The time-dependent von K\'arm\'an shell equation as a limit of three-dimensional nonlinear elasticity
Analysis of PDEs
2018-04-17 v2
Abstract
The asymptotic behaviour of solutions of three-dimensional nonlinear elastodynamics in a thin shell is considered, as the thickness of the shell tends to zero. Given the appropriate scalings of the applied force and of the initial data in terms of it's verified that three-dimensional solutions of the nonlinear elastodynamic equations converge to solutions of the time-dependent von K\'arm\'an equations or dynamic linear equations for shell of arbitrary geometry.
Cite
@article{arxiv.1802.00593,
title = {The time-dependent von K\'arm\'an shell equation as a limit of three-dimensional nonlinear elasticity},
author = {Yizhao Qin and Pengfei Yao},
journal= {arXiv preprint arXiv:1802.00593},
year = {2018}
}