The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity

2009/12/21 by Abels, Helmut, Mora, Maria Giovanna, Müller, Stefan · 1 citation
#35L70 #74B20 #74H10 #74K20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0912.4135

Abstract

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.

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• Dimension reduction for time-dependent von Kármán rods

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