不可展曲面近似展开的保形映射法

The Shape-Preserving Mapping Method in Approximately Developing Complex Surface

提出了以保形作为基本展开原则,对不可展曲面进行近似展开的保形映射法。以船体帆型板为例,给出了整张板的展开方法及顺序,并通过对船厂实船板保形映射展开后所得到的各项数据进行分析,来阐明该方法的正确性。

Line heating is concerned by the whole shipbuilding manufacture because of it＇s advantages, such as difficult to spring once taken shaped, easy to reverse process after correction and so on. Many researches about this line heating process have been made in recent years in order to realize the process automatization. Through the efforts of many researchers, great achievements of the line heating craft in it＇s automatization have been gained. But this is not enough. Because the hull can not be taken shaped through one process now, it is necessary to make another process, which is normally called second process. If we can supply correct ,data, the precision of the process will be improved and the quality of the taken shaped hull will be guaranteed. Following the step of the ancestor, we have done some researches as follows to solve this problem： （1） The researches to the expression of the undevelopable surface. The plate used in production and experiment is almost complex curvature surface which can not be developed, so we use Non-uniform B-spline and de-Boor algorithms to express the complex curvature surface with quadrangled gridding. （2） The researches to the development of the undevelopable surface. We present the fundamental development principle of shape-preserving, which can approximately develop the undevelopable surface. （3） The researches to the split of the surface. There will be some splits when a surface is developed, and the width of the splits is the width of the shrinking in the line healing process. We calculate numerical value of the split width which can supply the correct data to the continuative process.