Importance of Three-Dimensional Piezoelectric Coupling Modeling in Quantitative Analysis of Piezoelectric Actuators

This paper demonstrates the importance of three-dimensional(3-D)piezoelectric coupling in the electromechanical behavior of piezoelectric devices using three-dimensional finite element analyses based on weak and strong coupling models for a thin cantilevered piezoelectric bimorph actuator.It is found that there is a significant difference between the strong and weak coupling solutions given by coupling direct and inverse piezoelectric effects(i.e.,piezoelectric coupling effect).In addition,there is significant longitudinal bending caused by the constraint of the inverse piezoelectric effect in the width direction at the fixed end(i.e.,3-D effect).Hence,modeling of these effects or 3-D piezoelectric coupling modeling is an electromechanical basis for the piezoelectric devices,which contributes to the accurate prediction of their behavior.

Shear behavior of intact granite under thermo-mechanical coupling and three-dimensional morphology of shear-formed fractures

The shear failure of intact rock under thermo-mechanical(TM)coupling conditions is common,such as in enhanced geothermal mining and deep mine construction.Under the effect of a continuous engineering disturbance,shear-formed fractures are prone to secondary instability,posing a severe threat to deep engineering.Although numerous studies regarding three-dimensional(3D)morphologies of fracture surfaces have been conducted,the understanding of shear-formed fractures under TM coupling conditions is limited.In this study,direct shear tests of intact granite under various TM coupling conditions were conducted,followed by 3D laser scanning tests of shear-formed fractures.Test results demonstrated that the peak shear strength of intact granite is positively correlated with the normal stress,whereas it is negatively correlated with the temperature.The internal friction angle and cohesion of intact granite significantly decrease with an increase in the temperature.The anisotropy,roughness value,and height of the asperities on the fracture surfaces are reduced as the normal stress increases,whereas their variation trends are the opposite as the temperature increases.The macroscopic failure mode of intact granite under TM coupling conditions is dominated by mixed tensileeshear and shear failures.As the normal stress increases,intragranular fractures are developed ranging from a local to a global distribution,and the macroscopic failure mode of intact granite changes from mixed tensileeshear to shear failure.Finally,3D morphological characteristics of the asperities on the shear-formed fracture surfaces were analyzed,and a quadrangular pyramid conceptual model representing these asperities was proposed and sufficiently verified.

An Efficient Three-Dimensional Coupled Normal Mode Model and Its Application to Internal Solitary Wave Problems

We present an efficient three-dimensional coupled-mode model based on the Fourier synthesis technique. In principle, this model is a one-way model, and hence provides satisfactory accuracy for problems where the forward scattering dominates. At the same time, this model provides an efficiency gain of an order of magnitude or more over two-way coupled-mode models. This model can be applied to three-dimensional range-dependent problems with a slowly varying bathymetry or internal waves. A numerical example of the latter is demonstrated in this work. Comparisons of both accuracy and efficiency between the present model and a benchmark model are also provided.

Numerical Solutions of Three-Dimensional Coupled Burgers’ Equations by Using Some Numerical Methods

In this paper, we found the numerical solution of three-dimensional coupled Burgers’ Equations by using more efficient methods: Laplace Adomian decomposition method, Laplace transform homotopy perturbation method, variational iteration method, variational iteration decomposition method and variational iteration homotopy perturbation method. Example is examined to validate the efficiency and accuracy of these methods and they reduce the size of computation without the restrictive assumption to handle nonlinear terms and it gives the solutions rapidly.

