As mentioned in the introduction to this report, the frictional contact/impact problem itself is very complicated and involves lots of theoretical, technical, and computational efforts.
Some issues still remain. The most important issues include the follows:
1. The virtual work equation for node-to-node contact algorithm is applicable to both planar and 3D problems. The finite element applications discussed in this report focus on planar problems and the algorithm was implemented with the bilinear quadrilateral element. While straightforward, expanding the node-to-node contact algorithm to three dimensional contact problems involves more computational ef- forts of prediction of contact positions. The mesh smoothing strategy in three di- mensions presents additional challenges.
2. Higher order elements have advantages over linear elements in some situation and the incorporation of higher order elements into the node-to-node contact algorithm would be useful. Implementation of other structural elements such as beams or plates may also be of interest.
3. Error analysis is very important for numerical methods and deserves further re- search. The node-to-node algorithm simplifies the integration in the contact inter- face, but frequent interpolation of the kinematic variables, such as displacement or velocity fields, may introduce new deficiencies. Algorithmic stability is another concern. The influence of the ALE algorithm on the stability performance needs additional research.
4. Efficiency still remains an issue because mesh smoothing, no matter how small, changes the mesh and requires regeneration of the system tangent stiffness matrix and the mass matrix. Thus, more computational efforts are needed in the new ap- proach compared with the traditional node-to-segment method. Improving the effi- ciency is urgent if the node-to-node contact method is to be a real competitor with the traditional methods. Developing highly efficient strategies to predict the contact positions and reducing the regeneration times of system matrixes might be achiev- able. Parallel computation in super computers is another opportunity to accelerate the solving procedure.
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