2138 Nonlinear Theory of Thin Elastic Shells under the Kirchhoff Hypothesis(Structures)

The Nonlinear Theory of Elastic Shells with Phase Transitions

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Intrinsic nonlinear models of shells for Saint Venant-Kirchhoff materials

The first complete linear theory, based on Kirchhoff’s [1850] earlier works on plates, was given by Love [1888]. The modern theory (linear and nonlinear) comes from the works by Naghdi and Koiter in the sixties. In such models the displacement variables are functions defined on the mean surface and the resulting equations are differential equations on a smooth 2-dimensional submanifold of the t...

A simplified model for elastic thin shells

We introduce a simplified model for the minimization of the elastic energy in thin shells. This model is not obtained by an asymptotic analysis. The thickness of the shell remains a parameter as in Reisner-Mindlin’s model for plates and Koiter’s model for shells in the linear case. The simplified model admits always minimizers by contrast with the original one. We show the relevance of our appr...

Influence of the Elastic Foundation on the Free Vibration and Buckling of Thin-Walled Piezoelectric-Based FGM Cylindrical Shells Under Combined Loadings

In this paper, the influence of the elastic foundation on the free vibration and buckling of thin-walled piezoelectric-based functionally graded materials (FGM) cylindrical shells under combined loadings is investigated. The equations of motion are obtained by using the principle of Hamilton and Maxwell's equations and the Navier's type solution used to solve these equations. Material propertie...

Local Symmetry Group in the General Theory of Elastic Shells