Validation and application of three-dimensional discontinuous deformation analysis with tetrahedron finite element meshed block

In the last decade, three dimensional discontin- uous deformation analyses （3D DDA） has attracted more and more attention of researchers and geotechnical engineers worldwide. The original DDA formulation utilizes a linear displacement function to describe the block movement and deformation, which would cause block expansion under rigid body rotation and thus limit its capability to model block de- formation. In this paper, 3D DDA is coupled with tetrahe- dron finite elements to tackle these two problems. Tetrahe- dron is the simplest in the 3D domain and makes it easy to implement automatic discretization, even for complex topol- ogy shape. Furthermore, element faces will remain planar and element edges will remain straight after deformation for tetrahedron finite elements and polyhedral contact detection schemes can be used directly. The matrices of equilibrium equations for this coupled method are given in detail and an effective contact searching algorithm is suggested. Valida- tion is conducted by comparing the results of the proposed coupled method with that of physical model tests using one of the most common failure modes, i.e., wedge failure. Most of the failure modes predicted by the coupled method agree with the physical model results except for 4 cases out of the total 65 cases. Finally, a complex rockslide example demon- strates the robustness and versatility of the coupled method.

Flow Field and Temperature Field of Water-Cooling-Type Magnetic Coupling

At present, the water-cooling simulation of the water-cooled magnetic coupler is based on the water-cooled motor and the hydraulic coupler, which cannot accurately characterize the temperature distribution of the rotating watercooled coupling of the coupler. Focusing on rotating water cooling radiating, the present paper proposes simulating the water cooling temperature field as well as the flow field through the method of combining fluid-solid coupled heat transfer and MRF(Multiphase Reference Frame). In addition, taking an 800 kW magnetic coupling as an example, the paper optimizes the shape, number, cooling water inlet speed? and so on? of the cooling channel. Considering factors such as the complete machine’s temperature, and drag torque, it is proved that the cooling e ect is best when there are 36 involute curved channels and when the inlet speed is 3 m/s. Further, through experiments, the actual temperature values at six di erent positions when 50 kW and 70 kW thermal losses di er are measured. The measured values agree with the simulation results, proving the correctness of the proposed method. Further, data have been collected during the entire experimental procedure? and the variation in the coupling’s temperature is analyzed in depth, with the objective of laying a foundation for the estimation of the inner temperature rise as well as for the optimization of the structural design.

Three Dimensional Coupling between Elastic and Thermal Fields in the Static Analysis of Multilayered Composite Shells

This new work aims to develop a full coupled thermomechanical method including both the temperature profile and displacements as primary unknowns of the model.This generic full coupled 3D exact shell model permits the thermal stress investigation of laminated isotropic,composite and sandwich structures.Cylindrical and spherical panels,cylinders and plates are analyzed in orthogonal mixed curved reference coordinates.The 3D equilibrium relations and the 3D Fourier heat conduction equation for spherical shells are coupled and they trivially can be simplified in those for plates and cylindrical panels.The exponential matrix methodology is used to find the solutions of a full coupled model based on coupled differential relations with respect to the thickness coordinate.The analytical solution is based on theories of simply supported edges and harmonic relations for displacement components and sovra-temperature.The sovra-temperature magnitudes are directly applied at the outer faces through static state hypotheses.As a consequence,the sovra-temperature description is assumed to be an unknown variable of themodel and it is calculated in the sameway as the three displacements.The final systemis based on a set of coupled homogeneous differential relations of second order in the thickness coordinate.This system is reduced in a first order differential relation system by redoubling the number of unknowns.Therefore,the exponential matrix methodology is applied to calculate the solution.The temperature field effects are evaluated in the static investigation of shells and plates in terms of displacement and stress components.After an appropriate preliminary validation,new benchmarks are discussed for several thickness ratios,geometrical data,lamination sequences,materials and sovra-temperature values imposed at the outer faces.Results make evident the accordance between the uncoupled thermo-mechanical model and this new full coupled thermo-mechanical model without the need to separately solve the Fourier heat conduction relation.Both effects connected with the thickness layer and the related embedded materials are included in the conducted thermal stress analysis.

