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Existence of a solution for a nonlinearly elastic plane membrane “under tension”

Daniel Coutand (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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 $ℝ^{3}$ , is equivalent to finding the critical points...

Existence of equilibrium states of hollow elastic cylinders submerged in a fluid.

Elgindi, M.B.M., Yen, D.H.Y. (1992)

International Journal of Mathematics and Mathematical Sciences

Existence of maximal and minimal solutions to a boundary value problem for the equation of the bending of an elastic beam.

Hong, Shihuang, Xie, Suying, Zhang, Chunguo, He, Zerong (2007)

Sibirskij Matematicheskij Zhurnal

Existence of positive solutions of a discrete elastic beam equation.

Ma, Ruyun, Li, Jiemei, Gao, Chenghua (2010)

Discrete Dynamics in Nature and Society

Existence of solutions for prestressed shallow shells

W. Piechocki (1973)

Applicationes Mathematicae

Existence, uniqueness and stabilization for a nonlinear plate system with nonlinear damping

Carlos Frederico Vasconcellos, Lucia Maria Teixeira (1999)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Exponential stability and global attractors for a thermoelastic bresse system.

Ma, Zhiyong (2010)

Advances in Difference Equations [electronic only]

Exponential stability of a flexible structure with history and thermal effect

Roberto Díaz, Jaime Muñoz, Carlos Martínez, Octavio Vera (2020)

Applications of Mathematics

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.

Exponential stability of a von Kármán model with thermal effects.

Benabdallah, Assia, Teniou, Djamel (1998)

Electronic Journal of Differential Equations (EJDE) [electronic only]

External approximation of first order variational problems via W-1,p estimates

Cesare Davini, Roberto Paroni (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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 $W^{- 1, p}$ norms obtained by Nečas and on the general framework of Γ-convergence theory.

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