A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines...A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines as trial functions to approximate the state and costate variables in two space dimensions.A Crank-Nicolson difference scheme is constructed for time discretization.The resulting numerical solutions belong to C2in space,and the order of the coefficient matrix is low.Moreover,the Bogner-Fox-Schmit element is considered for comparison.Two numerical experiments demonstrate the feasibility and effectiveness of the proposed method.展开更多
For singularly perturbed convection-diffusion problems,supercloseness analysis of the finite element method is still open on Bakhvalov-type meshes,especially in the case of 2D.The difficulties arise from the width of ...For singularly perturbed convection-diffusion problems,supercloseness analysis of the finite element method is still open on Bakhvalov-type meshes,especially in the case of 2D.The difficulties arise from the width of the mesh in the layer adjacent to the transition point,resulting in a suboptimal estimate for convergence.Existing analysis techniques cannot handle these difficulties well.To fill this gap,here a novel interpolation is designed delicately for the smooth part of the solution,bringing about the optimal supercloseness result of almost order 2 under an energy norm for the finite element method.Our theoretical result is uniform in the singular perturbation parameterεand is supported by the numerical experiments.展开更多
In polar regions, floating ice exhibits distinct characteristics across a range of spatial scales. It is well recognized that the irregular geometry of these ice formations markedly influences their dynamic behavior. ...In polar regions, floating ice exhibits distinct characteristics across a range of spatial scales. It is well recognized that the irregular geometry of these ice formations markedly influences their dynamic behavior. This study introduces a polyhedral Discrete Element Method (DEM) tailored for polar ice, incorporating the Gilbert-Johnson-Keerthi (GJK) and Expanding Polytope Algorithm (EPA) for contact detection. This approach facilitates the simulation of the drift and collision processes of floating ice, effectively capturing its freezing and fragmentation. Subsequently, the stability and reli ability of this model are validated by uniaxial compression on level ice fields, focusing specifically on the influence of compression strength on deformation resistance. Additionally, clusters of ice floes nav igating through narrow channels are simulated. These studies have qualitatively assessed the effects of Floe Size Distribution (FSD), initial concentration, and circularity on their flow dynamics. The higher power-law exponent values in the FSD, increased circularity, and decreased concentration are each as sociated with accelerated flow in ice floe fields. The simulation results distinctly demonstrate the con siderable impact of sea ice geometry on the movement of clusters, offering valuable insights into the complexities of polar ice dynamics.展开更多
Due to the wide application of closely spaced multi-well horizontal pads for developing unconventional gas reservoirs,interference between wells becomes a significant concern.Communication between wells mainly occurs ...Due to the wide application of closely spaced multi-well horizontal pads for developing unconventional gas reservoirs,interference between wells becomes a significant concern.Communication between wells mainly occurs through natural fractures.However,previous studies have found that interwell communication through natural fractures is varied,and non-communication also appears in the mid and late stages of production due to natural fracture closure.This study proposes a boundary element method for coupling multi-connected regions for the first time.Using this method,we coupled multiple flow fields to establish dual-well models with various connectivity conditions of the stimulated reservoir volume(SRV)region.These models also take into consideration of adsorption and desorption mechanism of natural gas as well as the impact of fracturing fluid retention.The study found that when considering the non-communication of SRV regions between multi-well horizontal pads,the transient behavior of the targeted well exhibits a transitional flow stage occurring before the well interference flow stage.In addition,sensitivity analysis shows that the well spacing and production regime,as well as the connectivity conditions of the SRV region,affect the timing of interwell interference.Meanwhile,the productivity of the two wells,reservoir properties,and fracturing operations affect the intensity of interwell interference.展开更多
