Inserted: 21 dec 2009
Last Updated: 14 oct 2011
Journal: Calc. Var. Partial Differential Equations
The asymptotic behaviour of the 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.
Keywords: dimension reduction, nonlinear elasticity, von Kármán plate equation, wave equation, elastodynamics