基于单元等变形的复杂曲面展开算法研究

针对板壳类零件展开问题提出了一种基于单元等变形的复杂曲面展开算法。首先利用有限元网格生成算法将零件曲面划分成三角形单元 ,然后按照单元等变形假设将三角形单元映射到平面上 ,从而得到曲面的展开形状与尺寸 ,并通过重新计算单元的变形率得到曲面内的应变分布。该算法可以将各种可展曲面和不可展曲面采用统一的形式展开 ,实际应用表明采用该算法展开复杂曲面时具有快速准确的特点 ,可以显著缩短零件从设计造型到求取其毛料外形的时间 ,适用于航空航天及汽车制造等工业领域内具有复杂曲面的金属板料零件的数字化展开。

Research on the Development Algorithm of Cruved Surfaces

This paper presents an algorithm for the development of a doubly curved surface into a planar shape. The curved surface is first divided into triangular elements. It is assumed that the strain distribution within every element is even. With this assumption, every element is mapped into the planar surface by solving a least square equation, and as a result, the size and shape of the plate blank is obtained. The strain distribution of the deformed surface is obtained by re-calculating the element deformation ratio. This algorithm can develop the developable and doubly curved surfaces in the same routine. An example of developable surface shows that the result is acceptable. The algorithm can be generalized for calculating plane blanks of sheet metal parts in aeronautical and automobile industry.