Terahara, TakuyaTakizawa, KenjiTezduyar, Tayfun E.2023-03-102023-03-102023Terahara, Takuya, Takizawa, Kenji and Tezduyar, Tayfun E.. "T-splines computational membrane–cable structural mechanics with continuity and smoothness: I. Method and implementation." <i>Computational Mechanics,</i> 71, (2023) Springer Nature: 657-675. https://doi.org/10.1007/s00466-022-02256-w.https://hdl.handle.net/1911/114509We present a T-splines computational method and its implementation where structures with different parametric dimensions are connected with continuity and smoothness. We derive the basis functions in the context of connecting structures with 2D and 1D parametric dimensions. Derivation of the basis functions with a desired smoothness involves proper selection of a scale factor for the knot vector of the 1D structure and results in new control-point locations. While the method description focuses on $$C^0$$and $$C^1$$continuity, paths to higher-order continuity are marked where needed. In presenting the method and its implementation, we refer to the 2D structure as “membrane” and the 1D structure as “cable.” It goes without saying that the method and its implementation are applicable also to other 2D–1D cases, such as shell–cable and shell–beam structures. We present test computations not only for membrane–cable structures but also for shell–cable structures. The computations demonstrate how the method performs.engThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.Journal articles00466-022-02256-whttps://doi.org/10.1007/s00466-022-02256-w