Influence of control polygon on the generalization of the conversion between ANCF and B-spline surfaces

TL;DR

This paper develops a general transformation matrix between B-spline and ANCF surfaces, improving conversion efficiency and accuracy in engineering applications, especially for distorted configurations in CAD systems.

Contribution

It introduces a non-recursive, simplified transformation matrix between ANCF and B-spline surfaces, including a special Bezier control polygon for efficient conversion with fewer degrees of freedom.

Findings

A general transformation matrix between Bezier and ANCF surfaces is established.

The method simplifies conversion, reducing degrees of freedom in ANCF surface elements.

The approach enhances efficiency in transferring distorted configurations back to CAD.

Abstract

The aim of this study is to establish a general transformation matrix between B-spline surfaces and ANCF surface elements. This study is a further study of the conversion between the ANCF and B-spline surfaces. In this paper, a general transformation matrix between the Bezier surfaces and ANCF surface element is established. This general transformation matrix essentially describes the linear relationship between ANCF and Bezier surfaces. Moreover, the general transformation matrix can help to improve the efficiency of the process to transfer the distorted configuration in the CAA back to the CAD, an urgent requirement in engineering practice. In addition, a special Bezier surface control polygon is given in this study. The Bezier surface described with this control polygon can be converted to an ANCF surface element with fewer d.o.f.. And the converted ANCF surface element with 36 d.o.f. was once addressed by Dufva and Shabana. So the special control polygon can be regarded as the geometric condition in conversion to an ANCF surface element with 36 d.o.f. Based on the fact that a B-spline surface can be seen as a set of Bezier surfaces connected together, the method to establish a general transformation matrix between the ANCF and lower-order B-spline surfaces is given. Specially, the general transformation is not in a recursive form, but in a simplified form.