Behavior of traditional concrete dams and three-dimensional printed concrete dams under the debris flow impact

This study investigated the resilience of traditional concrete dams compared to 3D printed concrete dams(3DPC)when subjected to debris flow.Three types of dams,namely check dams,arch dams,and curve dams,were numerically analyzed using a three-dimensional Coupled Eulerian-Lagrangian(CEL)methodology.The research focused on critical factors such as impact force and viscous energy dissipation to compare dam performance.Additionally,the study examined the printing and service phases of 3DPC models,determining potential failure modes and analyzing printing parameters.The results demonstrated that 3DPC dams outperformed traditional concrete dams,with filament deposition orientation,perpendicular to the debris flow direction,identified as a pivotal factor.Infill percentage and pattern were also found to influence the behavior of 3DPC models.Notably,curved dams exhibited superior performance based on dam geometry.These findings have significant potential for advancing the development of resilient dam structures capable of withstanding debris flow impacts.

Numerical simulation of three-dimensional fracturing fracture propagation in radial wells

A fracture propagation model of radial well fracturing is established based on the finite element-meshless method.The model considers the coupling effect of fracturing fluid flow and rock matrix deformation.The fracture geometries of radial well fracturing are simulated,the induction effect of radial well on the fracture is quantitatively characterized,and the influences of azimuth,horizontal principle stress difference,and reservoir matrix permeability on the fracture geometries are revealed.The radial wells can induce the fractures to extend parallel to their axes when two radial wells in the same layer are fractured.When the radial wells are symmetrically distributed along the direction of the minimum horizontal principle stress with the azimuth greater than 15,the extrusion effect reduces the fracture length of radial wells.When the radial wells are symmetrically distributed along the direction of the maximum horizontal principal stress,the extrusion increases the fracture length of the radial wells.The fracture geometries are controlled by the rectification of radial borehole,the extrusion between radial wells in the same layer,and the deflection of the maximum horizontal principal stress.When the radial wells are distributed along the minimum horizontal principal stress symmetrically,the fracture length induced by the radial well decreases with the increase of azimuth;in contrast,when the radial wells are distributed along the maximum horizontal principal stress symmetrically,the fracture length induced by the radial well first decreases and then increases with the increase of azimuth.The fracture length induced by the radial well decreases with the increase of horizontal principal stress difference.The increase of rock matrix permeability and pore pressure of the matrix around radial wells makes the inducing effect of the radial well on fractures increase.

Numerical investigation of radio-frequency negative hydrogen ion sources by a three-dimensional fluid model

A three-dimensional fluid model is developed to investigate the radio-frequency inductively coupled H2 plasma in a reactor with a rectangular expansion chamber and a cylindrical driver chamber,for neutral beam injection system in CFETR.In this model,the electron effective collision frequency and the ion mobility at high E-fields are employed,for accurate simulation of discharges at low pressures(0.3 Pa-2 Pa)and high powers(40 kW-100 kW).The results indicate that when the high E-field ion mobility is taken into account,the electron density is about four times higher than the value in the low E-field case.In addition,the influences of the magnetic field,pressure and power on the electron density and electron temperature are demonstrated.It is found that the electron density and electron temperature in the xz-plane along permanent magnet side become much more asymmetric when magnetic field enhances.However,the plasma parameters in the yz-plane without permanent magnet side are symmetric no matter the magnetic field is applied or not.Besides,the maximum of the electron density first increases and then decreases with magnetic field,while the electron temperature at the bottom of the expansion region first decreases and then almost keeps constant.As the pressure increases from 0.3 Pa to 2 Pa,the electron density becomes higher,with the maximum moving upwards to the driver region,and the symmetry of the electron temperature in the xz-plane becomes much better.As power increases,the electron density rises,whereas the spatial distribution is similar.It can be summarized that the magnetic field and gas pressure have great influence on the symmetry of the plasma parameters,while the power only has little effect.

Three-dimensional solitons in two-component Bose–Einstein condensates

We investigate a kind of solitons in the two-component Bose-Einstein condensates with axisymmetric configurations in the R2 × S1 space. The corresponding topological structure is referred to as Hopfion. The spin texture differs from the conventional three-dimensional （3D） skyrmion and knot, which is characterized by two homotopy invariants. The stability of the Hopfion is verified numerically by evolving the Gross-Pitaevskii equations in imaginary time.

