基于弹簧-质点系统的薄膜结构曲面展开算法

将用三角形描述的空间膜片映射到初始二维膜片上，并使初始二维膜片与被展空间膜片在参
数域与空间域具有相同的拓扑结构。描述空间膜片的三角形与描述平面膜片的三角形的边长存在差异，采
用单元节点力代替此差异，节点质量由节点周围的膜单元面积确定，得到了描述系统运动的拉格朗日方程
。在求解方程时，每个时间段迭代初始速度置为零，计算过程中节点匀速运动，从而有效地避免了振幅过
大和发散问题，收敛速度明显加快。平面膜片的局部精度通过弹簧弹性变形系数予以控制，能够满足膜片
边界要求。该曲面展开方法具有精度高、计算速度快和易收敛的特点。

Membrane surface flattening algorithm based on spring-mass system

Membrane surface was divided into several strips composed of triangular elements. The membrane strips were projected to a plane to obtain the initial shape which had the same topology structures as the spatial strip in the parameter and spatial fields. The node forces induced by the difference between the boundary lengths of the spatial triangular elements and the plane triangular elements were applied to the element nodes of the plane strips. Each node's mass of triangular elements was calculated by the area of the elements which surrounded the node. Lagrange dynamic equation was set up for the system. The nodes' velocities maintain invariable in an interval for convergence. The local precision of membrane strip flattening was easily controlled by adjusting the spring distortion coefficients. Numerical examples show that the algorithm has good precision and convergence characteristics.