Sudden and unforeseen seismic failures of coal mine overburden(OB)dump slopes interrupt mining operations,cause loss of lives and delay the production of coal.Consideration of the spatial heterogeneity of OB dump mate...Sudden and unforeseen seismic failures of coal mine overburden(OB)dump slopes interrupt mining operations,cause loss of lives and delay the production of coal.Consideration of the spatial heterogeneity of OB dump materials is imperative for an adequate evaluation of the seismic stability of OB dump slopes.In this study,pseudo-static seismic stability analyses are carried out for an OB dump slope by considering the material parameters obtained from an insitu field investigation.Spatial heterogeneity is simulated through use of the random finite element method(RFEM)and the random limit equilibrium method(RLEM)and a comparative study is presented.Combinations of horizontal and vertical spatial correlation lengths were considered for simulating isotropic and anisotropic random fields within the OB dump slope.Seismic performances of the slope have been reported through the probability of failure and reliability index.It was observed that the RLEM approach overestimates failure probability(P_(f))by considering seismic stability with spatial heterogeneity.The P_(f)was observed to increase with an increase in the coefficient of variation of friction angle of the dump materials.Further,it was inferred that the RLEM approach may not be adequately applicable for assessing the seismic stability of an OB dump slope for a horizontal seismic coefficient that is more than or equal to 0.1.展开更多
In modern ZnO varistors,traditional aging mechanisms based on increased power consumption are no longer relevant due to reduced power consumption during DC aging.Prolonged exposure to both AC and DC voltages results i...In modern ZnO varistors,traditional aging mechanisms based on increased power consumption are no longer relevant due to reduced power consumption during DC aging.Prolonged exposure to both AC and DC voltages results in increased leakage current,decreased breakdown voltage,and lower nonlinearity,ultimately compromising their protective performance.To investigate the evolution in electrical properties during DC aging,this work developed a finite element model based on Voronoi networks and conducted accelerated aging tests on commercial varistors.Throughout the aging process,current-voltage characteristics and Schottky barrier parameters were measured and analyzed.The results indicate that when subjected to constant voltage,current flows through regions with larger grain sizes,forming discharge channels.As aging progresses,the current focus increases on these channels,leading to a decline in the varistor’s overall performance.Furthermore,analysis of the Schottky barrier parameters shows that the changes in electrical performance during aging are non-monotonic.These findings offer theoretical support for understanding the aging mechanisms and condition assessment of modern stable ZnO varistors.展开更多
This study presents and verifies a hybrid methodology for reliable determination of parameters in structural rheological models(Zener,Burgers,and Maxwell)describing the viscoelastic behavior of polyurethane specimens ...This study presents and verifies a hybrid methodology for reliable determination of parameters in structural rheological models(Zener,Burgers,and Maxwell)describing the viscoelastic behavior of polyurethane specimens manufactured using extrusion-based 3D printing.Through comprehensive testing,including cyclic compression at strain rates ranging from 0.12 to 120 mm/min(0%-15%strain)and creep/relaxation experiments(10%-30%strain),the lumped parameters were independently determined using both analytical and numerical solutions of the models’differential equations,followed by cross-verification in additional experiments.Numerical solutions for creep and relaxation problems were obtained using finite element analysis,with the three-parameter Mooney-Rivlin model and Prony series employed to simulate elastic and viscous stress components,respectively.Energy dissipation per cycle was quantified during cyclic compression tests.The results demonstrate that all three models adequately describe material behavior within the 0%-15%strain range across various strain rates.Comparative analysis revealed the Burgers model’s superior performance in characterizing creep and stress relaxation at low strain levels.While Zener and Burgers model parameters from uniaxial compression showed limited applicability for energy dissipation calculations,the generalized Maxwell model effectively captured viscoelastic properties across different strain rates.Notably,parameters derived from creep tests provided a more universal assessment of dissipative properties due to optimization based on characteristic curve regions.Both parameter sets described polyurethane’s elastic-hysteretic behavior with approximately 20%error,proving significantly more accurate than the linear strain-time dependence hypothesis.Finite element analysis(FEA)complemented numerical modeling by demonstrating that while the generalized Maxwell model effectively describes initial rapid stress-strain changes,FEA provides superior characterization of steady-state processes.This computational approach yields more physically representative results compared to simplified analytical solutions,despite certain limitations in transient analysis.展开更多
A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue prob...A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).展开更多
