In this research, the bending analysis of rectangular nanoplates subjected to mechanical loading is investigated. For this purpose, the strain gradient elasticity theory with one gradient parameter is presented to study the nanoplates. From the best knowledge of authors, it is the first time that the exponential shear deformation formulation based on strain gradient elasticity theory is carried...

A study of existence and uniqueness weak solutions to boundary value problems describing an elastic body with weakly nonlocal surface elasticity is presented. The chosen model incorporates the strain energy as a quadratic function tensor deformation gradients up Nth order. virtual work principle, extended for higher-order gradient media, serves basis defining solution. In order characterize smo...

linear dynamic response of simply supported nanobeams subjected to a variable axial force is assessed by galerkin numerical approach. constitutive behavior is described by three functional forms of elastic energy densities enclosing nonlocal and strain gradient effects and their combination. linear stationary dynamics of nanobeams is modulated by an axial force which controls the global stiffne...

Abstract We call nonlinear dilatational strain gradient elasticity the theory in which specific class of second continua is considered: those whose deformation energy depends, an objective way, on placement and determinant placement. It interesting particular case complete Toupin–Mindlin elasticity: indeed, it, only effects are due to inhomogeneous dilatation state considered deformable body. T...

in this research, the bending analysis of rectangular nanoplates subjected to mechanical loading is investigated. for this purpose, the strain gradient elasticity theory with one gradient parameter is presented to study the nanoplates. from the best knowledge of authors, it is the first time that the exponential shear deformation formulation based on strain gradient elasticity theory is carried...

A (linear) nonsingular solution for the edge dislocation in the translational gauge theory of defects is presented. The stress function method is used and a modified stress function is obtained. All field quantities are globally defined and the solution agrees with the classical solution for the edge dislocation in the far field. The components of the stress, strain, distortion and displacement...

In this paper, a nonlocal foundation model is proposed to analyze the vibration and instability of a Y-shaped single-walled carbon nanotube (Y-SWCNT) conveying fluid. In order to achieve more accurate results, fourth order beam theory is utilized to obtain strain-displacement relations. For the first time, a nonlocal model is presented based on nonlocal elasticity and the effects of nonlocal fo...

Classical continuum models exhibit strong mesh dependency during strain softening. For such materials, the phenomenon may be regularized via the gradient-enhanced nonlocal formulation. The paper discusses the implicit gradient framework and demonstrates that standard nonlocal enhancement may serve only as a partial localization limiter. The over-nonlocal approach, where the weight for the nonlo...