Dynamic frictionless contact of a nonlinear beam with two stops

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.

Keywords:

• dynamic contact
• Gao beam
• Signorini contact conditions
• complementarity conditions

AMS Subject Classifications:

• Primary: 74M20
• 74K10
• Secondary: 35L85

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].