Magnetization configurations were calculated under various magnetic fields for nanocrystalline Pr-Fe-B permanent magnets by micromagnetic finite element method.According to the configurations during demagnetization pr...Magnetization configurations were calculated under various magnetic fields for nanocrystalline Pr-Fe-B permanent magnets by micromagnetic finite element method.According to the configurations during demagnetization process, the mechanism of magnetization reversal was analyzed.For the Pr2Fe14B with 10 nm grains or its composite with 10vol.% α-Fe, the coercivity was determined by nucleation of reversed domain that took place at grain boundaries.However, for Pr2Fe14B with 30 nm grains, coercivity was controlled by pinning of the nucle-ated domain.For Pr2Fe14B/α-Fe with 30vol.% α-Fe, the demagnetization behavior was characterized by continuous reversal of α-Fe moment.展开更多
In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body...In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.展开更多
In this paper,we consider the numerical schemes for a timefractionalOldroyd-B fluidmodel involving the Caputo derivative.We propose two efficient finite element methods by applying the convolution quadrature in time g...In this paper,we consider the numerical schemes for a timefractionalOldroyd-B fluidmodel involving the Caputo derivative.We propose two efficient finite element methods by applying the convolution quadrature in time generated by the backward Euler and the second-order backward difference methods.Error estimates in terms of data regularity are established for both the semidiscrete and fully discrete schemes.Numerical examples for two-dimensional problems further confirmthe robustness of the schemes with first-and second-order accurate in time.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
On triangle or quadrilateral meshes, two finite element methods are proposed for solving the Reissner-Mindlin plate problem either by augmenting the Galerkin formulation or modifying the plate-thickness. In these meth...On triangle or quadrilateral meshes, two finite element methods are proposed for solving the Reissner-Mindlin plate problem either by augmenting the Galerkin formulation or modifying the plate-thickness. In these methods, the transverse displacement is approximated by conforming （bi）linear macroelements or （bi）quadratic elements, and the rotation by conforming （bi）linear elements. The shear stress can be locally computed from transverse displacement and rotation. Uniform in plate thickness, optimal error bounds are obtained for the transverse displacement, rotation, and shear stress in their natural norms. Numerical results are presented to illustrate the theoretical results.展开更多
In this article,two kinds of expandable parallel finite element methods,based on two-grid discretizations,are given to solve the linear elliptic problems.Compared with the classical local and parallel finite element m...In this article,two kinds of expandable parallel finite element methods,based on two-grid discretizations,are given to solve the linear elliptic problems.Compared with the classical local and parallel finite element methods,there are two attractive features of the methods shown in this article:1)a partition of unity is used to generate a series of local and independent subproblems to guarantee the final approximation globally continuous;2)the computational domain of each local subproblem is contained in a ball with radius of O(H)(H is the coarse mesh parameter),which means methods in this article are more suitable for parallel computing in a large parallel computer system.Some a priori error estimation are obtained and optimal error bounds in both H^1-normal and L^2-normal are derived.Finally,numerical results are reported to test and verify the feasibility and validity of our methods.展开更多
The demagnetization curves were calculated using micromagnetic finite-element method for nanocomposite Pr 2Fe 14B/α-Fe permanent magnets with precipitate-typed microstructure. Due to intergrain exchange coupling,...The demagnetization curves were calculated using micromagnetic finite-element method for nanocomposite Pr 2Fe 14B/α-Fe permanent magnets with precipitate-typed microstructure. Due to intergrain exchange coupling, both remanence enhancement and a single magnetic phase behavior in demagnetization curve were found. For the samples with the hard phase as the precipitate and the soft one as the matrix, a coercivity μ 0H c of 0.78 T, a remanence J r of 1.18 T and a large energy product (BH) max of 200 kJ·m -3 are obtained for the sample with hard grain size being 23 nm. While, for the sample with the soft phase as the precipitate, μ 0H c of 0.95 T, J r of 1.24 T and (BH) max of 240 kJ·m -3 are obtained for the sample with soft grain size being 10 nm. The calculating results were compared with the experimental Pr 8Fe 87B 5 ribbons. The dependence of remanence and coercivity on the microstructure was discussed extensively.展开更多
Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained result...Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained results is verified by the finite difference method（FDM）and the finite element method（FEM）with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes（regular and non-regular）.The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.展开更多
This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite differenc...This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The L2 norm and H1 semi-norm error estimates are obtained for the first scheme and second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.展开更多
Cylindrical coplanar-grid configurations,which offer a lot of advantages over established designs,can effectively overcome the problem of poor hole collection.Finite element analysis is utilized for simulating the pot...Cylindrical coplanar-grid configurations,which offer a lot of advantages over established designs,can effectively overcome the problem of poor hole collection.Finite element analysis is utilized for simulating the potential distribution of the cylindrical coplanar-grid detector under different models by varying the widths of grid and pitch of electrodes. In addition, a modified grid pattern has been discussed to improve the weighting potential match between two grids. In this way, the geometry of electrodes for cylindrical coplanar-grid detectors is optimized.展开更多
