In this article we propose and analyze a Virtual Element Method (VEM) to approximate the isolated solutions of von Kármán equations, which describe deformation very thin elastic plates. We consider variational formulation in terms two variables: transverse displacement plate Airy stress function. The VEM scheme is conforming H 2 for both variables has advantages supporting general polygonal mes...

In this paper, we prove the local exact null controllability of the thermoelastic plate model, in the absence of rotational inertia, and under the influence of the (non-Lipschitz) von Kármán nonlinearity. The plate component may be taken to satisfy either the clamped or higher order (and physically relevant) free boundary conditions. In the accompanying analysis, critical use is made of sharp o...

We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large times under appropriate scaling of the initial values such that the limit system as h → 0 is either the nonlinear von Kármán plate equation or the linear fourth order Germain-Lagrange equa...