A non-classical model for first-ordershear deformation circular cylindrical thin shells incorporating microstructure and surface energy effects

A new non-classical model for first-order shear deformation circular cylindrical thin shells is developed by using a modified couple stress theory and a surface elasticity theory. Through a variational formulation based on Hamilton’s principle, the equations of motion and boundary conditions are simultaneously obtained, and the microstructure and surface energy effects are treated in a unified manner. The newly developed non-classical shell model contains one material length-scale parameter to account for the microstructure effect and three surface elastic constants to capture the surface energy effect. The new model includes shell models considering the microstructure effect only or the surface energy effect alone as special cases and recovers the first-order shear deformation circular cylindrical thin shell model based on classical elasticity as a limiting case. In addition, the current shell model reduces to the non-classical model for Mindlin plates incorporating the microstructure and surface energy effects when the thin shell radius tends to infinity. To illustrate the new model, the static bending and free vibration problems of a simply supported circular cylindrical thin shell are analytically solved. The numerical results reveal that the inclusion of the microstructure and surface energy effects leads to reduced shell deflections and rotation angles and increased natural frequencies. The differences are significant when the shell is very thin, but they diminish as the shell thickness increases. These predicted size effects at the micron scale agree with the general trends observed in experiments.

A Surface Energy Density-Based Theory of Nanoelastic Dynamics and Its Application in the Scattering of P-Wave by a Cylindrical Nanocavity

The scattering of elastic waves in nanoporous materials is inevitably influenced by the surface effect of nanopores. In order to investigate such a dynamic problem with surface effect of nanomaterials, a new theory of nanoelastic dynamics is proposed, in which both the effect of surface free energy and the effect of surface inertia force are included. With the new theory, a scattering of plane compressional waves (P-wave) by a cylindrical nanocavity is analyzed, and the corresponding dynamic stress concentration factor (DSCF) around the nanocavity is analytically solved. It is found that, when the size of cavity is at a nanoscale, the surface energy effect leads to a reduction of the maximum DSCF comparing with the classical counterpart without surface effect, while the surface inertial effect enlarges the maximum DSCF. The surface inertial effect gradually becomes dominant over the surface energy effect with an increasing incident wave frequency. Although both kinds of surface effects tend to vanish with an increasing cavity radius, the surface inertial effect can exist in a submicron-sized cavity if the wave frequency is sufficiently high. All these results should be of guiding value not only for an optimal design of porous structure possessing a better dynamic load bearing capacity but also for the non-destructive detection of nano-defects.