Analysis of a curved Timoshenko nano-beam with flexoelectricity

A Timoshenko beam model is applied for the analysis of the flexoelectric effect for a curved nano-beam. This theory transforms the beam to a 1-d problem along the beam axis. The electric intensity vector for the open-circuit condition can be expressed by mechanical quantities, namely strains and strain gradients. The variational principle is applied to derive the system of ordinary differential equations (ODEs) for the beam deflection, cross-section rotation, and in-plane displacement. A numerical solution based on the Taylor series expansion with Cartesian coordinate along the beam is proposed for the system of ODEs. A convergence analysis with respect to the number of terms in the Taylor series expansion is performed. Numerical results for the beam deflection, rotation, in-plane displacement, and induced electric intensity vector are presented for various flexoelectric coefficients and the beam curvature.

Automated summary

In this study, a Timoshenko beam model was used to analyze the flexoelectric effect of a curved nano-beam, transforming the beam problem into a one-dimensional problem along the beam axis. The system of ordinary differential equations for beam deflection, rotation, and displacement was derived using the variational principle, and a numerical solution based on Taylor series expansion was proposed. Convergence analysis was performed on the number of terms in the Taylor series expansion, and numerical results were presented for various flexoelectric coefficients and beam curvature.