Dynamic frictionless contact of a nonlinear beam with two stops |
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Authors: | Jeongho Ahn Eun-Jae Park |
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Institution: | 1. Department of Mathematics and Statistics, Arkansas State University, State University, AR, USA.jahn@astate.edu;3. Department of Mathematics, Yonsei University, Seoul 120-749, Korea.;4. Department of Computational Science and Engineering, Yonsei University, Seoul 120-749, Korea. |
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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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Keywords: | dynamic contact Gao beam Signorini contact conditions complementarity conditions |
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