Nonlocal and gradient parameter effects on static bending of functionally graded rectangular microcantilevers under surface stress

Abstract This paper investigates the static deformation of a functionally graded (FG) microcantilever beam with a rectangular cross-section induced by surface stress, employing Eringen’s nonlocal elasticity theory to account for small-scale effects. Under the assumption of uniform surface stress distribution, a governing differential-integral equation with variable coefficients is derived. The Taylor series expansion method is utilized to solve this equation, yielding explicit relationships between the surface stress and the resulting deformations (deflection, rotation, and curvature). Numerical examples examine the influence of the material gradient parameter and the nonlocal size effect parameter on the static deformation of the FG microcantilever beam. The results indicate that the gradient index β leads to a nearly span-independent amplification of the nondimensional deflection. Specifically, increasing β from 0 to 0.5, 1.0, and 2.0 enhances the tip deflection by approximately 15.6%, 26.1%, and 39.9% at q = 1, and by 12.3%, 19.9%, and 29.1% at q = 12, respectively. In contrast, the nonlocal size parameter consistently stiffens the beam, reducing its deflection by a nearly constant fraction compared to the local model. Therefore, FG materials are demonstrated to significantly improve the sensitivity of microcantilever sensors induced by surface stress. These findings provide a theoretical basis for the optimal structural design of microcantilever sensors.