A finite element model is proposed permitting prediction of elastic wave bandgaps of periodic composite microplates incorporating flexoelectric effect.In this model,we applied curvature-based flexoelectricity and Mind...A finite element model is proposed permitting prediction of elastic wave bandgaps of periodic composite microplates incorporating flexoelectric effect.In this model,we applied curvature-based flexoelectricity and Mindlin plate theories and derived a finite element formulation that has been implemented for bandgap analysis.The finite element model utilizes a three-node triangle element with 30 degrees of freedom satisfying Mindlin kinematics assumptions.It is based on a non-conforming interpolation scheme which provides nodal C^(1) continuity and ensures compatibility with curvature-based flexoelectricity.The approach accounts for microstructure effects and,owing to the triangular element topology,can be used to assist the design of microplates with complex microstructures.Validation of the approach is performed through comparison with both analytical and numerical models,in which the effect of flexoelectricity on the bandgap is studied based on cases demonstrating size dependence.展开更多
Based on the negative exponential pair-potential （I/R）n, the interaction potential between the micro/nano planar curve and the particle located outside the curve is studied. We verified that, whatever the value of e...Based on the negative exponential pair-potential （I/R）n, the interaction potential between the micro/nano planar curve and the particle located outside the curve is studied. We verified that, whatever the value of exponent n may be the potential of particle/plane-curve is always of unified curvature form. Furthermore, we proved that the driving forces acted on the particle may be induced by the highly curved micro/nano curve, and the curvature and gradient of curvature are confirmed to be the essential factors forming the driving force. Through the idealized numerical experiments, the accuracy and reliability of the curvature-based potential are examined.展开更多
Based on the natural exponential pair potential, the interaction potential between curved surface body and on surface particle is studied. Firstly, the interaction potential is written as a function of curvatures thro...Based on the natural exponential pair potential, the interaction potential between curved surface body and on surface particle is studied. Firstly, the interaction potential is written as a function of curvatures through the differential geometry. Secondly, idealized numerical experiments are designed to test the accuracy of curvature-based potential. Then, the driving forces induced by curvatures are analyzed, which confirms that micro/nano curved surface body can induce driving forces, curvatures and the gradient of curvatures are the essential elements forming the driving forces. Finally, by combing with the curvature based potential and driving forces, the movements of on surface particles and the evolution of surface morphology of curved surface body are predicted.展开更多
The natural exponential potential (Ce^R/λ0) widely exists at micro/nanoscales;this paper studies the interaction potential between a curved-surface body and an outside particle base on the natural exponential potenti...The natural exponential potential (Ce^R/λ0) widely exists at micro/nanoscales;this paper studies the interaction potential between a curved-surface body and an outside particle base on the natural exponential potential. Mat hematical derivation proves t hat the int er act ion potential can be expressed as a function of curvatures. Then, idealized numerical experiments are designed to verify the accuracy of the curvature-based potential. The driving forces exerted on the particle are discussed and confirmed to be a function of curvatures and the gradient of curvatures, which may explain some abnormal movements at micro/nanoscales.展开更多
This paper focuses on the interaction between a micro/nano curved surface and a particle located inside the surface (hereafter abbreviated as in-surface-particle).Based on the exponential pair potential (namely 1/R2k)...This paper focuses on the interaction between a micro/nano curved surface and a particle located inside the surface (hereafter abbreviated as in-surface-particle).Based on the exponential pair potential (namely 1/R2k) between particles,the interaction potential between the micro/nano curved surface and the in-surface-particle is derived.The following results are shown:(a) For an even number of exponents in the pair potential,the interaction potential between the micro/nano curved surface and the in-surface-particle can be expressed as a unified function of the mean curvature and Gaussian curvature of the curved surface;(b) the curvatures and the gradients of curvatures of the micro/nano curved surface are the essential factors that dominate the driving force acting on the particle.展开更多
We verify the accuracy of the curvature-based potential.By means of the idealized numerical experiment,we show that the curvature-based potential is in good agreement with the numerical experiment,and the errors are w...We verify the accuracy of the curvature-based potential.By means of the idealized numerical experiment,we show that the curvature-based potential is in good agreement with the numerical experiment,and the errors are within a reasonable range.Based on the curvature-based potential,the equipotential surfaces of particles are derived,and the intrinsic relations between the equipotential surfaces and Weingarten helicoids are shown.展开更多
文摘A finite element model is proposed permitting prediction of elastic wave bandgaps of periodic composite microplates incorporating flexoelectric effect.In this model,we applied curvature-based flexoelectricity and Mindlin plate theories and derived a finite element formulation that has been implemented for bandgap analysis.The finite element model utilizes a three-node triangle element with 30 degrees of freedom satisfying Mindlin kinematics assumptions.It is based on a non-conforming interpolation scheme which provides nodal C^(1) continuity and ensures compatibility with curvature-based flexoelectricity.The approach accounts for microstructure effects and,owing to the triangular element topology,can be used to assist the design of microplates with complex microstructures.Validation of the approach is performed through comparison with both analytical and numerical models,in which the effect of flexoelectricity on the bandgap is studied based on cases demonstrating size dependence.
