T-splines computational membrane-cable structural mechanics with continuity and smoothness: I. Method and implementation

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-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.

Automated summary

We introduce a T-splines computational method and its implementation that allows for connecting structures of different parametric dimensions with continuity and smoothness. We derive the basis functions for connecting structures with 2D and 1D parametric dimensions, involving proper selection of a scale factor for the knot vector of the 1D structure. The method can be extended to achieve higher-order continuity when needed.