This paper introduces a novel method for shape optimization and form-finding of free-form, triangular grid shells, based on geometric deep learning. We define an architecture which consumes a 3D mesh representing the initial design of a free-form grid shell, and outputs vertex displacements to get an optimized grid shell that minimizes structural compliance, while preserving design intent. The main ingredients of the architecture are layers that produce deep vertex embeddings from geometric input features, and a differentiable loss implementing structural analysis. We evaluate the method performance on a benchmark of eighteen free-form grid shell structures characterized by various size, geometry, and tessellation. Our results demonstrate that our approach can solve the shape optimization and form finding problem for a diverse range of structures, more effectively and efficiently than existing common tools.

本文介绍了一种基于几何深度学习的自由形状三角形网格壳形状优化和找形的新方法。我们定义了一种架构，它使用代表自由形式网格壳初始设计的 3D 网格，并输出顶点位移以获得优化的网格壳，最大限度地减少结构合规性，同时保留设计意图。该架构的主要组成部分是从几何输入特征生成深度顶点嵌入的层，以及实现结构分析的可微损失。我们以十八个自由形式网格壳结构为基准来评估该方法的性能，这些结构具有不同的尺寸、几何形状和镶嵌形状。我们的结果表明，我们的方法可以比现有的常用工具更有效和高效地解决各种结构的形状优化和找形问题。