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Newmark Structural Laboratory Report Series (NSEL Report Series ISSN 1940-9826) >
Please use this identifier to cite this item:
http://hdl.handle.net/2142/5318
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| Title: |
A New Node-Node to-Node Approach to Contact/Impact Problems for Two-Dimensional Elastic Solids Subject to Finite Deformation |
| Authors: |
Xu, Daqing
Hjelmstad, Keith D. |
| Keywords: |
Contact
Impact
Finite Element
Moving Mesh
Arbitrary Lagrangian Eulerian (ALE) |
| Issue Date: |
2008-May |
| Publisher: |
Newmark Structural Engineering Laboratory. University of Illinois at Urbana-Champaign. |
| Series Name / Report no.: |
Newmark Structural Engineering Laboratory Report Series 009 |
| Abstract / Summary: |
Contact analysis is an important branch of solid mechanics. Numerical simulation using
the finite element method has become the dominant approach recently because of
the high nonlinearity of contact problems. In the traditional Lagrangian description for
solid mechanics, the numerical nodes are attached to the material particles, making it
impossible to maintain node-to-node contact due to independent deformation. Various
node-to-segment or segment-to-segment treatments are proposed to discretize the contact
interface. But some issues still exist. Specifically, mesh distortion or element entanglement
may be present if deformation is large.
A new node-to-node approach for 2D contact/impact problems subject to finite deformation
is proposed in this report to offer an alternative approach to these traditional
methods, wherein node-to-node contact is maintained throughout the contact process.
This method is based on the Arbitrary Lagrangian-Eulerian algorithm (ALE). One or
both bodies in the two-body contact problem have an ALE mesh, which is independent
of the material particles and has prescribed motion set to maintain node-to-node contact.
The strategy of the ALE mesh motion has two steps: (1) to move nodes in the active set
to maintain node-to-node contact (2) to smooth ALE mesh to improve mesh quality using
the Laplacian or angle-based smoothing algorithm.
Problems of interest in this study are contact/impact problems wherein the implicit
mid-point rule is used as the primary time stepping algorithm to find the solution incrementally.
In order to conserve the system energy, the persistency condition is incorporated
as the contact constraint. The augmented Lagrangian method is primarily used to
apply contact constraints. Non-classical Coulomb friction laws are used where friction
is present. Several quasi-static and impact examples are given to demonstrate the performance
and validity of the new approach. |
| URI: |
http://hdl.handle.net/2142/5318 |
| ISSN: |
1940-9826 |
| Type of Resource: |
text |
| Genre of Resource: |
technical report |
| Publication Status: |
published or submitted for publication |
| Appears in Collections: |
Newmark Structural Laboratory Report Series (NSEL Report Series ISSN 1940-9826)
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