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A justification of the two-dimensional nonlinear “membrane”
equations for a plate made of a Saint Venant-Kirchhoff material has
been given by Fox et al. [9] by means of the method of formal
asymptotic expansions applied to the three-dimensional equations of
nonlinear elasticity. This model, which retains the material-frame
indifference of the original
three dimensional problem in the sense that its energy density is
invariant under the rotations of , is equivalent to finding the
critical points...
In this paper we study the asymptotic behavior of a system composed of an integro-partial differential equation that models the longitudinal oscillation of a beam with a memory effect to which a thermal effect has been given by the Green-Naghdi model type III, being physically more accurate than the Fourier and Cattaneo models. To achieve this goal, we will use arguments from spectral theory, considering a suitable hypothesis of smoothness on the integro-partial differential equation.
Here we present an approximation method for a rather broad class of first order
variational problems in spaces of piece-wise constant functions over
triangulations of the base domain. The convergence of the method is based on an
inequality involving norms obtained by Nečas and on the general
framework of Γ-convergence theory.
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