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...

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 nonlinear simplified model admits always minimizers by contrast with the original one. We show the relevance of our approach by proving that the rescaled minimum of the simplified model and the rescaled infimum of the full model have the same limit...

We summarize some recent results of the authors and their collaborators, regarding the derivation of thin elastic shell models (for shells with mid-surface of arbitrary geometry) from the variational theory of 3d nonlinear elasticity. We also formulate a conjecture on the form and validity of infinitely many limiting 2d models, each corresponding to its proper scaling range of the body forces i...

The applicability and limitations of simplified models thin elastic circular cylindrical shells for linear vibrations double-walled carbon nanotubes (DWCNTs) are considered. models, which based on the assumptions membrane moment approximate thin-shell theories, compared with extended Sanders–Koiter shell theory. Actual discrete DWCNTs modelled by means couples concentric equivalent continuous t...

This paper presents a finite element based numerical study on controlling the postbuckling behavior of thin-walled cylindrical shells under axial compression. With the increasing interest of various disciplines for harnessing elastic instabilities in materials and mechanical systems, the postbuckling behavior of thin-walled cylindrical shells may have a new role to design materials and structur...

Thin-walled structures like crash boxes may be used as energy absorption members in automotive chassis. There have been many studies addressing the behaviors of energy absorption members on frontal crash. These researches have attempted to predict the energy absorption and maximum impact load in shell structures. The energy absorption and maximum impact load depend on many parameters including ...

The open profile thin elastic wavy shell natural oscillations problem is considered. proposed method for determining the numerical values of lowest frequencies and corresponding forms vibrations shells with a complicated shape based on Rayleigh-Ritz energy method. results calculation rigidly pinched lower contour are presented.

The object of considerations is a thin linear-elastic cylindrical shell having a periodic structure along one direction tangent to the shell midsurface. The aim of this paper is to propose a new averaged nonasymptotic model of such shells, which makes it possible to investigate free and forced vibrations, parametric vibrations, and dynamical stability of the shells under consideration. As a too...

The spectral problem of thin elastic shells in membrane approximation does not satisfy the classical properties of compactness and so there exists an essential spectrum. In the first part, we propose to determinate this spectrum and the weakness directions in the shell. We particularly study the case of homogeneous and isotropic shells with some examples. In the second part, we consider an elem...