Computational generation and conformal fabrication of woven fabric structures by harmonic foliation

• Published in: Computer methods in applied mechanics and engineering Vol. 363; pp. 1 - 19
• Main Authors: Guo, Yang, Ye, Qian, Zheng, Xiaopeng, Chen, Shikui, Lei, Na, Zhang, Yuanqi, Gu, David Xianfeng
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-05-2020; Elsevier BV
• Subjects: Aircraft performance; Avionics; Conformal; Fabric structures; Foliation; Free form; Freeform surfaces; Harmonic map; Lower bounds; Metal sheets; Orthogonality; Shells (structural forms); Smoothness; Tensors; Thin-shell structure; Topology; Warp; Weft; Woven composites; Woven fabrics; Conformal; Thin-shell structure; Freeform surfaces; Foliation; Harmonic map; Woven fabrics
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2020.112874

This paper presents a framework for computational generation and conformal fabrication of woven thin-shell structures with arbitrary topology based on the foliation theory which decomposes a surface into a group of parallel leaves. By solving graph-valued harmonic maps on the input surface, we construct two sets of harmonic foliations perpendicular to each other. The warp and weft threads are created afterward and then manually woven to reconstruct the surface. The proposed computational method guarantees the smoothness of the foliation and the orthogonality between each pair of leaves from different foliations. Moreover, it minimizes the number of singularities to theoretical lower bound and produces the tensor product structure as globally as possible. This method is ideal for the physical realization of woven surface structures on a variety of applications, including wearable electronics, sheet metal craft, architectural designs, and conformal woven composite parts in the automotive and aircraft industries. The performance of the proposed method is demonstrated through the computational generation and physical fabrication of several free-form thin-shell structures.
•Use foliation theory for woven fabric, link free-form surface with in-plane textiles.•General to surfaces with arbitrary topologies.•Global tensor product structure with minimal singularities, orthogonal crossing angles, no dangling threads.•Computation algorithm is robust, efficient and automatic.