基金supported by the National Natural Science Foundation of China(Nos.11072125 and 11272175)the NSF of Jiangsu Province(Nos.BK2011075 and BK20130910)the research found for doctor student education
文摘Based on the negative exponential pair-potential （I/R）n, the interaction potential between the micro/nano planar curve and the particle located outside the curve is studied. We verified that, whatever the value of exponent n may be the potential of particle/plane-curve is always of unified curvature form. Furthermore, we proved that the driving forces acted on the particle may be induced by the highly curved micro/nano curve, and the curvature and gradient of curvature are confirmed to be the essential factors forming the driving force. Through the idealized numerical experiments, the accuracy and reliability of the curvature-based potential are examined.
基金the Natural Science Foundation of Jiangsu Province (Grants BK2018041 1 and BK20180429)start-up funding awarded by the Nanjing University of Aeronautics and Astronautics (Grants 56SYAH 17065 and 90YAH17065)the Fundamental Research Funds for the Central Universities (Grant NS2018004).
文摘Based on the natural exponential pair potential, the interaction potential between curved surface body and on surface particle is studied. Firstly, the interaction potential is written as a function of curvatures through the differential geometry. Secondly, idealized numerical experiments are designed to test the accuracy of curvature-based potential. Then, the driving forces induced by curvatures are analyzed, which confirms that micro/nano curved surface body can induce driving forces, curvatures and the gradient of curvatures are the essential elements forming the driving forces. Finally, by combing with the curvature based potential and driving forces, the movements of on surface particles and the evolution of surface morphology of curved surface body are predicted.
基金by the Natural Science Foundation of Jiangsu Province (Nos. BK20180411, BK20180416)the start-up funding awarded by Nanjing University of Aeronautics and Astronautics (Nos. 56SYAH17065, 90YAH17065).
文摘The natural exponential potential (Ce^R/λ0) widely exists at micro/nanoscales;this paper studies the interaction potential between a curved-surface body and an outside particle base on the natural exponential potential. Mat hematical derivation proves t hat the int er act ion potential can be expressed as a function of curvatures. Then, idealized numerical experiments are designed to verify the accuracy of the curvature-based potential. The driving forces exerted on the particle are discussed and confirmed to be a function of curvatures and the gradient of curvatures, which may explain some abnormal movements at micro/nanoscales.
基金supported by the National Natural Sciences Foundation of China (Grant Nos.11072125 and 10872114)the Natural Science Foundation of Jiangsu province (Grant No. SBK201140044)
文摘This paper focuses on the interaction between a micro/nano curved surface and a particle located inside the surface (hereafter abbreviated as in-surface-particle).Based on the exponential pair potential (namely 1/R2k) between particles,the interaction potential between the micro/nano curved surface and the in-surface-particle is derived.The following results are shown:(a) For an even number of exponents in the pair potential,the interaction potential between the micro/nano curved surface and the in-surface-particle can be expressed as a unified function of the mean curvature and Gaussian curvature of the curved surface;(b) the curvatures and the gradients of curvatures of the micro/nano curved surface are the essential factors that dominate the driving force acting on the particle.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11072125 and 10872114)the Natural Science Foundation of Jiangsu Province (Grant No. SBK201140044)
文摘We verify the accuracy of the curvature-based potential.By means of the idealized numerical experiment,we show that the curvature-based potential is in good agreement with the numerical experiment,and the errors are within a reasonable range.Based on the curvature-based potential,the equipotential surfaces of particles are derived,and the intrinsic relations between the equipotential surfaces and Weingarten helicoids are shown.