The equilibrium equations and the functional for tubing buckling in arbitrary straight wells are derived. The entire buckling process of tubing in deviated wells is analyzed for the first time by utilizing the finite ...The equilibrium equations and the functional for tubing buckling in arbitrary straight wells are derived. The entire buckling process of tubing in deviated wells is analyzed for the first time by utilizing the finite element method. The effects of gravity and torques on the buckling are included in the analyses and the calculated results are well compared with existing solutions. It is shown that the buckling only occurs at the lower portion of the tubing where the axial load is the largest, and the contact force of the well, the bending moment of the tubing and the buckling displacement of this portion vary periodically. The buckling spreads upwards from the bit with the increase of axial load. There is no buckling at the upper portion of the tubing where the bending moment is zero. And the contact force of this section increases only slightly with the increase of the axial load. With the increase of the deviation angle, the length of buckling portion and buckling displacement amplitude decrease, the contact force increases with the increase of load at the upper portion and its amplitude decreases at the lower buckling section, the bending moment remains zero at the upper portion and its amplitude decreases at the lower buckling portion. The buckling displacement increases with the increase of the torque, but the increment is very small.展开更多
A discontinuous Galerkin finite element method （DG-FEM） is developed for solving the axisymmetric Euler equations based on two-dimensional conservation laws. The method is used to simulate the unsteady-state underex...A discontinuous Galerkin finite element method （DG-FEM） is developed for solving the axisymmetric Euler equations based on two-dimensional conservation laws. The method is used to simulate the unsteady-state underexpanded axisymmetric jet. Several flow property distributions along the jet axis, including density, pres- sure and Mach number are obtained and the qualitative flowfield structures of interest are well captured using the proposed method, including shock waves, slipstreams, traveling vortex ring and multiple Mach disks. Two Mach disk locations agree well with computational and experimental measurement results. It indicates that the method is robust and efficient for solving the unsteady-state underexpanded axisymmetric jet.展开更多
A numerical simulation of the toroidal shock wave focusing in a co-axial cylindrical shock tube is inves- tigated by using discontinuous Galerkin （DG） finite element method to solve the axisymmetric Euler equations....A numerical simulation of the toroidal shock wave focusing in a co-axial cylindrical shock tube is inves- tigated by using discontinuous Galerkin （DG） finite element method to solve the axisymmetric Euler equations. For validating the numerical method, the shock-tube problem with exact solution is computed, and the computed results agree well with the exact cases. Then, several cases with higher incident Mach numbers varying from 2.0 to 5.0 are simulated. Simulation results show that complicated flow-field structures of toroidal shock wave diffraction, reflection, and focusing in a co-axial cylindrical shock tube can be obtained at different incident Mach numbers and the numerical solutions appear steep gradients near the focusing point, which illustrates the DG method has higher accuracy and better resolution near the discontinuous point. Moreover, the focusing peak pres- sure with different grid scales is compared.展开更多
The stochastic boundary element method(SBEM)is developed in this paper for 3D problems with body forces and reliability analysis of engineering structures.The integral equations of SBEM are established by the approach...The stochastic boundary element method(SBEM)is developed in this paper for 3D problems with body forces and reliability analysis of engineering structures.The integral equations of SBEM are established by the approach of partial derivation with respect to stochastic variables,considering the yield limit,rotation speeds and material density to be the fundamental stochastic variables.Through analyzing a numerical example and a turbo-disk of an aeroengine,the results show that the method developed is successful.展开更多
The static behavior of piezoelectric circular spherical shallow shells under both electrical and mechanical loads is studied by using the differential quadrature element method (DQEM). Geometrical nonlinearity effect ...The static behavior of piezoelectric circular spherical shallow shells under both electrical and mechanical loads is studied by using the differential quadrature element method (DQEM). Geometrical nonlinearity effect is considered. Detailed formulations and procedures are given for the first time. Several examples are analyzed and accurate results are obtained by the DQEM. Based on the results in this paper, one may conclude that the DQEM is a useful tool for obtaining solutions of structural elements. It can be seen that the shell shape may be theore tically controlled and snap through may occur when the applied voltage reaches a critical value even without mechanical load for certain geometric configurations.展开更多
A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element...A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.展开更多
The Runge-Kutta discontinuous Galerkin finite element method （RK-DGFEM） is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and ...The Runge-Kutta discontinuous Galerkin finite element method （RK-DGFEM） is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and it is explicit in the time domain. Consequently it is a best mixture of FEM and finite volume method （FVM）. RK-DGFEM can obtain local high-order accuracy by using high-order polynomial basis. Numerical experiments of transverse magnetic （TM） wave propagation in a 2-D resonator are performed. A high-order Lagrange polynomial basis is adopted. Numerical results agree well with analytical solution. And different order Lagrange interpolation polynomial basis impacts on simulation result accuracy are discussed. Computational results indicate that the accuracy is evidently improved when the order of interpolation basis is increased. Finally, L^2 errors of different order polynomial basis in RK-DGFEM are presented. Computational results show that L^2 error declines exponentially as the order of basis increases.展开更多
