This paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. The characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal Mindlin plate. This theory is considering both the small length scale effects and transverse shear deformation ef...

This paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. The characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal Mindlin plate. This theory is considering both the small length scale effects and transverse shear deformation ef...

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...

The nonlinear bending behavior of sector graphene sheets is studied subjected to uniform transverse loads resting on a Winkler-Pasternak elastic foundation using the nonlocal elasticity theory. Considering the nonlocal differential constitutive relations of Eringen theory based on first order shear deformation theory and using the von-Karman strain field, the equilibrium partial differential eq...

A model for the quasistatic evolution of martensitic phase boundaries is presented. The model is essentially the gradient flow of an energy that can contains elastic energy due to the underlying change in crystal structure in the course of the phase transformation and surface energy penalizing the area of the phase boundary. This leads to a free boundary problem with a nonlocal velocity that ar...

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...