Size dependent buckling analysis of microbeams based on modified couple stress theory with high order theories and general boundary conditions

In this research, buckling analysis of three microbeam models are investigated based on modified couple stress theory. Using Euler–Bernoulli beam theory (EBT), Timoshenko beam theory (TBT) and Reddy beam theory (RBT), the effect of shear deformation is presented. To examine the effect of boundary condition, three kinds of boundary conditions i.e. hinged–hinged, clamped–hinged and clamped–clamped boundary conditions, are considered. These nonclassical microbeam models incorporated with Poisson effect, contain a material length scale parameter and can capture the size effect. These models can degenerate into the Classical models if the material length scale parameter and Poisson’s ratio are both taken to be zero. Governing equations and boundary conditions are derived by using principle of minimum potential energy. Generalized differential quadrature (GDQ) method is employed to solve the governing differential equations. Also an analytical solution is applied to determine the critical buckling load of microbeams with hinged–hinged boundary condition. Comparison between the results of GDQ and analytical methods reveals the accuracy of GDQ method. Some numerical results are exhibited to indicate the influences of beam thickness, material length scale parameter and Poisson’s ratio on the critical buckling load of these microbeams.