Abstract
The efficient solution of discrete models of contacting elastic bodies is investigated. At each discrete zone of the model the bodies are either in contact or not, so one of two possible linear system equations applies. The choice of equation in each zone is defined to be a binary nonlinearity. A weighting-function description of the elastic system is developed in which the binary nonlinearity is incorporated by use of partial Gauss-Jordan elimination of a model of full contact. This allows rapid solution to the contact problem. The solution scheme is shown to be stable as each iteration reduces the energy stored in the system. Worked examples are given. The work applies not only in contact mechanics, but also to other discrete models in which binary nonlinearities appear.
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Allwood, J., Stubbs, R. & Bryant, G. An efficient treatment of binary nonlinearities applied to elastic contact problems without friction. Journal of Engineering Mathematics 31, 81–98 (1997). https://doi.org/10.1023/A:1004205601629
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DOI: https://doi.org/10.1023/A:1004205601629