BUCKLING OF FGM TIMOSHENKO MICROBEAMS UNDER IN-PLANE THERMAL LOADING BASED ON THE MODIFIED STRAIN GRADIENT THEORY

According to the theory of thermal elasticity mechanics, thermal buckling characteristics of microbeams made of functionally graded materials (FGMs) are presented. The material properties of FGM microbeams are considered to be graded in the thickness direction on the basis of the Mori-Tanaka homogenization scheme. Based on the strain gradient elasticity theory, a size-dependent elastic beam model within the framework of the Timoshenko beam theory is developed containing three internal material length scale parameters to interpret size effect. By using Hamilton's principle, the higher-order governing differential equations of motion and related boundary conditions are derived. Afterward, the generalized differential quadrature (GDQ) method is employed to discretize the governing differential equations along various end supports and then the critical thermal buckling loads of FGM microbeams with three commonly used sets of boundary conditions are determined. The applicability of the present nonclassical beam model to predict thermal buckling behavior of FGM microbeams is established via various numerical results. It is found that the difference between thermal buckling of microbeams subjected to the uniform, linear, and nonlinear temperature distributions is more significant corresponding to the higher values of material property gradient index.