Three-dimensional buckling of embedded multilayered magnetoelectroelastic nanoplates/graphene sheets with nonlocal effect

This article presents an exact analysis for the three-dimensional buckling problem of embedded multilayered magnetoelectroelastic and simply supported nanoplates/graphene sheets with nonlocal effect. The interaction between the multilayered nanoplates/graphene sheets and their surrounding medium is simulated by a Pasternak-type foundation. The critical loads for embedded multilayered magnetoelectroelastic nanoplates/graphene sheets under uniaxial and biaxial compression at small scale are then derived by solving the linear eigensystem and making use of the propagator matrix method. A comparison between the present anisotropic three-dimensional model and previous results (an asymptotic nonlocal elasticity theory for single elastic graphene sheet and classical orthotropic plate theories) is made to show the effectiveness and correctness of the present anisotropic three-dimensional model. Numerical examples are then presented for the variation of the dimensionless critical buckling loads for the homogeneous elastic graphene sheet with nonlocal effect, the homogeneous orthotropic thick plate without nonlocal effect, and the sandwich magnetoelectroelastic nanoplates made of piezoelectric and magnetostrictive materials with nonlocal effect. Furthermore, the effects of the thickness of nanoplates, nonlocal parameter, Winkler stiffness, and shear modulus of the elastic medium on the critical load of sandwich magnetoelectroelastic nanoplates/graphene sheets are demonstrated. These results should be very useful as benchmarks for the future development of approximate nanoplate/graphene sheet theories and numerical methods for modeling and simulation of multilayered nanoplates/graphene sheets with nonlocal effect.