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
In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is de...In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is developed using the trigonometric scheme,which is based on zero,first,and second moments,and the direct discontinuous Galerkin(DDG)flux is used to discretize the diffusion term.Moreover,the DDG method directly applies the weak form of the parabolic equation to each computational cell,which can better capture the characteristics of the solution,especially the discontinuous solution.Meanwhile,the third-order TVD-Runge-Kutta method is applied for temporal discretization.Finally,the effectiveness and stability of the method constructed in this paper are evaluated through numerical tests.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
This study proposes a class of augmented subspace schemes for the weak Galerkin(WG)finite element method used to solve eigenvalue problems.The augmented subspace is built with the conforming linear finite element spac...This study proposes a class of augmented subspace schemes for the weak Galerkin(WG)finite element method used to solve eigenvalue problems.The augmented subspace is built with the conforming linear finite element space defined on the coarse mesh and the eigen-function approximations in the WG finite element space defined on the fine mesh.Based on this augmented subspace,solving the eigenvalue problem in the fine WG finite element space can be reduced to the solution of the linear boundary value problem in the same WG finite element space and a low dimensional eigenvalue problem in the augmented sub-space.The proposed augmented subspace techniques have the second order convergence rate with respect to the coarse mesh size,as demonstrated by the accompanying error esti-mates.Finally,a few numerical examples are provided to validate the proposed numerical techniques.展开更多
In this paper,we propose and analyze two second-order accurate finite difference schemes for the one-dimensional heat equation with concentrated capacity on a computa-tional domain=[a,b].We first transform the target ...In this paper,we propose and analyze two second-order accurate finite difference schemes for the one-dimensional heat equation with concentrated capacity on a computa-tional domain=[a,b].We first transform the target equation into the standard heat equation on the domain excluding the singular point equipped with an inner interface matching(IIM)condition on the singular point x=ξ∈(a,b),then adopt Taylor’s ex-pansion to approximate the IIM condition at the singular point and apply second-order finite difference method to approximate the standard heat equation at the nonsingular points.This discrete procedure allows us to choose different grid sizes to partition the two sub-domains[a,ξ]and[ξ,b],which ensures that x=ξ is a grid point,and hence the pro-posed schemes can be generalized to the heat equation with more than one concentrated capacities.We prove that the two proposed schemes are uniquely solvable.And through in-depth analysis of the local truncation errors,we rigorously prove that the two schemes are second-order accurate both in temporal and spatial directions in the maximum norm without any constraint on the grid ratio.Numerical experiments are carried out to verify our theoretical conclusions.展开更多
This paper presents a nonlinear micropolar nonclassical continuum theory (MPNCCT) for finite deformation, finite strain deformation physics of thermosviscoelastic solid medium with memory (polymeric micropolar solids)...This paper presents a nonlinear micropolar nonclassical continuum theory (MPNCCT) for finite deformation, finite strain deformation physics of thermosviscoelastic solid medium with memory (polymeric micropolar solids) based on classical rotations cΘand their rates. Contravariant second Piola-Kirchhoff stress and moment tensors, in conjunction with finite deformation measures derived by the authors in recent paper, are utilized in deriving the conservation and balance laws and the constitutive theories based on conjugate pairs in entropy inequality and the representation theorem. This nonlinear MPNCCT for TVES with rheology: 1) incorporates nonlinear ordered rate dissipation mechanism based on Green’s strain rates up to order n;2) also incorporates an additional ordered rate dissipation mechanism due to microconstituents, the viscosity of the medium and the rates of the symmetric part of the rotation gradient (of cΘ) tensor up to order n, referred to as micropolar dissipation or micropolar viscous dissipation mechanism;3) incorporates the primary mechanism of memory or rheology due to long chain molecules of the polymer and the viscosity of the medium by using the contravaraint second Piola-Kirchhoff stress tensor and its rates up to order m, resulting in a relaxation spectrum;4) incorporates second mechanism of memory or rheology due to nonclassical physics, interaction of microconstituents with the viscous medium and long chain molecules by considering rates of the contravariant second Piola-Kirchhoff moment tensor up to order m, resulting in relaxation of second Piola-Kirchhoff moment tensor. This results in another relaxation spectrum for the second Piola-Kirchhoff moment tensor due to microconstituents, referred to as micropolar relaxation spectrum consisting of micropolar relaxation time constants of the material. This nonlinear MPNCCT for TVES with memory is thermodynamically and mathematically consistent, and the mathematical model consisting of conservation and balance laws and the constitutive theories has closure and naturally reduces to linear MPNCCT based on infinitesimal deformation assumption. BMM is the essential balance law for all MPNCCT and is used in the present work as well. In the absence of this balance law, a valid thermodynamically and mathematically consistent nonlinear MPNCCT is not possible. The nonlinear MPNCCT based on rotations (cΘ+αΘ) and αΘ(ignoring cΘ) is not considered due to the fact that even the linear MPNCCT based on these rotations is invalid and is thermodynamically and mathematically inconsistent MPNCCT.展开更多
