Decomposition of the deformations of a thin shell. Nonlinear elastic models
نویسندگان
چکیده
We investigate the behavior of the deformations of a thin shell, whose thickness δ tends to zero, through a decomposition technique of these deformations. The terms of the decomposition of a deformation v are estimated in terms of the L-norm of the distance from ∇v to SO(3). This permits in particular to derive accurate nonlinear Korn’s inequalities for shells (or plates). Then we use this decomposition technique and estimates to justify a nonlinear bending model for elastic shells for an elastic energy of order δ.
منابع مشابه
Postbuckling Equilibrium Path of a Long Thin-Walled Cylindrical Shell (Single-Walled Carbon Nanotube) under Axial Compression Using Energy Method
In this paper, an elastic shell model is presented for postbuckling prediction of a long thinwalledcylindrical shell under axial compression. The Ritz method is applied to solve the governingequilibrium equation of a cylindrical shell model based on the von-Karman type nonlinear differentialequations. The postbuckling equilibrium path is obtained using the energy method for a long thin-walledcy...
متن کاملDecomposition of the deformations of a thin shell. Asymptotic behavior of the Green-St Venant's strain tensor
We investigate the behavior of the deformations of a thin shell, whose thickness δ tends to zero, through a decomposition technique of these deformations. The terms of the decomposition of a deformation v are estimated in terms of the L-norm of the distance from ∇v to SO(3). This permits in particular to derive accurate nonlinear Korn’s inequalities for shells (or plates). Then we use this deco...
متن کاملModelling of Random Geometrical Imperfections and Reliability Calculations for Thin Cylindrical Shell Subjected to Lateral Pressure
It is well known that it is very difficult to manufacture perfect thin cylindrical shell. Initial geometrical imperfections existing in the shell structure is one of the main determining factor for load bearing capacity of thin cylindrical shell under uniform lateral pressure. As these imperfections are random, the strength of same size cylindrical shell will also random and a statistical metho...
متن کاملRadial Breathing Mode Frequency of Multi-Walled Carbon Nanotube Via Multiple-Elastic Thin Shell Theory
In this paper, the radial breathing mode (RBM) frequencies of multi-walled carbon nanotubes (MWCNTs) are obtained based on the multiple-elastic thin shell model. For this purpose, MWCNT is considered as a multiple concentric elastic thin cylindrical shells, which are coupled through van der Waals (vdW) forces between two adjacent tubes. Lennard-Jones potential is used to calculate the vdW ...
متن کاملA General Form Solution for Elastic Buckling of Thin Cylinders Made of FGM under Axial Loading
In this article, the axisymmetric mechanical buckling of thin cylindrical shell made of functionally graded material (FGM) is considered. The governing equations for a thin cylinder based on the first-order shell theory and Timoshenko's assumptions are obtained. The equations are derived using the Sanders simplified kinematic relations and the principle of work and energy. The constituent mater...
متن کامل