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We consider functionals of a potential energy $\PP_{\psi} (u)$ corresponding to $\it {an axisymmetric boundary-value problem}$. We are dealing with $\it {a deflection of a thin annular plate}$ with $\it {Neumann boundary conditions}$. Various types of the subsoil of the plate are described by various types of the $\it {nondifferentiable}$ nonlinear term $\psi (u)$. The aim of the paper is to find a suitable computational algorithm.
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