@article {2011, title = {The time-dependent von K{\'a}rm{\'a}n plate equation as a limit of 3d nonlinear elasticity}, journal = {Calculus of Variations and Partial Differential Equations 41 (2011) 241-259}, number = {SISSA;74/2009/M}, year = {2011}, publisher = {Springer}, 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 K\\\\\\\'arm\\\\\\\'an plate equation.}, doi = {10.1007/s00526-010-0360-0}, url = {http://hdl.handle.net/1963/3835}, author = {Helmut Abels and Maria Giovanna Mora and Stefan M{\"u}ller} }