The effect of interconnect linewidth on the evolution of intragranular microcracks due to surface diffusion induced by electromigration is analyzed by finite element method.The numerical results indicate that there ex...The effect of interconnect linewidth on the evolution of intragranular microcracks due to surface diffusion induced by electromigration is analyzed by finite element method.The numerical results indicate that there exists critical values of the linewidth hc,the electric fieldχc and the aspect ratioβc.When h>hc,χ<χc orβ<βc,the microcrack will evolve into a stable shape as it migrates along the interconnect line.When h≤hc,χ≥χc orβ≥βc,the microcrack will split into two smaller microcracks.The critical electric field,the critical aspect ratio and the splitting time have a stronger dependence on the linewidth when h≤6.In addition,the decrease of the linewidth,the increase of the electric field or the aspect ratio is beneficial to accelerate microcrack splitting,which may delay the open failure of the interconnect line.展开更多
Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on e...Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on element faces.Discontinuity of velocity field leads this method not to conserve mass locally.Moreover,the accuracy and stability of a solution is highly affected by a non-conservative method.In this paper,a three dimensional control volume finite element method is developed for twophase fluid flow simulation which overcomes the deficiency of the standard finite element method,and attains high-orders of accuracy at a reasonable computational cost.Moreover,this method is capable of handling heterogeneity in a very rational way.A fully implicit scheme is applied to temporal discretization of the governing equations to achieve an unconditionally stable solution.The accuracy and efficiency of the method are verified by simulating some waterflooding experiments.Some representative examples are presented to illustrate the capability of the method to simulate two-phase fluid flow in heterogeneous porous media.展开更多
A two-dimensional axisymmetric finite element model based on an improved cohesive element method was developed to simulate interfacial debonding, sliding friction, and residual thermal stresses in SiC composites durin...A two-dimensional axisymmetric finite element model based on an improved cohesive element method was developed to simulate interfacial debonding, sliding friction, and residual thermal stresses in SiC composites during single-fiber push-out tests to extract the interfacial bond strength and frictional stress. The numerical load–displacement curves agree well with experimental curves,indicating that this cohesive element method can be used for calculating the interfacial properties of SiC composites.The simulation results show that cracks are most likely to occur at the ends of the experimental sample, where the maximum shear stress is observed and that the interfacial shear strength and constant sliding friction stress decrease with an increase in temperature. Moreover, the load required to cause complete interfacial failure increases with the increase in critical shear strength, and the composite materials with higher fiber volume fractions have higher bearing capacities. In addition, the initial failure load increases with an increase in interphase thickness.展开更多
This paper discusses the forward and inverse problem for cardiac magnetic fields and electric potentials. A torso-heart model established by boundary element method （BEM） is used for studying the distributions of ca...This paper discusses the forward and inverse problem for cardiac magnetic fields and electric potentials. A torso-heart model established by boundary element method （BEM） is used for studying the distributions of cardiac magnetic fields and electric potentials. Because node-to-node and triangle-to-triangle BEM can lead to discrepant field distributions, their properties and influences are compared. Then based on constructed torso-heart model and supposed current source functional model-current dipole array, the magnetic and electric imaging by optimal constrained linear inverse method are applied at the same time. Through figure and reconstructing parameter comparison, though the magnetic current dipole array imaging possesses better reconstructing effect, however node-to-node BEM and triangleto-triangle BEM make little difference to magnetic and electric imaging.展开更多
An increment-dimensional scaled boundary finite element method (ID-SBFEM) is developed to solve the transient temperature field.To improve the accuracy of SBFEM,the effect of high frequency factor on dynamic stiffness...An increment-dimensional scaled boundary finite element method (ID-SBFEM) is developed to solve the transient temperature field.To improve the accuracy of SBFEM,the effect of high frequency factor on dynamic stiffness is considered,and the first-order continued fraction technique is used.After the derivation,the SBFE equations are obtained,and the dimensions of thermal conduction,the thermal capacity matrix and the vector of the right side term in the equations are doubled.An example is presented to illustrate the feasibility and good accuracy of the proposed method.展开更多
