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A dynamic evolution model for perfectly plastic plates
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DOI：10.1142/S0218202516500469.png)
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We consider the dynamic evolution of a linearly elastic-perfectly plastic thin plate subject to a purely vertical body load. As the thickness of the plate goes to zero, we prove that the three-dimensional evolutions converge to a solution of a certain reduced model. In the limiting model admissible displacements are of Kirchhoff-Love type. Moreover, the motion of the body is governed by an equilibrium equation for the stretching stress, a hyperbolic equation involving the vertical displacement and the bending stress, and a rate-independent plastic flow rule. Some further properties of the reduced model are also discussed.
Keyword:
Perfect plasticity
thin plates
Prandtl-Reuss plasticity
dynamic evolution
functions of bounded deformation
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