Abstract
The asymptotic behaviour of solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness h of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values in terms of h, it is shown that three-dimensional solutions of the nonlinear elastodynamic equation converge to solutions of the time-dependent von Kármán plate equation.
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Communicated by L. Ambrosio.
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Abels, H., Mora, M.G. & Müller, S. The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity. Calc. Var. 41, 241–259 (2011). https://doi.org/10.1007/s00526-010-0360-0
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DOI: https://doi.org/10.1007/s00526-010-0360-0