Abstract
In this work, we provide mathematical and numerical analyses for a thermoviscoelastic nonlinear beam model with Coulomb friction dry law. Since the dynamic frictional conditions are nonsmooth, a regularization technique with smoothing parameters is applied to approximate a nonlinear variational formulation. We prove the existence of weak solutions satisfying the regularized variational formulation based on a priori estimates and results for a pseudomonotone operator. Then, we pass to limits, as the smoothing parameters tend to be zero, in order to show convergence results for the regularized formulation. We propose the fully discrete numerical schemes in which a guarded Newton method is used to compute fully discrete numerical approximations of a nonlinear system at each time step. Numerical experiments are performed with selected data to present numerical simulations as well.
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Ahn, J. Dynamic frictional thermoviscoelastic Gao beams. Z. Angew. Math. Phys. 72, 194 (2021). https://doi.org/10.1007/s00033-021-01632-5
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DOI: https://doi.org/10.1007/s00033-021-01632-5
Keywords
- Nonlinear Gao beams
- Coulomb friction
- Discontinuous frictional coefficient
- Pseudomonotone operator
- Fully discrete numerical schemes