Stability analysis of gradient elastic microbeams with arbitrary boundary conditions

Based on gradient elasticity theory with surface energy, a simple and unified method is presented for the stability analysis of a generally supported microbeam. The proposed method conveniently computes an accurate buckling parameter for microbeams using both classical and non-classical boundary conditions restrained by translational and rotational springs. The Fourier coefficient and fundamental relations of strain gradient beams are obtained first. Stokes' transformation is applied to transform these equations into a set of algebraic equations with buckling parameter. The derived expressions can be useful for theoretical investigation that leads to a determinant calculation of a 4 x 4 matrix. The critical buckling loads of microbeams for variant scale parameters under different boundary conditions are computed using the proposed method. Comparing results with those in the literature validates the present analysis.