In this article, on the basis of two-level discretizations and multiscale finite element method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique ...In this article, on the basis of two-level discretizations and multiscale finite element method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique is first to use a standard finite element discretization on a coarse mesh to approximate low frequencies, then to apply the simple and Newton scheme to linearize discretizations on a fine grid. At this process, multiscale finite element method as a stabilized method deals with the lowest equal-order finite element pairs not satisfying the inf-sup condition. Under the uniqueness condition, error analyses for both algorithms are given. Numerical results are reported to demonstrate the effectiveness of the simple and Newton scheme.展开更多
Propagation characteristics of surface acoustic waves（SAWs） in ZnO films/glass substrates are theoretically investigated by the three-dimensional（3D） finite element method. At first, for（11ˉ20） ZnO films/glass ...Propagation characteristics of surface acoustic waves（SAWs） in ZnO films/glass substrates are theoretically investigated by the three-dimensional（3D） finite element method. At first, for（11ˉ20） ZnO films/glass substrates, the simulation results confirm that the Rayleigh waves along the [0001] direction and Love waves along the [1ˉ100] direction are successfully excited in the multilayered structures. Next, the crystal orientations of the ZnO films are rotated, and the influences of ZnO films with different crystal orientations on SAW characterizations, including the phase velocity, electromechanical coupling coefficient, and temperature coefficient of frequency, are investigated. The results show that at appropriate h/λ, Rayleigh wave has a maximum k^2 of 2.4% in（90°, 56.5°, 0°） ZnO film/glass substrate structure; Love wave has a maximum k^2 of 3.81% in（56°, 90°, 0°） ZnO film/glass substrate structure. Meantime, for Rayleigh wave and Love wave devices, zero temperature coefficient of frequency（TCF） can be achieved at appropriate ratio of film thickness to SAW wavelength. These results show that SAW devices with higher k^2 or lower TCF can be fabricated by flexibly selecting the crystal orientations of ZnO films on glass substrates.展开更多
Interdigitated finger capacitance of a continuous-wave terahertz photomixer is calculated using the finite element method.For the frequently used electrode width（0.2 μm） and gap width（1.8 μm）,the finger capacita...Interdigitated finger capacitance of a continuous-wave terahertz photomixer is calculated using the finite element method.For the frequently used electrode width（0.2 μm） and gap width（1.8 μm）,the finger capacitance increases quasi-quadratically with the number of electrodes increasing.The quasi-quadratic dependence can be explained by a sequence of lumped capacitors connected in parallel.For a photomixer composed of 10 electrodes and 9 photoconductive gaps,the finger capacitance increases as the gap width increases at a small electrode width,and follows the reverse trend at a large electrode width.For a constant electrode width,the finger capacitance first decreases and then slightly increases as the gap broadens until the smallest finger capacitance is formed.We also investigate the finger capacitances at different electrode and gap configurations with the 8 μm × 8 μm photomixer commonly used in previous studies.These calculations lead to a better understanding of the finger capacitance affected by the finger parameters,and should lead to terahertz photomixer optimization.展开更多
In this paper, the complex variable reproducing kernel particle （CVRKP） method and the finite element （FE） method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE metho...In this paper, the complex variable reproducing kernel particle （CVRKP） method and the finite element （FE） method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, then the computational efficiency is higher. A hybrid approximation function is applied to combine the CVRKP method with the FE method, and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme. The corresponding formulations of the CVRKP-FE method are presented in detail. Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method.展开更多
基金supported by the National Natural Science Foundation of China(11871312,12131014)the Natural Science Foundation of Shandong Province,China(ZR2023MA086)。
文摘A bicubic B-spline finite element method is proposed to solve optimal control problems governed by fourth-order semilinear parabolic partial differential equations.Its key feature is the selection of bicubic B-splines as trial functions to approximate the state and costate variables in two space dimensions.A Crank-Nicolson difference scheme is constructed for time discretization.The resulting numerical solutions belong to C2in space,and the order of the coefficient matrix is low.Moreover,the Bogner-Fox-Schmit element is considered for comparison.Two numerical experiments demonstrate the feasibility and effectiveness of the proposed method.