Simulating robust far-field coupling to traveling waves in large three-dimensional nanostructured high-Q microresonators

Ultra-high quality(Q) whispering gallery mode(WGM) microtoroid optical resonators have demonstrated highly sensitive biomolecular detection down to the single molecule limit;however, the lack of a robust coupling method has prevented their widespread adoption outside the laboratory. We demonstrate through simulation that a phased array of nanorods can enable free-space coupling of light both into and out of a microtoroid while maintaining a high Q. To simulate large nanostructured WGM resonators, we developed a new approach known as FloWBEM,which is an efficient and compact 3D wedge model with custom boundary conditions that accurately simulate the resonant Fano interference between the traveling WGM waves and a nanorod array. Depending on the excitation conditions, we find loaded Q factors of the driven system as high as 2.1 × 10~7 and signal-to-background ratios as high as 3.86%, greater than the noise levels of many commercial detectors. These results can drive future experimental implementation.

High efficiency,small size,and large bandwidth vertical interlayer waveguide coupler

Since the advent of three-dimensional photonic integrated circuits,the realization of efficient and compact optical interconnection between layers has become an important development direction.A vertical interlayer coupler between two silicon layers is presented in this paper.The coupling principle of the directional coupler is analyzed,and the traditional method of using a pair of vertically overlapping inverse taper structures is improved.For the coupling of two rectangular waveguide layers,a pair of nonlinear tapers with offset along the transmission direction is demonstrated.For the coupling of two ridge waveguide layers,a nonlinear taper in each layer is used to achieve high coupling efficiency.The simulation results show that the coupling efficiency of the two structures can reach more than 90%in a wavelength range from 1500 nm to 1650 nm.Moreover,the crosstalk is reduced to less than-50 d B by using multimode waveguides at intersections.The vertical interlayer coupler with a nonlinear taper is expected to realize the miniaturization and dense integration of photonic integrated chips.

Three-dimensional mode coupling around a seamount

A recently developed three-dimensional normal-mode model is adopted to investigate mode coupling around a seamount in a deep water environment. As indicated by the theoretical analysis and verified by the numerical results, strong mode coupling occurs at the edge of a seamount under certain conditions. Therefore, mode coupling is critical for the investigation of the acoustic field in the presence of a seamount. In addition, the issue regarding the number of sectors assuring convergence is also presented. This issue is important in a two-way coupled-mode approach, especially for solving three-dimensional problems, because the computational effort increases dramatically with the number of sectors in representing a varying bathymetry. The theoretical analysis as well as the numerical example in this paper shows that artificial diffraction lobes form in the event that uniform discretization is used with a horizontal step size greater than half of the acoustic wavelength. However, by using random discretization instead, such artificial diffraction lobes are diffused, resulting in a faster convergence rate.

Characteristic fractional step finite difference method for nonlinear section coupled system

For the section coupled system of multilayer dynamics of fluids in porous media, a parallel scheme modified by the characteristic finite difference fractional steps is proposed for a complete point set consisting of coarse and fine partitions. Some tech- niques, such as calculus of variations, energy method, twofold-quadratic interpolation of product type, multiplicative commutation law of difference operators, decomposition of high order difference operators, and prior estimates, are used in theoretical analysis. Optimal order estimates in 12 norm are derived to show accuracy of the second order approximation solutions. These methods have been used to simulate the problems of migration-accumulation of oil resources.

Preparation and characterization of three-dimensional micro-electrode for micro-supercapacitor based on inductively coupled plasma reactive etching technology

The capacity of supercapacitor charge storage depends on the size of the electrode surface area and the active material on the electrodes.To enhance the charge storage capacity with a reduced volume,silicon is used as the electrode material,and three-dimensional electrode structure is prepared to increase the electrode surface area on the footprint area by inductively coupled plasma reactive etching(ICP) techniques.The anodic constant current deposition method is employed to deposit manganese oxide on the electrode surface as the electroactive material.For comparison,samples without slot are prepared with a two-dimensional electrode.Scanning Electron Microscopy(SEM) and Energy Dispersive Spectroscopy(EDS) are used to characterize the surface morphology of the electrode structure and the deposited electroactive material.Electrochemical properties of the electrode are characterized by the cyclic voltammetry(CV) and the constant current charge-discharge method.Experimental results show that our approach can effectively increase the electrode surface area with more electroactive substances,and hence can increase storage capacity of the micro-supercapacitor.

