Effect of gradient on the deflection of functionally graded rectangular microcantilever induced by surface stress

Abstract The problems of surface stress-induced deflection for a rectangular microcantilever beam with arbitrary axial nonhomogeneity are analyzed in this paper. The surface stress is assumed to be uniformly distributed on the entire upper and lower surfaces of the beam. Based on the principle of virtual work, the second-order integral-differential governing equation is derived. Furtherly, a simple method, the Taylor series expansion method, is utilized to calculate the surface stress by static deformation. The obtained approximate solution of functionally graded rectangular microbeams can be degenerated into the solution of the homogeneous microbeam. Meanwhile, the explicit expressions of static deformation and surface stress of beam are derived. Additionally, when Young's modulus varies along the axial direction with power-law and Voigt functions, the influence of the gradient parameter and elastic modulus ratio on the static deflection of functionally graded rectangular microcantilever beams is also presented and analyzed. Obtained results indicate that choosing appropriate material properties and gradient will be beneficial to the evaluation of surface stress. 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.