TY - JOUR
T1 - T-splines computational membrane–cable structural mechanics with continuity and smoothness
T2 - I. Method and implementation
AU - Terahara, Takuya
AU - Takizawa, Kenji
AU - Tezduyar, Tayfun E.
N1 - Funding Information:
This work was supported in part by Grant-in-Aid for Scientific Research (A) 18H04100 from Japan Society for the Promotion of Science, JST-CREST JPMJCR1911, Rice–Waseda research agreement, and International Technology Center Indo-Pacific (ITC IPAC) Contract FA520921C0010. The work was also supported by Grant-in-Aid for Research Activity Start-up 20K22401 and Grant-in-Aid for Early-Career Scientists 22K17903 from Japan Society for the Promotion of Science (first author). The mathematical model and computational method parts of the work were supported in part by ARO Grant W911NF-17-1-0046 and Top Global University Project of Waseda University (third author).
Publisher Copyright:
© 2023, The Author(s).
PY - 2023/4
Y1 - 2023/4
N2 - We 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 and C1 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.
AB - We 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 and C1 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.
KW - Continuity
KW - Isogeometric analysis
KW - Membrane–cable structure
KW - Shell–beam structure
KW - Shell–cable structure
KW - Smoothness
KW - T-splines
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U2 - 10.1007/s00466-022-02256-w
DO - 10.1007/s00466-022-02256-w
M3 - Article
AN - SCOPUS:85145831326
SN - 0178-7675
VL - 71
SP - 657
EP - 675
JO - Computational Mechanics
JF - Computational Mechanics
IS - 4
ER -