In this paper, we represent a new numerical method for solving the nonstationary Stokes equations in an unbounded domain. The technique consists in coupling the boundary integral and finite element methods. The variat...In this paper, we represent a new numerical method for solving the nonstationary Stokes equations in an unbounded domain. The technique consists in coupling the boundary integral and finite element methods. The variational formulation and well posedness of the coupling method are obtained. The convergence and optimal estimates for the approximation solution are provided.展开更多
The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density. The electric potential equ...The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density. The electric potential equation is discretized by a mixed finite element method. The electron and hole density equations are treated by implicit-explicit multistep finite element methods. The schemes are very efficient. The optimal order error estimates both in time and space are derived.展开更多
This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their...This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.展开更多
This work presents a locking-free smoothed finite element method(S-FEM)for the simulation of soft matter modelled by the equations of quasi-incompressible hyperelasticity.The proposed method overcomes well-known issue...This work presents a locking-free smoothed finite element method(S-FEM)for the simulation of soft matter modelled by the equations of quasi-incompressible hyperelasticity.The proposed method overcomes well-known issues of standard finite element methods(FEM)in the incompressible limit:the over-estimation of stiffness and sensitivity to severely distorted meshes.The concepts of cell-based,edge-based and node-based S-FEMs are extended in this paper to three-dimensions.Additionally,a cubic bubble function is utilized to improve accuracy and stability.For the bubble function,an additional displacement degree of freedom is added at the centroid of the element.Several numerical studies are performed demonstrating the stability and validity of the proposed approach.The obtained results are compared with standard FEM and with analytical solutions to show the effectiveness of the method.展开更多
The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are...The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are asymptotically convergent. Both methods are considered in continnous time.展开更多
This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress...This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress can be naturally satisfied. The gene-rallzed variational principles with mixed hybrid incompatible finite elements are alsopresented and proved, and they can reduce the computation of incompatible elements indynamics of viscous barotropic flows.展开更多
基金the financial support provided by MHRD,Govt.of IndiaCoal India Limited for providing financial assistance for the research(Project No.CIL/R&D/01/73/2021)the partial financial support provided by the Ministry of Education,Government of India,under SPARC project(Project No.P1207)。
文摘Sudden and unforeseen seismic failures of coal mine overburden(OB)dump slopes interrupt mining operations,cause loss of lives and delay the production of coal.Consideration of the spatial heterogeneity of OB dump materials is imperative for an adequate evaluation of the seismic stability of OB dump slopes.In this study,pseudo-static seismic stability analyses are carried out for an OB dump slope by considering the material parameters obtained from an insitu field investigation.Spatial heterogeneity is simulated through use of the random finite element method(RFEM)and the random limit equilibrium method(RLEM)and a comparative study is presented.Combinations of horizontal and vertical spatial correlation lengths were considered for simulating isotropic and anisotropic random fields within the OB dump slope.Seismic performances of the slope have been reported through the probability of failure and reliability index.It was observed that the RLEM approach overestimates failure probability(P_(f))by considering seismic stability with spatial heterogeneity.The P_(f)was observed to increase with an increase in the coefficient of variation of friction angle of the dump materials.Further,it was inferred that the RLEM approach may not be adequately applicable for assessing the seismic stability of an OB dump slope for a horizontal seismic coefficient that is more than or equal to 0.1.
文摘In modern ZnO varistors,traditional aging mechanisms based on increased power consumption are no longer relevant due to reduced power consumption during DC aging.Prolonged exposure to both AC and DC voltages results in increased leakage current,decreased breakdown voltage,and lower nonlinearity,ultimately compromising their protective performance.To investigate the evolution in electrical properties during DC aging,this work developed a finite element model based on Voronoi networks and conducted accelerated aging tests on commercial varistors.Throughout the aging process,current-voltage characteristics and Schottky barrier parameters were measured and analyzed.The results indicate that when subjected to constant voltage,current flows through regions with larger grain sizes,forming discharge channels.As aging progresses,the current focus increases on these channels,leading to a decline in the varistor’s overall performance.Furthermore,analysis of the Schottky barrier parameters shows that the changes in electrical performance during aging are non-monotonic.These findings offer theoretical support for understanding the aging mechanisms and condition assessment of modern stable ZnO varistors.
