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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2019029391
pages 29-43

A FINITE-ELEMENT METHOD OF FLEXOELECTRIC EFFECTS ON NANOSCALE BEAM

Xu Yang
School of Civil Engineering, Shandong University, Jinan, 250061, China
Yarong Zhou
School of Civil Engineering, Shandong University, Jinan, 250061, China
Binglei Wang
School of Civil Engineering, Shandong University, Jinan, 250061, China; State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, China
Bo Zhang
School of Civil Engineering, Shandong University, Jinan, 250061, China

ABSTRACT

Flexoelectricity is a linear coupling between the strain gradient and the electric polarization, which is present in all dielectric materials. Strain gradients cause flexoelectricity to be size-dependent, especially significant for nanoscale structures. However, strain gradients involve higher-order partial derivate of displacements which brings difficulties to the solution of flexoelectric problems. The effect of strain gradient elasticity was ignored in most previous works on flexoelectricity. Thus, it is necessary to develop an effective numerical method that accounts for both strain gradient elasticity and flexoelectricity.We have developed a size-dependent finite-element model of a nanoscale Euler beam based on a reformulated strain gradient elasticity theory. The new model contains three independent material length scale parameters which capture the size effect. The developed C2 weak continuous element with two nodes has three degrees of freedom at each node. Using the Finite Element Method (FEM), with the Euler cantilever beam as an example, the effects of flexoelectricity and strain gradient elasticity on the beam have been investigated. The results were compared with those available in literature and an excellent agreement was achieved.


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