This work is the second part of a previous paper which was devoted to scalar problems. Here we study shape derivative eigenvalue problems elasticity theory for various kinds boundary conditions, that Dirichlet, Neumann, Robin, and Wentzell conditions. We also case composite materials, having in mind applications sensitivity analysis mechanical devices manufactured by additive printing. The main...

This paper deals with the equilibrium problem of slender beams inflexed under variable curvature in framework fully nonlinear elasticity. For specific case uniform flexion, authors have recently proposed a mathematical model. In that analysis, complete three-dimensional kinematics beam is taken into account and both deformations displacements are considered large. present paper, aforementioned ...

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-...

In this paper, analysis of linear and nonlinear buckling of relatively thick orthotropic graphene sheets is carried out under mechanical load based on elasticity theories. With the help of  nonlocal elasticity theory, the principle of virtual work, first order shear theory and Von-Karman nonlinear strain, the dominant relationship in terms of obtained displacements has been obtained, and the me...

In this study, the small scale effect on the linear free-field vibration of a nano-circular plate has been investigated using nonlocal elasticity theory. The formulation is based on the classical theory and the linear strain in cylindrical coordinates. To take into account the small scale and the linear geometric effects, the governing differential equation based on the nonlocal elasticity theo...