基金supported by National Natural Science Foundation of China(11771257)the Shandong Provincial Natural Science Foundation of China(ZR2023YQ002,ZR2023MA007,ZR2021MA004)。
文摘For singularly perturbed convection-diffusion problems,supercloseness analysis of the finite element method is still open on Bakhvalov-type meshes,especially in the case of 2D.The difficulties arise from the width of the mesh in the layer adjacent to the transition point,resulting in a suboptimal estimate for convergence.Existing analysis techniques cannot handle these difficulties well.To fill this gap,here a novel interpolation is designed delicately for the smooth part of the solution,bringing about the optimal supercloseness result of almost order 2 under an energy norm for the finite element method.Our theoretical result is uniform in the singular perturbation parameterεand is supported by the numerical experiments.
文摘In polar regions, floating ice exhibits distinct characteristics across a range of spatial scales. It is well recognized that the irregular geometry of these ice formations markedly influences their dynamic behavior. This study introduces a polyhedral Discrete Element Method (DEM) tailored for polar ice, incorporating the Gilbert-Johnson-Keerthi (GJK) and Expanding Polytope Algorithm (EPA) for contact detection. This approach facilitates the simulation of the drift and collision processes of floating ice, effectively capturing its freezing and fragmentation. Subsequently, the stability and reli ability of this model are validated by uniaxial compression on level ice fields, focusing specifically on the influence of compression strength on deformation resistance. Additionally, clusters of ice floes nav igating through narrow channels are simulated. These studies have qualitatively assessed the effects of Floe Size Distribution (FSD), initial concentration, and circularity on their flow dynamics. The higher power-law exponent values in the FSD, increased circularity, and decreased concentration are each as sociated with accelerated flow in ice floe fields. The simulation results distinctly demonstrate the con siderable impact of sea ice geometry on the movement of clusters, offering valuable insights into the complexities of polar ice dynamics.
基金supported by the National Science Fund for Excellent Young Scholars(No.52222402)State Key Program of National Natural Science Foundation of China(No.U23A2022)+7 种基金State Key Program of National Natural Science Foundation of China(No.52234003)Sichuan Science and Technology Program(No.2022JDJQ0009)National Natural Science Foundation of China(No.52074235)Science and Technology Cooperation Project of the CNPC-SWPU Innovation Alliance(Nos.2020CX020202 and 2020CX030202)Shale Gas industry Development Institute of Sichuan Province111 Project(No.D18016)China Postdoctoral Science Foundation(No.2022M722637)the Science Foundation of Sichuan Province(No.2022NSFSC0186)。
文摘Due to the wide application of closely spaced multi-well horizontal pads for developing unconventional gas reservoirs,interference between wells becomes a significant concern.Communication between wells mainly occurs through natural fractures.However,previous studies have found that interwell communication through natural fractures is varied,and non-communication also appears in the mid and late stages of production due to natural fracture closure.This study proposes a boundary element method for coupling multi-connected regions for the first time.Using this method,we coupled multiple flow fields to establish dual-well models with various connectivity conditions of the stimulated reservoir volume(SRV)region.These models also take into consideration of adsorption and desorption mechanism of natural gas as well as the impact of fracturing fluid retention.The study found that when considering the non-communication of SRV regions between multi-well horizontal pads,the transient behavior of the targeted well exhibits a transitional flow stage occurring before the well interference flow stage.In addition,sensitivity analysis shows that the well spacing and production regime,as well as the connectivity conditions of the SRV region,affect the timing of interwell interference.Meanwhile,the productivity of the two wells,reservoir properties,and fracturing operations affect the intensity of interwell interference.