文摘This study presents and verifies a hybrid methodology for reliable determination of parameters in structural rheological models(Zener,Burgers,and Maxwell)describing the viscoelastic behavior of polyurethane specimens manufactured using extrusion-based 3D printing.Through comprehensive testing,including cyclic compression at strain rates ranging from 0.12 to 120 mm/min(0%-15%strain)and creep/relaxation experiments(10%-30%strain),the lumped parameters were independently determined using both analytical and numerical solutions of the models’differential equations,followed by cross-verification in additional experiments.Numerical solutions for creep and relaxation problems were obtained using finite element analysis,with the three-parameter Mooney-Rivlin model and Prony series employed to simulate elastic and viscous stress components,respectively.Energy dissipation per cycle was quantified during cyclic compression tests.The results demonstrate that all three models adequately describe material behavior within the 0%-15%strain range across various strain rates.Comparative analysis revealed the Burgers model’s superior performance in characterizing creep and stress relaxation at low strain levels.While Zener and Burgers model parameters from uniaxial compression showed limited applicability for energy dissipation calculations,the generalized Maxwell model effectively captured viscoelastic properties across different strain rates.Notably,parameters derived from creep tests provided a more universal assessment of dissipative properties due to optimization based on characteristic curve regions.Both parameter sets described polyurethane’s elastic-hysteretic behavior with approximately 20%error,proving significantly more accurate than the linear strain-time dependence hypothesis.Finite element analysis(FEA)complemented numerical modeling by demonstrating that while the generalized Maxwell model effectively describes initial rapid stress-strain changes,FEA provides superior characterization of steady-state processes.This computational approach yields more physically representative results compared to simplified analytical solutions,despite certain limitations in transient analysis.
基金supported by the National Natural Science Foundation of China(12401482)the second author was supported by the National Natural Science Foundation of China(12371371,12261160361,11971366)supported by the Open Research Fund of Hubei Key Laboratory of Computational Science,Wuhan University.
文摘A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).
基金supported by the National Natural Science Foundation of China (10574156)
文摘Magnetization configurations were calculated under various magnetic fields for nanocrystalline Pr-Fe-B permanent magnets by micromagnetic finite element method.According to the configurations during demagnetization process, the mechanism of magnetization reversal was analyzed.For the Pr2Fe14B with 10 nm grains or its composite with 10vol.% α-Fe, the coercivity was determined by nucleation of reversed domain that took place at grain boundaries.However, for Pr2Fe14B with 30 nm grains, coercivity was controlled by pinning of the nucle-ated domain.For Pr2Fe14B/α-Fe with 30vol.% α-Fe, the demagnetization behavior was characterized by continuous reversal of α-Fe moment.
基金supported by the US ARO grants 49308-MA and 56349-MAthe US AFSOR grant FA9550-06-1-024+1 种基金he US NSF grant DMS-0911434the State Key Laboratory of Scientific and Engineering Computing of Chinese Academy of Sciences during a visit by Z.Li between July-August,2008.
文摘In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.
基金The work is supported by the Guangxi Natural Science Foundation[Grant Numbers 2018GXNSFBA281020,2018GXNSFAA138121]the Doctoral Starting up Foundation of Guilin University of Technology[Grant Number GLUTQD2016044].
文摘In this paper,we consider the numerical schemes for a timefractionalOldroyd-B fluidmodel involving the Caputo derivative.We propose two efficient finite element methods by applying the convolution quadrature in time generated by the backward Euler and the second-order backward difference methods.Error estimates in terms of data regularity are established for both the semidiscrete and fully discrete schemes.Numerical examples for two-dimensional problems further confirmthe robustness of the schemes with first-and second-order accurate in time.
