Thermal buckling and postbuckling analysis of size-dependent composite laminated microbeams based on a new modified couple stress theory

Based on a new modified couple stress theory for composite laminates, considering geometric nonlinear theory and Timoshenko beam hypothesis, the governing equations for size-dependent composite laminated microbeams in thermal environment are derived using Hamilton's principle. Analytical and numerical solutions are employed in solving the present problem, respectively. An auxiliary function is introduced to reduce the governing equations to a single fourth-order integral-differential equation, and the exact solutions for the thermal buckling and postbuckling of microbeams with combination of in-plane immovable simply supported boundary conditions are obtained. By introducing the differential quadrature method, the governing equations are transferred into a system of nonlinear algebraic eigenvalue equations. In numerical examples, comparison between the present results and those obtained in the literature verifies the validity and efficiency of the present analytical and numerical methods. The effects of thermal expansion coefficients and material length scale parameter are discussed. Numerical results indicate that the above-mentioned effects play very important roles for the thermal buckling and postbuckling of the composite laminated microbeams.