文摘The equilibrium equations and the functional for tubing buckling in arbitrary straight wells are derived. The entire buckling process of tubing in deviated wells is analyzed for the first time by utilizing the finite element method. The effects of gravity and torques on the buckling are included in the analyses and the calculated results are well compared with existing solutions. It is shown that the buckling only occurs at the lower portion of the tubing where the axial load is the largest, and the contact force of the well, the bending moment of the tubing and the buckling displacement of this portion vary periodically. The buckling spreads upwards from the bit with the increase of axial load. There is no buckling at the upper portion of the tubing where the bending moment is zero. And the contact force of this section increases only slightly with the increase of the axial load. With the increase of the deviation angle, the length of buckling portion and buckling displacement amplitude decrease, the contact force increases with the increase of load at the upper portion and its amplitude decreases at the lower buckling section, the bending moment remains zero at the upper portion and its amplitude decreases at the lower buckling portion. The buckling displacement increases with the increase of the torque, but the increment is very small.
文摘A discontinuous Galerkin finite element method （DG-FEM） is developed for solving the axisymmetric Euler equations based on two-dimensional conservation laws. The method is used to simulate the unsteady-state underexpanded axisymmetric jet. Several flow property distributions along the jet axis, including density, pres- sure and Mach number are obtained and the qualitative flowfield structures of interest are well captured using the proposed method, including shock waves, slipstreams, traveling vortex ring and multiple Mach disks. Two Mach disk locations agree well with computational and experimental measurement results. It indicates that the method is robust and efficient for solving the unsteady-state underexpanded axisymmetric jet.
基金Supported by the National Natural Science Foundation of China(50976072,51106099,10902070)the Leading Academic Discipline Project of Shanghai Municipal Education Commission(J50501)the Science Foundation for the Excellent Youth Scholar of Higher Education of Shanghai(slg09003)~~
文摘A numerical simulation of the toroidal shock wave focusing in a co-axial cylindrical shock tube is inves- tigated by using discontinuous Galerkin （DG） finite element method to solve the axisymmetric Euler equations. For validating the numerical method, the shock-tube problem with exact solution is computed, and the computed results agree well with the exact cases. Then, several cases with higher incident Mach numbers varying from 2.0 to 5.0 are simulated. Simulation results show that complicated flow-field structures of toroidal shock wave diffraction, reflection, and focusing in a co-axial cylindrical shock tube can be obtained at different incident Mach numbers and the numerical solutions appear steep gradients near the focusing point, which illustrates the DG method has higher accuracy and better resolution near the discontinuous point. Moreover, the focusing peak pres- sure with different grid scales is compared.
文摘The stochastic boundary element method(SBEM)is developed in this paper for 3D problems with body forces and reliability analysis of engineering structures.The integral equations of SBEM are established by the approach of partial derivation with respect to stochastic variables,considering the yield limit,rotation speeds and material density to be the fundamental stochastic variables.Through analyzing a numerical example and a turbo-disk of an aeroengine,the results show that the method developed is successful.
文摘The static behavior of piezoelectric circular spherical shallow shells under both electrical and mechanical loads is studied by using the differential quadrature element method (DQEM). Geometrical nonlinearity effect is considered. Detailed formulations and procedures are given for the first time. Several examples are analyzed and accurate results are obtained by the DQEM. Based on the results in this paper, one may conclude that the DQEM is a useful tool for obtaining solutions of structural elements. It can be seen that the shell shape may be theore tically controlled and snap through may occur when the applied voltage reaches a critical value even without mechanical load for certain geometric configurations.
基金Project supported by the National Basic Research Program of China (973Project) (No.2002CB412709) and the National Natural Science Foundation of China (Nos.50278012,10272027,19832010)
文摘A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.