Accurately simulating water flow movement in vadose zone is crucial for effective water resources assessment.Richards'equation,which describes the movement of water flow in the vadose zone,is highly nonlinear and ...Accurately simulating water flow movement in vadose zone is crucial for effective water resources assessment.Richards'equation,which describes the movement of water flow in the vadose zone,is highly nonlinear and challenging to solve.Existing numerical methods often face issues such as numerical dispersion,oscillation,and mass non-conservation when spatial and temporal discretization conditions are not appropriately configured.To address these problems and achieve accurate and stable numerical solutions,a finite analytic method based on water content-based Richards'equation(FAM-W)is proposed.The performance of the FAM-W is compared with analytical solutions,Finite Difference Method(FDM),and Finite Analytic Method based on the pressure Head-based Richards'equation(FAM-H).Compared to analytical solution and other numerical methods(FDM and FAM-H),FAM-W demonstrates superior accuracy and efficiency in controlling mass balance errors,regardless of spatial step sizes.This study introduces a novel approach for modelling water flow in the vadose zone,offering significant benefits for water resources management.展开更多
A modified inner-element edge-based smoothed finite element method(IES-FEM)is developed and integrated with ABAQUS using a user-defined element(UEL)in this study.Initially,the smoothing domain discretization of IES-FE...A modified inner-element edge-based smoothed finite element method(IES-FEM)is developed and integrated with ABAQUS using a user-defined element(UEL)in this study.Initially,the smoothing domain discretization of IES-FEM is described and compared with ES-FEM.A practical modification of IES-FEM is then introduced that used the technique employed by ES-FEM for the nodal strain calculation.The differences in the strain computation among ES-FEM,IES-FEM,and FEM are then discussed.The modified IES-FEM exhibited superior performance in displacement and a slight advantage in stress compared to FEM using the same mesh according to the results obtained from both the regular and irregular elements.The robustness of the IES-FEM to severely deformed meshes was also verified.展开更多
In the field of discretization-based meshfree/meshless methods,the improvements in the higher-order consistency,stability,and computational efficiency are of great concerns in computational science and numerical solut...In the field of discretization-based meshfree/meshless methods,the improvements in the higher-order consistency,stability,and computational efficiency are of great concerns in computational science and numerical solutions to partial differential equations.Various alternative numerical methods of the finite particle method(FPM)frame have been extended from mathematical theories to numerical applications separately.As a comprehensive numerical scheme,this study suggests a unified resolved program for numerically investigating their accuracy,stability,consistency,computational efficiency,and practical applicability in industrial engineering contexts.The high-order finite particle method(HFPM)and corrected methods based on the multivariate Taylor series expansion are constructed and analyzed to investigate the whole applicability in different benchmarks of computational fluid dynamics.Specifically,four benchmarks are designed purposefully from statical exact solutions to multifaceted hydrodynamic tests,which possess different numerical performances on the particle consistency,numerical discretized forms,particle distributions,and transient time evolutional stabilities.This study offers a numerical reference for the current unified resolved program.展开更多
A theory based on the superposition principle is developed to uncover the basic physics of wave behavior in a finite grating of N unit cells.The theory reveals that bound states in the continuum(BICs)of infinite quali...A theory based on the superposition principle is developed to uncover the basic physics of wave behavior in a finite grating of N unit cells.The theory reveals that bound states in the continuum(BICs)of infinite quality factor(Q-factor)can be supported by such a grating when perfect reflection is introduced at its boundaries.If geometrical perturbations are introduced into the structure,the dark BICs transform into bright quasi-BICs with finite Q-factor,maintaining spectral characteristics nearly identical to those of quasi-BICs supported by infinite gratings.When the boundaries are replaced with high-reflectivity metallic mirrors,the Q-factor of the resonant mode is reduced to be finite;however,it can be much larger than that in the corresponding nanostructure with open boundaries and can be tuned over a large range by varying the number of unit cells or boundary conditions.展开更多
In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow e...In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow equation.The velocity and pressure are computed simultaneously.The accuracy of velocity is improved one order.The concentration equation is solved by using mixed finite element,multi-step difference and upwind approximation.A multi-step method is used to approximate time derivative for improving the accuracy.The upwind approximation and an expanded mixed finite element are adopted to solve the convection and diffusion,respectively.The composite method could compute the diffusion flux and its gradient.It possibly becomes an eficient tool for solving convection-dominated diffusion problems.Firstly,the conservation of mass holds.Secondly,the multi-step method has high accuracy.Thirdly,the upwind approximation could avoid numerical dispersion.Using numerical analysis of a priori estimates and special techniques of differential equations,we give an error estimates for a positive definite problem.Numerical experiments illustrate its computational efficiency and feasibility of application.展开更多
