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

Abels, Helmut and Mora, Maria Giovanna and Müller, Stefan (2010) The time-dependent von Kármán plate equation as a limit of 3D nonlinear elasticity. Preprintreihe der Fakultät Mathematik 1/2010, Working Paper. (Unpublished)

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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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Item type:Monograph (Working Paper)
Series of the University of Regensburg:Preprintreihe der Fakultät Mathematik
Date:2010
Institutions:Mathematics > Prof. Dr. Helmut Abels
Classification:
NotationType
74K20MSC
74B20MSC
74H10MSC
35L70MSC
Keywords:dimension reduction, nonlinear elasticity, von Kármán plate equation, wave equation, elastodynamics
Dewey Decimal Classification:500 Science > 510 Mathematics
Status:Unpublished
Refereed:No, this version has not been refereed yet (as with preprints)
Created at the University of Regensburg:Yes
Deposited on:12 Feb 2010 09:43
Last modified:13 Mar 2014 12:53
Item ID:12837
Owner only: item control page

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