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 NSFC(11571266,91430106,11171168,11071132)NSFC-RGC(China-Hong Kong)(11661161017)
文摘On triangle or quadrilateral meshes, two finite element methods are proposed for solving the Reissner-Mindlin plate problem either by augmenting the Galerkin formulation or modifying the plate-thickness. In these methods, the transverse displacement is approximated by conforming （bi）linear macroelements or （bi）quadratic elements, and the rotation by conforming （bi）linear elements. The shear stress can be locally computed from transverse displacement and rotation. Uniform in plate thickness, optimal error bounds are obtained for the transverse displacement, rotation, and shear stress in their natural norms. Numerical results are presented to illustrate the theoretical results.
基金Subsidized by NSFC (11701343)partially supported by NSFC (11571274,11401466)
文摘In this article,two kinds of expandable parallel finite element methods,based on two-grid discretizations,are given to solve the linear elliptic problems.Compared with the classical local and parallel finite element methods,there are two attractive features of the methods shown in this article:1)a partition of unity is used to generate a series of local and independent subproblems to guarantee the final approximation globally continuous;2)the computational domain of each local subproblem is contained in a ball with radius of O(H)(H is the coarse mesh parameter),which means methods in this article are more suitable for parallel computing in a large parallel computer system.Some a priori error estimation are obtained and optimal error bounds in both H^1-normal and L^2-normal are derived.Finally,numerical results are reported to test and verify the feasibility and validity of our methods.
文摘The demagnetization curves were calculated using micromagnetic finite-element method for nanocomposite Pr 2Fe 14B/α-Fe permanent magnets with precipitate-typed microstructure. Due to intergrain exchange coupling, both remanence enhancement and a single magnetic phase behavior in demagnetization curve were found. For the samples with the hard phase as the precipitate and the soft one as the matrix, a coercivity μ 0H c of 0.78 T, a remanence J r of 1.18 T and a large energy product (BH) max of 200 kJ·m -3 are obtained for the sample with hard grain size being 23 nm. While, for the sample with the soft phase as the precipitate, μ 0H c of 0.95 T, J r of 1.24 T and (BH) max of 240 kJ·m -3 are obtained for the sample with soft grain size being 10 nm. The calculating results were compared with the experimental Pr 8Fe 87B 5 ribbons. The dependence of remanence and coercivity on the microstructure was discussed extensively.
文摘Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained results is verified by the finite difference method（FDM）and the finite element method（FEM）with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes（regular and non-regular）.The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.
文摘This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The L2 norm and H1 semi-norm error estimates are obtained for the first scheme and second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.
文摘Cylindrical coplanar-grid configurations,which offer a lot of advantages over established designs,can effectively overcome the problem of poor hole collection.Finite element analysis is utilized for simulating the potential distribution of the cylindrical coplanar-grid detector under different models by varying the widths of grid and pitch of electrodes. In addition, a modified grid pattern has been discussed to improve the weighting potential match between two grids. In this way, the geometry of electrodes for cylindrical coplanar-grid detectors is optimized.
文摘In this paper, we represent a new numerical method for solving the nonstationary Stokes equations in an unbounded domain. The technique consists in coupling the boundary integral and finite element methods. The variational formulation and well posedness of the coupling method are obtained. The convergence and optimal estimates for the approximation solution are provided.
文摘The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density. The electric potential equation is discretized by a mixed finite element method. The electron and hole density equations are treated by implicit-explicit multistep finite element methods. The schemes are very efficient. The optimal order error estimates both in time and space are derived.
文摘This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.
基金Changkye Lee and Jurng-Jae Yee would like to thank the support by Basic Science Research Program through the National Research Foundation(NRF)funded by Korea through Ministry of Education(No.2016R1A6A1A03012812).
文摘This work presents a locking-free smoothed finite element method(S-FEM)for the simulation of soft matter modelled by the equations of quasi-incompressible hyperelasticity.The proposed method overcomes well-known issues of standard finite element methods(FEM)in the incompressible limit:the over-estimation of stiffness and sensitivity to severely distorted meshes.The concepts of cell-based,edge-based and node-based S-FEMs are extended in this paper to three-dimensions.Additionally,a cubic bubble function is utilized to improve accuracy and stability.For the bubble function,an additional displacement degree of freedom is added at the centroid of the element.Several numerical studies are performed demonstrating the stability and validity of the proposed approach.The obtained results are compared with standard FEM and with analytical solutions to show the effectiveness of the method.
文摘The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are asymptotically convergent. Both methods are considered in continnous time.
文摘This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress can be naturally satisfied. The gene-rallzed variational principles with mixed hybrid incompatible finite elements are alsopresented and proved, and they can reduce the computation of incompatible elements indynamics of viscous barotropic flows.
