Spline-based smooth beam-to-beam contact model

Numerical strategy for solving general C1‐continuous beam‐to‐beam contact problems

“…The objective of this section is not to show in detail the already established spline‐based contact formulation adopted, but to provide a basis for the contact problem discussions presented further. More information about the spline‐based contact formulation is found in Reference 20.…”

“…Spline element basis functions, curve, and spline‐based surface. Extracted from Reference 20. (A) Spline element basis functions produced with the reduced knot vector $$$ \Xi =\left\{0,0,1/3,2/3,1,1\right\} $$$; (B) Spline element curve; (C) Spline‐based surface.…”

“…When penetration is characterized, nonlinear normal and tangential interface laws are used to represent the mechanical interaction. To keep the present work concise, such interface laws are not here discussed but presented in detail in Reference 20.…”

“…Moreover, the existence of sharp corners in $$$ {C}^0 $$$ meshes leads to singularities in normal vector description, which can potentially lead to convergence difficulties. To circumvent this issue, a possible procedure is to decouple the contact formulation from the solid/structural model by introducing smooth geometric descriptions such as splines, Bézier curves, or Hermite polynomials, see References 14‐20. The overall objective of these smooth geometrical descriptions is to avoid possible continuity issues related to ill‐defined geometries.…”

“…To show the robustness of the proposed scheme, challenging examples with conformal contacts are discussed. The structural model and contact formulations adopted are, respectively, the geometrically exact beam theory and the spline‐based $$$ {C}^1 $$$ master–master contact model 20 . In the adopted spline‐based formulation all contact forces are calculated with respect to the centerlines of the beams.…”