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Applicable Analysis
An International Journal
Volume 94, 2015 - Issue 7
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Articles

Dynamic frictionless contact of a nonlinear beam with two stops

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Pages 1355-1379 | Received 25 Mar 2014, Accepted 30 May 2014, Published online: 27 Jun 2014
 

Abstract

In this work, we consider mathematical and numerical approaches to a dynamic contact problem with a highly nonlinear beam, the so-called Gao beam. Its left end is rigidly attached to a supporting device, whereas the other end is constrained to move between two perfectly rigid stops. Thus, the Signorini contact conditions are imposed to its right end and are interpreted as a pair of complementarity conditions. We formulate a time discretization based on a truncated variational formulation. We prove the convergence of numerical trajectories and also derive a new form of energy balance. A fully discrete numerical scheme is implemented to present numerical results.

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Notes

1 This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology [NRF-2012R1A2A2A01046471].

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