Designing a curved architectural envelope is a challenging task, as it requires a balance between structural efficiency, fabricability, and architectural requirements. In this article, we introduce a new conceptual design tool: Linear‐Weingarten membranes, with boundaries either simply supported or realized as funicular cables or arches. We present a generation method for these surfaces, with a focus on how to treat free funicular boundaries. The method uses a surface discretization by triangular meshes, and computes a shape iteratively by a combination of dynamic relaxation and guided projections. The method can be used to generate the shape of self‐stressed membranes, funicular vaults, and gridshells. For gridshells, the method allows to find geometries that combine mechanical performance and ease of fabrication. For membranes, the method allows for an exploration of a rich design space, with very limited preprocessing work required for the designer: it is hence well suited as a conceptual design tool.

中文翻译：

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带缆索边界的线性Weingarten膜

设计弯曲的建筑围护结构是一项艰巨的任务，因为它需要在结构效率，可制造性和建筑要求之间取得平衡。在本文中，我们介绍了一种新的概念设计工具：线性魏恩加滕膜，其边界可以简单地支撑或实现为缆索缆索或拱形。我们介绍了这些表面的生成方法，重点是如何处理自由的缆索边界。该方法使用通过三角网格进行的表面离散化，并通过动态松弛和导向投影的组合迭代地计算形状。该方法可用于生成自应力膜，缆索拱顶和板壳的形状。对于板壳，该方法可以找到兼具机械性能和易加工性的几何形状。对于膜，