文摘The Runge-Kutta discontinuous Galerkin finite element method （RK-DGFEM） is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and it is explicit in the time domain. Consequently it is a best mixture of FEM and finite volume method （FVM）. RK-DGFEM can obtain local high-order accuracy by using high-order polynomial basis. Numerical experiments of transverse magnetic （TM） wave propagation in a 2-D resonator are performed. A high-order Lagrange polynomial basis is adopted. Numerical results agree well with analytical solution. And different order Lagrange interpolation polynomial basis impacts on simulation result accuracy are discussed. Computational results indicate that the accuracy is evidently improved when the order of interpolation basis is increased. Finally, L^2 errors of different order polynomial basis in RK-DGFEM are presented. Computational results show that L^2 error declines exponentially as the order of basis increases.
基金supported by the Natural Science Foundation of Jiangsu Province of China (No. BK20141407)a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘The effect of interconnect linewidth on the evolution of intragranular microcracks due to surface diffusion induced by electromigration is analyzed by finite element method.The numerical results indicate that there exists critical values of the linewidth hc,the electric fieldχc and the aspect ratioβc.When h>hc,χ<χc orβ<βc,the microcrack will evolve into a stable shape as it migrates along the interconnect line.When h≤hc,χ≥χc orβ≥βc,the microcrack will split into two smaller microcracks.The critical electric field,the critical aspect ratio and the splitting time have a stronger dependence on the linewidth when h≤6.In addition,the decrease of the linewidth,the increase of the electric field or the aspect ratio is beneficial to accelerate microcrack splitting,which may delay the open failure of the interconnect line.
基金Iranian Offshore Oil Company (IOOC) for financial support of this work
文摘Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on element faces.Discontinuity of velocity field leads this method not to conserve mass locally.Moreover,the accuracy and stability of a solution is highly affected by a non-conservative method.In this paper,a three dimensional control volume finite element method is developed for twophase fluid flow simulation which overcomes the deficiency of the standard finite element method,and attains high-orders of accuracy at a reasonable computational cost.Moreover,this method is capable of handling heterogeneity in a very rational way.A fully implicit scheme is applied to temporal discretization of the governing equations to achieve an unconditionally stable solution.The accuracy and efficiency of the method are verified by simulating some waterflooding experiments.Some representative examples are presented to illustrate the capability of the method to simulate two-phase fluid flow in heterogeneous porous media.
基金supported by the National Natural Science Foundation of China(No.11405124)Science Challenge Project(No.TZ2018004)+1 种基金Natural Science Basic Research Plan in Shaanxi Province of China(No.2015JQ1030)the Shaanxi Province Postdoctoral Science Foundation(2014)
文摘A two-dimensional axisymmetric finite element model based on an improved cohesive element method was developed to simulate interfacial debonding, sliding friction, and residual thermal stresses in SiC composites during single-fiber push-out tests to extract the interfacial bond strength and frictional stress. The numerical load–displacement curves agree well with experimental curves,indicating that this cohesive element method can be used for calculating the interfacial properties of SiC composites.The simulation results show that cracks are most likely to occur at the ends of the experimental sample, where the maximum shear stress is observed and that the interfacial shear strength and constant sliding friction stress decrease with an increase in temperature. Moreover, the load required to cause complete interfacial failure increases with the increase in critical shear strength, and the composite materials with higher fiber volume fractions have higher bearing capacities. In addition, the initial failure load increases with an increase in interphase thickness.
基金Project supported by the State Key Development Program for Basic Research of China (Grant No. 2006CB601007)the National Natural Science Foundation of China (Grant No. 10674006)the National High Technology Research and Development Program of China (Grant No. 2007AA03Z238)
文摘This paper discusses the forward and inverse problem for cardiac magnetic fields and electric potentials. A torso-heart model established by boundary element method （BEM） is used for studying the distributions of cardiac magnetic fields and electric potentials. Because node-to-node and triangle-to-triangle BEM can lead to discrepant field distributions, their properties and influences are compared. Then based on constructed torso-heart model and supposed current source functional model-current dipole array, the magnetic and electric imaging by optimal constrained linear inverse method are applied at the same time. Through figure and reconstructing parameter comparison, though the magnetic current dipole array imaging possesses better reconstructing effect, however node-to-node BEM and triangleto-triangle BEM make little difference to magnetic and electric imaging.
