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| Research on finite element method of nanobeam considering flexoelectricity based on general strain gradient elasticity theory |
| Received:November 04, 2019 Revised:January 14, 2020 |
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| DOI：10.7511/jslx20191104002 |
| KeyWord:flexoelectricity general strain gradient elasticity theory finite element method Euler beam size dependence |
| Author | Institution |
| 陈玲玲 |
山东大学 土建与水利学院工程力学系, 济南 |
| 杨旭 |
山东大学 土建与水利学院工程力学系, 济南 |
| 刘洋 |
山东大学 土建与水利学院工程力学系, 济南 |
| 王炳雷 |
山东大学 土建与水利学院工程力学系, 济南 |
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| Abstract: |
| Flexoelectricity is a special electromechanical coupling that exists in all dielectrics.It is essentially a linear coupling between strain gradient and polarization.However,the strain gradient introduces high-order partial derivate of displacements,which often make it difficult to solve the flexoelectric problem theoretically.Moreover,studies have shown that the strain gradient elastic term affects the electromechanical coupling responses in nanostructures,but the effect of strain gradient elasticity was mostly ignored in the existing research.Therefore,this paper proposed an effective numerical method that considered both strain gradient elasticity and flexoelectricity.Based on the general strain gradient elasticity theory,this paper established a theoretical model and a finite element model of nano-Euler beams.Three independent material length scale parameters were included in the two models.And an element with two nodes and six degrees of freedom was proposed,which satisfied C2 weak continuity.Based on the finite element method proposed in this study,a simply supported Euler beam was studied.By analyzing the deflection,electrical potential and energy efficiency,the effects of flexoelectricity and strain gradient elasticity on the electromechanical coupling responses were studied.The results show that the flexoelectricity is size-dependent,and the influence of the strain gradient elasticity on the flexoelectric response of nano-dielectric structures cannot be ignored. |
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