# Dynamic frictionless contact of a nonlinear beam with two stops

Jeongho Ahn, Eun Jae Park

Research output: Contribution to journalArticle

1 Citation (Scopus)

### 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.

Original language English 1355-1379 25 Applicable Analysis 94 7 https://doi.org/10.1080/00036811.2014.931026 Published - 2015 Jul 3

### Fingerprint

Frictionless Contact
Dynamic Contact
Energy balance
Trajectories
Energy Balance
Complementarity
Time Discretization
Variational Formulation
Dynamic Problem
Contact Problem
Numerical Scheme
Contact
Trajectory
Numerical Results
Form

### All Science Journal Classification (ASJC) codes

• Analysis
• Applied Mathematics

### Cite this

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title = "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.",
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In: Applicable Analysis, Vol. 94, No. 7, 03.07.2015, p. 1355-1379.

Research output: Contribution to journalArticle

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T1 - Dynamic frictionless contact of a nonlinear beam with two stops

AU - Ahn, Jeongho

AU - Park, Eun Jae

PY - 2015/7/3

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N2 - 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.

AB - 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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