A New Model for Thermal Buckling of FG-MEE Microbeams Based on a Non-Classical Third-Order Shear Deformation Beam Theory

A novel transversely isotropic functionally graded magneto-electro-elastic third-order shear deformation microbeam model is constructed by utilizing a variational formulation based on Hamilton’s principle. This work takes the microstructure effect into account by using an extended modified couple stress theory. Three types of temperature distributions are considered. Using the framework and approaches shown above, the equations of motion along with the complete boundary conditions can be obtained in a reasonable process. For illustration purposes, a numerical example is presented to examine the influences of temperature distributions, beam thickness and functionally graded power-law index on thermal buckling. In order to solve the governing equations, a specific set of Fourier series which satisfy the boundary conditions are introduced. Furthermore, it is indicated that the shear deformation effect should be considered in predicting the buckling response, especially for a smaller slenderness ratio. Additionally, two types of simplified versions of this innovative microbeam model were also created for more straightforward applications. The shape correction factor is involved in establishing the corresponding first-order shear deformation model (Timoshenko microbeam model) for the sake of approximating the overall effect of nonhomogeneous shear stress. This article can offer guidelines for the safe design of micro- and nano-electromechanical systems devices.