3D thermo-hydro-mechanical-migratory coupling model and FEM analyses for dual-porosity medium

One kind of 3D coupled thermo-hydro-mechanical-migratory model for saturated-unsaturated dual-porosity medium was established,in which the stress field and the temperature field are single,but the seepage field and the concentration field are double,and the influences of sets,spaces,angles,continuity ratios,stiffness of fractures on the constitutive relationship of the medium can be considered.The relative three-dimensional program of finite element method was also developed.By comparing with the existing computation example,reliability of the model and the program were verified.Taking a hypothetical nuclear waste repository as a calculation example,the radioactive nuclide leak was simulated numerically with both the rock mass and the buffer being unsaturated media,and the temperatures,negative pore pressures,flow velocities,nuclide concentrations and normal stresses in the rock mass were investigated.The results showed that the temperatures,negative pore pressures and nuclide concentrations in the buffer all present nonlinear changes and distributions that even though the saturation degree in porosity is only about 1/9 of that in fracture,the flow velocity of underground water in fracture is about 6 times of that in porosity because the permeability coefficient of fracture is almost four orders higher than that of porosity,and that the regions of stress concentration occur at the vicinity of two sides of the boundary between buffer and disposal pit wall.

A Three-Dimensional Size-Dependent Layered Model for Simply-Supported and Functionally Graded Magnetoelectroelastic Plates

A three-dimensional size-dependent layered model for simply-supported and func- tionally graded magnetoelectroelastic plates is presented based on the modified couple-stress theory. The functionally graded material is assumed to be exponential in the thickness direc- tion of the plate. The final governing equations are reduced to an eigensystem by expressing the extended displacements in terms of two-dimensional Fourier series. Using the propagator matrix method, the exact solutions of the magnetic, electric and mechanical fields of sandwich nanoplates with couple-stress effect and under the surface loads are derived. Numerical examples for two functionally graded sandwich plates made of piezoelectric BaTiO3 and magnetostrictive CoFe2O4 materials are presented to demonstrate the effect of the functional gradient factor and material length-scale parameter on the induced fields. The exact solutions presented in this work can also serve as benchmarks to various numerical methods for analyzing the size-dependent features in layered systems.

COUPLING COMPUTATION OF THE FLOW FIELD AND THE LARGE DEFORMATION OF MEMBRANE STRUCTURE OF STRATOSPHERE AIRSHIPS

In this article, the mathematical model of the coupling of the three-dimensional fluid flow and the large deformation of membrane structure is established. The fluid-structure coupling interaction is simulated using the computational codes developed by the authors. By analyzing the interactions of membrane and flow field, the aeroelasticity of the airship is detailed. All the results are adopted in the focused study of the stratosphere airship in trimmed state.

THEORY AND APPLICATION OF FRACTIONAL STEP CHARACTERISTIC FINITE DIFFERENCE METHOD IN NUMERICAL SIMULATION OF SECOND ORDER ENHANCED OIL PRODUCTION

A kind of second-order implicit fractional step characteristic finite difference method is presented in this paper for the numerically simulation coupled system of enhanced （chemical） oil production in porous media. Some techniques, such as the calculus of variations, energy analysis method, commutativity of the products of difference operators, decomposition of high-order difference operators and the theory of a priori estimates are introduced and an optimal order error estimates in l^2 norm is derived. This method has been applied successfully to the numerical simulation of enhanced oil production in actual oilfields, and the simulation results ate quite interesting and satisfactory.