Zusammenfassung
We derive a two-dimensional model for elastic plates as a Gamma-limit of three-dimensional nonlinear elasticity with the constraint of incompressibility. The energy density of the reduced problem describes plate bending, and is determined from the elastic moduli at the identity of the energy density of the three-dimensional problem. Without the constraint of incompressibility, Gamma-convergence ...
Zusammenfassung
We derive a two-dimensional model for elastic plates as a Gamma-limit of three-dimensional nonlinear elasticity with the constraint of incompressibility. The energy density of the reduced problem describes plate bending, and is determined from the elastic moduli at the identity of the energy density of the three-dimensional problem. Without the constraint of incompressibility, Gamma-convergence to a plate theory was first derived by Friesecke, James and Moller. The main difficulty in the present result is the construction of a recovery sequence which satisfies pointwise the nonlinear constraint of incompressibility.
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