Thermal fluctuations strongly modify the large length-scale elastic behavior of cross-linked membranes, giving rise to scale-dependent elastic moduli. Whereas thermal effects in flat membranes are well understood, many natural and artificial microstructures are modeled as thin elastic shells. Shells are distinguished from flat membranes by their nonzero curvature, which provides a size-dependen...

Smart adaptive structures and structronic systems have been increasingly investigated and developed in the last two decades. Although smart structures made of piezoelectrics, shape-memory materials, electrostrictive materials, and electro-/magnetorheological fluids have been evaluated extensively, studies of magnetostrictive continua, especially generic mathematical model(s), are still relative...

Free vibration of a simply-supported magneto-electro-elastic doubly-curved nano-shell is studied based on the first-order shear deformation theory in the presence of the rotary inertia effect. To model the electric and magnetic behaviors of the nano-shell, Gauss’s laws for electrostatics and magneto statics are used. By using Navier’s method, the partial differential equations of motion are red...

This paper presents a new modelling technique for the deformation of thin anatomical structures like membranes and hollow organs. We show that the behaviour of this type of surface tissue can be abstracted with a modelling of their elastic resistance using shell theory. In order to apply the shell theory in the context of medical simulation, our method propose to base the geometrical reconstruc...

The problem of a thin spherical linearly-elastic shell, perfectly bonded to an infinite linearly-elastic medium is considered. A constant axisymmetric stress field is applied at infinity in the matrix, and the displacement and stress fields in the shell and matrix are evaluated by means of harmonic potential functions. In order to examine the stability of this solution, the buckling problem of ...

Many thin three-dimensional elastic bodies can be reduced to elastic shells: two-dimensional elastic bodies whose reference shape is not necessarily flat. More generally, morphoelastic shells are elastic shells that can remodel and grow in time. These idealized objects are suitable models for many physical, engineering, and biological systems. Here, we formulate a general geometric theory of no...

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...

Treated herein is the elastic buckling problem of Single-Walled Carbon Nanotubes (SCNTs) under axial compression. Critical buckling strains cr ε of stocky SCNTs (length/diameter less than 8) that have been obtained by modeling them as first-order shear deformation (thick) shell theory (FSDST). The buckling strains are compared with those obtained by commonly used thin shell theories, such as th...

Third order shear deformation theory of cylindrical shells is employed to investigate the vibration characteristics of non-homogeneous cylindrical shells surrounded by an elastic medium. The kinematic relations are obtained using the strain-displacement relations of Donnell shell theory. The shell properties are considered to be dependent on both position and thermal environment. A suitable fun...

The scattering of plane steady-state sound waves from a viscous fluid-filled thin cylindrical shell weakened by a long linear slit and submerged in an ideal fluid is studied. For the description of vibrations of elastic objects the Kirchhoff–Love shell-theory approximation is used. An exact solution of this problem is obtained in the form of series with cylindrical harmonics. The numerical anal...