https://northumbria-test.eprints-hosting.org/id/document/265204

A review of continuum mechanics models for size-dependent analysis of beams and plates

https://northumbria-test.eprints-hosting.org/id/document/268107

A review on the mechanics of nanostructures

In this paper, a new size-dependent plate model is developed based on the higher-order nonlocal strain gradient theory. The influences of higher-order deformations in conjunction with the higher- and lower-order nonlocal effects are taken into account. The presence of three different kinds of scale parameters in the formulation results in a theory which is capable of capturing both reduction and increase in the stiffness of structures at nanoscale. The governing differential equations are derived for the buckling of nanoplates resting on a two-parameter elastic foundation using the principle of virtual work. The nanoplate is assumed to be orthotropic with size-dependent material properties. The influence of thermal stress caused by a temperature change is taken into consideration. An exact closed-form solution is obtained for the critical buckling loads of graphene sheets. The higher-order governing differential equation is also solved by the differential quadrature method. The results of the two solution methods are compared with each other. Excellent agreement between the exact and numerical results is observed. For numerical results, three types of graphene sheets with different aspect ratio are considered. The effects of various scale parameters together with the other parameters such as the coefficients of the elastic medium, temperature change and the length of the nanoplate on the buckling behavior of graphene sheets are investigated.

A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment

This paper investigates the thermo-electro-mechanical vibration of the rectangular piezoelectric nanoplate under various boundary conditions based on the nonlocal theory and the Mindlin plate theory. It is assumed that the piezoelectric nanoplate is subjected to a biaxial force, an external electric voltage and a uniform temperature rise. The Hamilton's principle is employed to derive the governing equations and boundary conditions, which are then discretized by using the differential quadrature (DQ) method to determine the natural frequencies and mode shapes. The detailed parametric study is conducted to examine the effect of the nonlocal parameter, thermo-electro-mechanical loadings, boundary conditions, aspect ratio and side-to-thickness ratio on the vibration behaviors.

Free vibration of nonlocal piezoelectric nanoplates under various boundary conditions

Electro-mechanical shear buckling of piezoelectric nanoplate using modified couple stress theory based on simplified first order shear deformation theory

Nonlinear bending analysis of orthotropic nanoscale plates in an elastic matrix based on nonlocal continuum mechanics

Nonuniform biaxial buckling of orthotropic nanoplates embedded in an elastic medium based on nonlocal Mindlin plate theory

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Nonlinear bending analysis of orthotropic nanoscale plates in an elastic matrix based on nonlocal continuum mechanics

Nonuniform biaxial buckling of orthotropic nanoplates embedded in an elastic medium based on nonlocal Mindlin plate theory