On microscopic scales, the crystallinity of flexible tethered or cross-linked membranes determines their mechanical response. We show that by controlling the type, number, and distribution of defects on a spherical elastic shell, it is possible to direct the morphology of these structures. Our numerical simulations show that by deflating a crystalline shell with defects, we can create elastic s...

We present a novel approach to probe elastic properties of polyelectrolyte multilayer microcapsules. The method is based on measurements of the capsule load-deformation curves with the atomic force microscope. The experiment suggests that at low applied load deformations of the capsule shell are elastic. Using elastic theory of membranes we relate force, deformation, elastic moduli, and charact...

A rational design evaluation procedure is investigated for the elastic overall buckling load carrying capacity of single layer cylindrical lattice shell roof structures. The nature of the imperfection sensitivity of these structures is for the first time reviewed in this paper. This allows the development of the reduced stiffness buckling analytical concept for the lattice shells based upon the...

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...

We study the asymptotic behavior of one-dimensional functionals associated to the energy of a thin nonlinear elastic spherical shell in the limit of vanishing thickness (proportional to a small parameter) ε and under the assumption of radial deformations. The functionals are characterized by the presence of a nonlocal potential term and defined on suitable weighted functional spaces. The transi...

Elastic theory of low-dimensional continua and its applications in bio-and nano-structures This review presents the elastic theory of low-dimensional (one-and two-dimensional) continua and its applications in bio-and nano-structures. First, the curve and surface theory, as the geometric representation of the low-dimensional continua , is briefly described through Cartan moving frame method. The...

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...

We study the asymptotic behavior of functionals associated to the energy of a thin nonlinear elastic spherical shell in the limit of vanishing thickness (proportional to a small parameter) ε and under the assumption of radial deformations. The functionals are characterized by the presence of a nonlocal potential term and defined on suitable weighted functional spaces. The transition shell-membr...

This paper investigates the reconstruction of elastic Green's function from the cross-correlation of waves excited by random noise in the context of scattering theory. Using a general operator equation-the resolvent formula-Green's function reconstruction is established when the noise sources satisfy an equipartition condition. In an inhomogeneous medium, the operator formalism leads to general...