A numerical form-finding method for the minimal surface of membrane structures
A numerical form-finding method for the minimal surface of membrane structures
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DOI：
10.1007/s00158-014-1127-6
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发表时间：
2014-08
影响因子：
3.9
通讯作者：
M. Shimoda;K. Yamane
中科院分区：
文献类型：
--
作者：
M. Shimoda;K. Yamane
本文提出了一种简便的数值寻形方法，用于设计具有指定任意边界的膜结构的最小曲面或等张曲面。将面积最小化问题描述为分布参数形状优化问题。根据结构类型，例如气动或悬浮膜，添加内部体积或周长作为约束。假设膜在表面的面外和/或面内方向上变化。用材料导数法导出了每个问题的形状灵敏度函数。在不需要形状参数的情况下，最小曲面由Hilbert空间中的一种梯度方法--自由形式最优化方法确定，其中形状是在Robin边界条件下由牵引力与灵敏度函数成比例变化的。计算结果表明，该方法用于膜结构的优化找形是有效的和实用的。
This paper proposes a convenient numerical form-finding method for designing the minimal surface, or the equally tensioned surface of membrane structures with specified arbitrary boundaries. Area minimization problems are formulated as a distributed-parameter shape optimization problem. The internal volume or the perimeter is added as a constraint according to the structure type such as a pneumatic or a suspension membrane. It is assumed that the membrane is varied in the out-of-plane and/or the in-plane direction to the surface. The shape sensitivity function for each problem is derived using the material derivative method. The minimal surface is determined without shape parameterization by the free-form optimization method, a gradient method in the Hilbert space, where the shape is varied by the traction force in proportion to the sensitivity function under the Robin boundary condition. The calculated results show the effectiveness and practical utility of the proposed method for optimal form-finding of membrane structures.