Thermal postbuckling behavior of size-dependent functionally graded Timoshenko microbeams

The thermal postbuckling characteristics of microbeams made of functionally graded materials (FGMs) undergoing thermal loads are investigated based on the modified strain gradient theory (MSGT). The volume fraction of the ceramic and metal phases of FGM microbeams is expressed by using a power low function. The non-classical beam model presented herein is capable of interpreting size effects through introducing material length scale parameters and encompasses the modified couple stress theory (MCST) and classical theory (CT). Based on the non-linear Timoshenko beam theory and the principle of virtual work, the stability equations and associated boundary conditions are derived and are then solved through the generalized differential quadrature (GDQ) method in conjunction with a direct approach without linearization. The influences of the material gradient index, length scale parameter, and boundary conditions on the thermal postbuckling behavior of FGM microbeams are comprehensively investigated. Also, this study compares the results obtained from the MSGT with those from CT. The effect of geometrical imperfection on the buckling deformation of microbeams in prebuckled and postbuckled states is discussed.

► Development of a nonlinear Timoshenko FGM beam model based on the MSGT.
► Prediction of thermal postbuckling behavior for a FGM microbeam with arbitrary end supports.
► Exploring effects of model parameters on the thermal postbuckling characteristics of microbeams.
► Comparing the results from the classical and non-classical theories at higher mode deflections.
► Study of the effect of imperfection on the first two thermal postbuckling modes.