Derivation of Nonlocal Finite Element Formulation for Nano Beams

Abstract

In the present paper, a new nonlocal formulation for vibration derived for nano beam lying on elastic matrix. The formulation is based on the cubic shape polynomial functions via finite element method. The size effect on finite element matrix is investigated using nonlocal elasticity theory. Finite element formulations and matrix coefficients have been obtained for nano beams. Size-dependent stiffness and mass matrix are derived for Euler-Bernoulli beams.