Contact-Impact Treatment in Explicit Transient Dynamics Using Isogeometric Analysis With Nurbs

Abstract eng:
The main difficulty in the contact analysis is a non-smoothness of contacting surfaces. It arises from inequality constraints as well as from geometric discontinuities induced by spatial discretization. The contact analysis based on traditional finite elements utilizes element facets to describe a contact surface. Unfortunately, the facet interfaces are only C0 continuous so that normal surface vectors may experience jump across element boundaries, which may lead to artificial oscillations of contact forces. A remedy to this geometric discontinuity may be provided by isogeometric formulation [1]. In this approach, the known geometry is accurately described by the Non-Uniform Rational B-Splines (NURBS) basis functions [2], which serve at the same time as the element basis functions. The isogeometric analysis provides some additional advantage, which is especially attractive to contact analysis, namely, preserving geometric continuity, facilitating patch-wise contact search, supporting a variationally consistent formulation, and having a uniform data structure for the contact surface and the underlying volumes. Recently, two penalty-based isogeometric contact algorithms were proposed in reference [3]. The former is the so-called knot-to-surface (KTS) algorithm. It is a straightforward extension of the classic node-to-surface (NTS) algorithm. Since the NURBS control points are not interpolatory, contact constraints are enforced directly at the quadrature points. It was shown in the same reference that this approach was over-constrained and therefore not acceptable if a robust formulation with accurate tractions was desired. The second algorithm is called the mortar-KTS algorithm. Here, a mortar projection of the contact pressures at control points is employed to obtain the correct number of constraints. In this paper, the mortar-KTS contact algorithm is utilized tohether with the central difference time integration scheme. The present algorithm is studied by means of a numerical example, which involves impact of two elastic tubes. The results clearly demonstrate the superiority of the NURBS discretization over the conventional Lagrange polynomial ansatz. Acknowledgements to GA101/09/1630 and GAP101/12/2315 under AV0Z20760514.

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