In this paper, thermo-elastic analysis of a rotating thick truncated conical shell subjected to the temperature gradient, internal pressure and external pressure is presented. Given the existence of shear stress in the conical shell due to thickness change along the axial direction, the governing equations are obtained based on first-order shear deformation theory (FSDT). These equations are so...

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...

We study the thin-shell limit of the nonlinear elasticity model for vesicles introduced in part I. We consider vesicles of width 2ε ↓ 0 with elastic energy of order ε 3. In this regime, we show that the limit model is a bending theory for generalized hypersurfaces — namely, co-dimension 1 oriented varifolds without boundary. Up to a positive factor, the limit functional is the Willmore energy. ...

We use a standard model for the low-temperature electron-phonon interaction in metals to calculate the rate of thermal energy transfer between electrons and acoustic phonons in suspended metallic nanoshells. The electrons are treated as three-dimensional and noninteracting, whereas the vibrational modes are that of an thin cylindrical elastic shell of radius R with a free surface and thickness ...

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 study the thin-shell limit of the nonlinear elasticity model for vesicles introduced in part I. We consider vesicles of width 2ε ↓ 0 with elastic energy of order ε. In this regime, we show that the limit model is a bending theory for generalized hypersurfaces— namely, co-dimension one oriented varifolds without boundary. Up to a positive factor, the limit functional is the Willmore energy. I...

Nanocapsules that can be tailored intelligently and specifically have drawn considerable attention in the fields of drug delivery and bioimaging. Here we conduct a theoretical study on cell uptake of a spherical nanocapsule which is modeled as a linear elastic solid thin shell in three dimensions. It is found that there exist five wrapping phases based on the stability of three wrapping states:...

Tanaka’s approach to swelling kinetics of a solid gel sphere is extended to a sphericalmicrogel shell. The boundary condition at the inner surface is obtained from the minimization of shear elastic energy. Temporal evolution of a shell is represented in a form of expansion over eigenfunctions of the corresponding diffusion equation. The swelling of Tanaka’s solid spherical gel is recovered as a...

A thin shell finite element approach based on Loop’s subdivision surfaces is proposed, capable of dealing with large deformations and anisotropic growth. To this end, the Kirchhoff-Love theory of thin shells is derived and extended to allow for arbitrary in-plane growth. The simplicity and computational efficiency of the subdivision thin shell elements is outstanding, which is demonstrated on a...