Size dependent analysis of functionally graded microbeams using strain gradient elasticity incorporated with surface energy

In this study, strain gradient theory is used to show the small scale effects on bending, vibration and stability of microscaled functionally graded (FG) beams. For this purpose, Euler–Bernoulli beam model is used and the numerical results are given for different boundary conditions. Analytical solutions are given for static deflection and buckling loads of the microbeams while generalized differential quadrature (GDQ) method is used to calculate their natural frequencies. The results are compared with classical elasticity ones to show the significance of the material length scale parameter (MLSP) effects and the general trend of the scale dependencies. In addition, it is shown the effect of surface energies relating to the strain gradient elasticity is negligible and can be ignored in vibration and buckling analyses. Combination of the well-known experimental setups with the results given in this paper can be used to find the effective MLSP for metal-ceramic FG microbeams. This helps to predict their accurate scale dependent mechanical behaviors by the introduced theoretical framework.