Large deflection analysis of a nanoscaled cantilever beam with strain gradient effect

Key words:  nanoscaled cantilever  large deformation  strain-gradient  energy method  variation

Abstract:

In this study, we discuss the deformation of a micro/nanoscaled cantilever under a concentrated load. The modeling is based on the strain gradient theory developed by Aifantis. Based on the Euler-Bernoulli beam theory, and considering the effect of strain gradient, the governing equation of the large deformation of a cantilever was built, and the boundary conditions were given. Using the shooting method and the MathCAD software, we obtain the numerical solution of a cantilever with strain gradient, under a concentrated load at the free end. This solution is compared with that of a beam with infinitesimal deformation. The result shows that at the micro/nano scale, the strain gradient has a great effect on the cantilever 's deformation. In this case, the gradient coefficient affects a beam more significantly when it is in the finite deformation than in the infinitesimal deformation. Moreover, the gradient coefficient will restrain the deformation of the beam.