Effect of the gradient on the deflection of functionally graded microcantilever beams with surface stress

The surface stress-induced deflection of a microcantilever beam with arbitrary axial nonhomogeneity and varying cross section is investigated. The surface stresses are assumed to be uniformly distributed on the upper surface of the beam. Based on the small deformation and Euler–Bernoulli beam theory, the second-order integral–differential governing equation is derived. A simple Taylor series expansion method is proposed to calculate the static deformation. The approximate solution of functionally graded microbeams can degenerate into the solution of homogeneous microbeams, and the explicit expressions for the static deflection, slope angle curvature, and surface stress are derived. Particularly, the influence of the gradient parameters on the static deformation of functionally graded rectangular and triangular microbeams is presented by Figures primarily. Obtained results indicate that choosing an appropriate gradient parameter is beneficial for different surface stresses. The proposed method and derived solution can be used as a theoretical benchmark for validating the obtained results of microcantilever beams as micro-mechanical sensors and atomic force microscopy.