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

作者：Farajpour, A.^*; Yazdi, M. R. Haeri; Rastgoo, A.; Mohammadi, M.

来源：Acta Mechanica, 2016, 227(7): 1849-1867.

DOI：10.1007/s00707-016-1605-6

• FREE-VIBRATION ANALYSIS
• CIRCULAR GRAPHENE SHEETS
• CARBON NANOTUBES
• NONLINEAR VIBRATION
• FORCED VIBRATIONS
• ELASTICITY
• CONTINUUM
• SURFACE
• ARMCHAIR

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.

• 出版日期2016-7