For fixed functions G,H:[0,∞)→[0,∞), consider the rotationally invariant probability density on Rn of form μn(ds)=1 ZnG(‖s‖2)e−nH(‖s‖2)ds. We show that when n is large, Euclidean norm ‖Yn‖2 a random vector Yn distributed according to μn satisfies thin-shell property, in its distribution highly likely concentrate around value s0 minimizing certain variational problem. Moreover, we fluctuations t...

We present a numerical study of the shape taken by a spherical elastic surface when the volume it encloses is decreased. For the range of 2D parameters where such a surface may model a thin shell of an isotropic elastic material, the mode of deformation that develops a single depression is investigated in detail. It occurs via buckling from sphere toward an axisymmetric dimple, followed by a se...

We rigorously establish the existence of the limit homogeneous constitutive law of a piezoelectric composite made of periodically perforated microstructures and whose reference configuration is a thin shell with fixed thickness. We deal with an extension of the Koiter shell model in which the three curvilinear coordinates of the elastic displacement field and the electric potential are coupled....

We consider three-dimensional reshaping of a thin nematoelastic film upon nematic-isotropic transition in the field of a charge one topological defect, leading to either cone or anticone (d-cone) shells. The analysis is based on the relation between the shell metric and the tensor order parameter under the assumption of no elastic deformation and volume change. The shape of the shell can be mod...

this study aimed to investigate the effects of stiffeners on buckling of thin cylindrical shells under uniform axial compression. to this end, more than 300 finite element models of stiffened cylindrical shells were prepared. the variables considered are shell thickness, number, dimension and the location of the vertical and horizontal stiffeners as well as circular symmetrical imperfections. r...

Our study presents a set of form-finding procedures to explore curved structures made from interlaced panels. Interlacing introduces a particular coupling between assembly components which has to be formulated along with a pertinent flexible body model. We examine here a hybrid approach: panels are simulated a first time using an elastic rod model formulated within a constrained elastic energy ...

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...

Thin-walled parts with curved surface are widely used in industrial applications and the high-quality machining is still a major problem because of low stiffness. By using machining-path obtained from design model thin-walled surface, accuracy requirement may easily not be met due to springback clamping deformation when process finished. It novel idea that mapping free-state clamped-state reali...