The derivation of the conversion equations is the discovery of the geometric invariance of the ANCF displacement field before and after the conversion. Our study starts from proposing the conversion equation between ANCF finite surface elements and Bezier surfaces which are the special cases of B-spline surfaces, followed by establishing a general conversion equation between ANCF finite surface elements and Bezier surfaces. This general conversion equation has functionalities (1) to realize the one-step direct conversion between ANCF and Bezier surfaces (2) to convert ANCF finite surface elements directly to Bezier surfaces provided the ANCF nodal coordinates are not independent. The direct conversion from a conditional ANCF finite surface to Bezier surfaces enhances the efficiency and ability to control and store data in computers during the conversion process. The conversion between ANCF finite surface elements and B-spline surfaces is derived from a conversion of B-spline surfaces to a more general conversion of B-spline surfaces. B-spline basis functions are utilized in the non-recursive form, from which a more efficient conversion equation is obtained compared with an intuitive conversion semantics where one converts firstly B-spline surfaces to composite Bezier surfaces by inserting knot and converts to ANCF finite surface elements afterward. The obtained conversion equations between ANCF and B-spline surfaces realize the one-step direct conversion.