FINITE BEAM ELEMENT BASED ON THE STRAIN-DRIVEN MODEL FOR ANALYSES OF NANOBEAMS ON SUBSTRATE MEDIA

Abstract

The nonlocal elasticity theory has been widely employed to represent the phenomena in small-scale effects, in micro/nano-structures. For the planar Euler-Bernoulli beam problem, the differential form of this nonlocal theory is preferable for use in conjunction with the classical beam model, due to its simple features. However, this form leads to paradoxical results in some cases. Therefore, this paper aimed to develop and propose a beam model to resolve the inconsistent responses via the integral form of nonlocal elasticity theory, for the analysis of nanobeam on substrate medium. The Gurtin-Murdoch surface model and the Winkler-foundation model are used to incorporate size- dependent and substrate-structure interaction effects into the nonlocal beam model. The proposed model is constructed based on the displacement-based finite element formulation. To demonstrate the capability of the novel proposed model and to characterize bending responses, three numerical simulations are used. The first simulation proves the model's competence to overcome the inconsistent results. The second simulation demonstrates the impact of the nonlocal and surface- energy effects in the bending responses of nanobeam on the elastic substrate medium. Finally, the third simulation examines the influences of several model parameters on contact stiffness.