Numerical study of large deflection of nanobeam according to the MCST and SE

Abstract

In the current study, the large deflection of nanobeam according to the modified couple stress theory (MCST) with surface effects (SE) was investigated by applying finite element method (FEM). For modeling of the nanobeam, we applying the Timoshenko beam theory (TBT), and for the solution of the problem, we used a total lagrangian finite element method. Also, shear deformation and axial displacements of nanobeams have been considered in this model. The FEM has been used for the solution of the problem. With the present model, small to large deflection of nanobeam with arbitrary loadings and boundary conditions can be studied. The numerical results for the small deflection of nanobeam achieved by the present model are well matched with results reported in the previous researches. Effects of the ratio of material length scale parameter to thickness on the large deflection of nanobeams have been investigated. Also, the influence of considering different beam constitutive theories in the large deflection analysis of nanobeams has been examined. The results achieved in this study show the relative importance of considering surfaces and size effects in the analysis of nanobeam.

Keywords:

• Modified couple stress theory
• surface effect
• large deflection
• total Lagrangian finite element method