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- 2018 (3) (entfernen)
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Eingeladener Vortrag
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In this paper, a contact problem between two bodies, discretized by finite elements, is solved by adding an auxiliary NURBS layer between the bodies. The advantages of a smooth contact formulation in a NURBS approach are combined with simple mesh generation procedures for the bodies discretized with finite elements. Mesh tying conditions are used to couple the NURBS layer with the finite element discretization. The NURBS layer is the master side for contact and mesh tying. Mesh tying is enforced either using pointwise or mortar type approaches. Frictionless 2D and 3D contact problems are considered using small deformations. The contact problem is discretized with the mortar method and a penalty approach is used to enforce the contact constraints. A robust element-based quadrature is applied for mortar tying and contact discretizations, thus avoiding computationally expensive Segmentation.
Coupling of an isogeometric surface and bulk finite element discretization for contact problems
(2018)
The finite element (FE) framework is a standard tool for the simulation of mechanical problems providing advantages like automated meshing algorithms and effcient quadrature rules. However, for contact problems, the FE discretization is - due to the C0 continuity at element intersections - characterized by a non-smooth normal feld.
Conversely, isogeometric discretizations provide a smooth normal feld also at interelement borders and were recently applied to contact mechanical problems using the mortar method. The application of isogeometric analysis for complex volumetric problems has not reached the same level of automation as the FE-framework, i.e. due to the intricate mesh generation.
This work aims at combining the advantages of both discretization procedures by coupling an isogeometric contact surface with a bulk FE-discretization. The isogeometric contact interface is represented by a NURBS surface, which is tied to the FE mesh. For the discretization of the bulk parts, higher order spectral elements are used. The contact problem is discretized with the mortar method and a penalty approach is used to enforce the contact constraints. Two different types of coupling of the NURBS surface and the bulk part are considered: mortar and pointwise mesh tying. The mortar mesh tying approach shows accurate results, whereas the pointwise tying leads to large oscillations in the contact stresses. Element-based quadrature is applied for mortar tying, as well as for mortar contact discretizations. Using an isogeometric layer, the related quadrature error can be effciently reduced by a higher degree interpolation or increased integration order.
Coupling of an isogeometric surface and bulk finite element discretization for contact problems
(2018)
This work aims at combining the advantages of both discretization procedures (IGA and FEM) by coupling an isogeometric contact surface with a bulk FE-discretization. The isogeometric contact interface is represented by a NURBS surface, which is tied to the FE mesh. For the discretization of the bulk parts, higher order spectral elements are used. The contact problem is discretized with the mortar method and a penalty approach is used to enforce the contact constraints. Two different types of coupling of the NURBS surface and the bulk part are considered: mortar and pointwise mesh tying. The mortar mesh tying approach shows accurate results, whereas the pointwise tying leads to large oscillations in the contact stresses. Element-based quadrature is applied for mortar tying, as well as for mortar contact discretizations. Using an isogeometric layer, the related quadrature error can be efficiently reduced by a higher degree interpolation or increased integration order.