任意空间曲面近似展开成平面的增量有限元算法

Truss element method for cutting pattern of membrane structures

提出了任意空间曲面近似展成平面的准则 ,证明了这一准则与有限单元法中节点残余力向量等于零的等效性 ,推导了空间曲面展成平面的增量有限单元计算方法。对于可展曲面 ,本文方法给出的是精确的展开平面 ;对于不可展曲面 ,本文方法给出的是最接近的展开平面。本文方法具有计算快速、收敛稳定、易于实现等特点。本文理论可用于工程中的各类曲面展开问题 。

In this paper the principle for development of arbitrary curved surface is proposed. Such principle is proved equivalent to the condition of zero residual forces of FEA equation for plane structures. The increment FEA method and iterative procedures are derived to develop curved surfaces. For developable surfaces the method of this paper will present the accurate flattened forms, and for non developable surfaces this paper can lead to the closest flattened form. Numerical examples show that the method of this paper has stable convergence and high efficiency. It can be easily used in solving the problems of surface development in different engineering fields, especially for cutting pattern of membrane structures.