基金supported by the Innovation Training Project for Students in NUAA(No.2016C-X0010-129)the Key Laboratory of Aircraft Environment Control and Life Support(NUAA),Ministry of Industry and Information Technology
文摘An increment-dimensional scaled boundary finite element method (ID-SBFEM) is developed to solve the transient temperature field.To improve the accuracy of SBFEM,the effect of high frequency factor on dynamic stiffness is considered,and the first-order continued fraction technique is used.After the derivation,the SBFE equations are obtained,and the dimensions of thermal conduction,the thermal capacity matrix and the vector of the right side term in the equations are doubled.An example is presented to illustrate the feasibility and good accuracy of the proposed method.
文摘In this article, on the basis of two-level discretizations and multiscale finite element method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique is first to use a standard finite element discretization on a coarse mesh to approximate low frequencies, then to apply the simple and Newton scheme to linearize discretizations on a fine grid. At this process, multiscale finite element method as a stabilized method deals with the lowest equal-order finite element pairs not satisfying the inf-sup condition. Under the uniqueness condition, error analyses for both algorithms are given. Numerical results are reported to demonstrate the effectiveness of the simple and Newton scheme.
基金supported by the National Natural Science Foundation of China(Grant No.11304160)the Natural Science Foundation of Jiangsu Provincial Higher Education Institutions,China(Grant No.13KJB140008)the Foundation of Nanjing University of Posts and Telecommunications,China(Grant No.NY213018)
文摘Propagation characteristics of surface acoustic waves（SAWs） in ZnO films/glass substrates are theoretically investigated by the three-dimensional（3D） finite element method. At first, for（11ˉ20） ZnO films/glass substrates, the simulation results confirm that the Rayleigh waves along the [0001] direction and Love waves along the [1ˉ100] direction are successfully excited in the multilayered structures. Next, the crystal orientations of the ZnO films are rotated, and the influences of ZnO films with different crystal orientations on SAW characterizations, including the phase velocity, electromechanical coupling coefficient, and temperature coefficient of frequency, are investigated. The results show that at appropriate h/λ, Rayleigh wave has a maximum k^2 of 2.4% in（90°, 56.5°, 0°） ZnO film/glass substrate structure; Love wave has a maximum k^2 of 3.81% in（56°, 90°, 0°） ZnO film/glass substrate structure. Meantime, for Rayleigh wave and Love wave devices, zero temperature coefficient of frequency（TCF） can be achieved at appropriate ratio of film thickness to SAW wavelength. These results show that SAW devices with higher k^2 or lower TCF can be fabricated by flexibly selecting the crystal orientations of ZnO films on glass substrates.
基金Project supported by the National High Technology Research and Development Program of China (Grant No. 2011AAxxx2008A)Hundred Talent Program of the Chinese Academy of Sciences (Grant No. J08-029)the Main Direction Program of Knowledge Innovation of the Chinese Academy of Sciences (Grant No. YYYJ-1123-4)
文摘Interdigitated finger capacitance of a continuous-wave terahertz photomixer is calculated using the finite element method.For the frequently used electrode width（0.2 μm） and gap width（1.8 μm）,the finger capacitance increases quasi-quadratically with the number of electrodes increasing.The quasi-quadratic dependence can be explained by a sequence of lumped capacitors connected in parallel.For a photomixer composed of 10 electrodes and 9 photoconductive gaps,the finger capacitance increases as the gap width increases at a small electrode width,and follows the reverse trend at a large electrode width.For a constant electrode width,the finger capacitance first decreases and then slightly increases as the gap broadens until the smallest finger capacitance is formed.We also investigate the finger capacitances at different electrode and gap configurations with the 8 μm × 8 μm photomixer commonly used in previous studies.These calculations lead to a better understanding of the finger capacitance affected by the finger parameters,and should lead to terahertz photomixer optimization.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11171208)the Special Fund for Basic Scientific Research of Central Colleges of Chang’an University, China (Grant No. CHD2011JC080)
文摘In this paper, the complex variable reproducing kernel particle （CVRKP） method and the finite element （FE） method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, then the computational efficiency is higher. A hybrid approximation function is applied to combine the CVRKP method with the FE method, and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme. The corresponding formulations of the CVRKP-FE method are presented in detail. Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method.
