In many practical applications of nanotechnology and in microelectromechanical devices, typical structural components are in the form of beams, plates, shells and membranes. When the scale of such components is very small, the material microstructural lengths become important and strain gradient elasticity can provide useful material modelling. In addition, small scale beams and bars can be use...

Abstract The fundamental problem of dislocations in incompatible isotropic strain gradient elasticity theory Mindlin type, unsolved for more than half a century, is solved this work. Incompatible type the generalization Mindlin’s compatible including plastic fields providing way proper eigenstrain framework study defects like dislocations. Exact analytical solutions displacement fields, elastic...

This paper deals with dynamic Stability of single walled carbon nanotube. Strain gradient theory and Euler-Bernouli beam theory are implemented to investigate the dynamic stability of SWCNT embedded in an elastic medium. The equations of motion were derived by Hamilton principle and non-local elasticity approach. The nonlocal parameter accounts for the small-size effects when dealing with nano-...

Abstract The equilibrium equations and the traction boundary conditions are evaluated on basis of condition stationarity Lagrangian for coupled strain gradient elasticity. quadratic form energy can be written as a function second displacement contains fourth-, fifth- sixth-order stiffness tensor $${\mathbb {C}}_4$$ C</...

We study the steady-state and transient responses of a second-order elastic plate by implementing an asymptotic analysis three-dimensional equations with respect to two geometric characteristics seen as parameters: thickness inner material length. Depending on their ratio, four different models arise. Conditions under which Reissner–Mindlin kinematics may appear are discussed while influence cr...