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.

翻译：本研究旨在建立B样条曲面与ANCF曲面单元之间的一般转换矩阵。本研究是对ANCF与B样条曲面间转换的进一步探索。本文建立了贝塞尔曲面与ANCF曲面单元之间的一般转换矩阵，该矩阵本质上描述了ANCF与贝塞尔曲面之间的线性关系。此外，该通用转换矩阵有助于提高将CAA中变形构型传回CAD过程的效率，这是工程实践中的迫切需求。本研究还提出了一种特殊的贝塞尔曲面控制多边形。采用该控制多边形描述的贝塞尔曲面可转换为具有较少自由度的ANCF曲面单元。所转换的36自由度ANCF曲面单元曾由Dufva与Shabana论述，因此该特殊控制多边形可视为转换为36自由度ANCF曲面单元的几何条件。基于B样条曲面可视为一组相连贝塞尔曲面的事实，本文给出了建立ANCF与低阶B样条曲面间通用转换矩阵的方法。特别指出的是，该通用转换矩阵并非递归形式，而是简化形式。