Postbuckling of functionally graded microbeams: a theoretical study based on a reformulated strain gradient elasticity theory

A size-dependent post buckling analysis of functionally graded (FG) microbeams is conducted by using an analytical solution based on a reformulated strain gradient elasticity theory (RSGET). The nonlinear behavior of post buckling is considered by employing the von-Karman nonlinear strain-displacement relation. The microstructure-dependent behavior of the microbeam is captured by the RSGET which incorporated both couple stress and strain gradient effects using one size-dependent parameter for each. The material properties of the FG microbeam changed along the thickness direction, which are described using a power law relation. Based on the principle of minimum potential energy, the equations of equilibrium and boundary conditions of the Euler-Bernoulli microbeam are obtained. The post buckling response of FG mcirobeams with different boundary conditions are analytically derived. Moreover, the effects of the length scale parameter, material gradient index, length-thickness ratio and Poisson's ratio on the post buckling responses are studied. In addition, the total critical pressure for the FG array structures is estimated. These results are helpful for designing FG-MEMS devices.