1-way multihead quantum finite state automata (1QFA(k)) can be thought of modified version of 1-way quantum finite state automata (1QFA) and k-letter quantum finite state automata (k-letter QFA) respectively. It has b...1-way multihead quantum finite state automata (1QFA(k)) can be thought of modified version of 1-way quantum finite state automata (1QFA) and k-letter quantum finite state automata (k-letter QFA) respectively. It has been shown by Moore and Crutchfield as well as Konadacs and Watrous that 1QFA can’t accept all regular language. In this paper, we show different language recognizing capabilities of our model 1-way multihead QFAs. New results presented in this paper are the following ones: 1) We show that newly introduced 1-way 2-head quantum finite state automaton (1QFA(2)) structure can accept all unary regular languages. 2) A language which can’t be accepted by 1-way deterministic 2-head finite state automaton (1DFA((2)) can be accepted by 1QFA(2) with bounded error. 3) 1QFA(2) is more powerful than 1-way reversible 2-head finite state automaton (1RMFA(2)) with respect to recognition of language.展开更多
Purpose–The brake pipe system was an essential braking component of the railway freight trains,but the existing E-type sealing rings had problems such as insufficient low-temperature resistance,poor heat stability an...Purpose–The brake pipe system was an essential braking component of the railway freight trains,but the existing E-type sealing rings had problems such as insufficient low-temperature resistance,poor heat stability and short service life.To address these issues,low-phenyl silicone rubber was prepared and tested,and the finite element analysis and experimental studies on the sealing performance of its sealing rings were carried out.Design/methodology/approach–The low-temperature resistance and thermal stability of the prepared lowphenyl silicone rubber were studied using low-temperature tensile testing,differential scanning calorimetry,dynamic thermomechanical analysis and thermogravimetric analysis.The sealing performance of the lowphenyl silicone rubber sealing ring was studied by using finite element analysis software abaqus and experiments.Findings–The prepared low-phenyl silicone rubber sealing ring possessed excellent low-temperature resistance and thermal stability.According to the finite element analysis results,the finish of the flange sealing surface and groove outer edge should be ensured,and extrusion damage should be avoided.The sealing rings were more susceptible to damage in high compression ratio and/or low-temperature environments.When the sealing effect was ensured,a small compression ratio should be selected,and rubbers with hardness and elasticity less affected by temperature should be selected.The prepared low-phenyl silicone rubber sealing ring had zero leakage at both room temperature(RT)and�508C.Originality/value–The innovation of this study is that it provides valuable data and experience for the future development of the sealing rings used in the brake pipe flange joints of the railway freight cars in China.展开更多
Total hip arthroplasty for adults with sequelae from childhood hip disorders poses significant challenges due to altered anatomy.The paper published by Oommen et al reviews the essential management strategies for thes...Total hip arthroplasty for adults with sequelae from childhood hip disorders poses significant challenges due to altered anatomy.The paper published by Oommen et al reviews the essential management strategies for these complex cases.This article explores the integration of finite element analysis(FEA)to enhance surgical precision and outcomes.FEA provides detailed biomechanical insights,aiding in preoperative planning,implant design,and surgical technique optimization.By simulating implant configurations and assessing bone quality,FEA helps in customizing implants and evaluating surgical techniques like subtrochanteric shortening osteotomy.Advanced imaging techniques,such as 3D printing,virtual reality,and augmented reality,further enhance total hip arthroplasty precision.Future research should focus on validating FEA models,developing patient-specific simulations,and promoting multidisciplinary collaboration.Integrating FEA and advanced technologies in total hip arthroplasty can improve functional outcomes,reduce complications,and enhance quality of life for patients with childhood hip disorder sequelae.展开更多
This article presents a micro-structure tensor enhanced elasto-plastic finite element(FE)method to address strength anisotropy in three-dimensional(3D)soil slope stability analysis.The gravity increase method(GIM)is e...This article presents a micro-structure tensor enhanced elasto-plastic finite element(FE)method to address strength anisotropy in three-dimensional(3D)soil slope stability analysis.The gravity increase method(GIM)is employed to analyze the stability of 3D anisotropic soil slopes.The accuracy of the proposed method is first verified against the data in the literature.We then simulate the 3D soil slope with a straight slope surface and the convex and concave slope surfaces with a 90turning corner to study the 3D effect on slope stability and the failure mechanism under anisotropy conditions.Based on our numerical results,the end effect significantly impacts the failure mechanism and safety factor.Anisotropy degree notably affects the safety factor,with higher degrees leading to deeper landslides.For concave slopes,they can be approximated by straight slopes with suitable boundary conditions to assess their stability.Furthermore,a case study of the Saint-Alban test embankment A in Quebec,Canada,is provided to demonstrate the applicability of the proposed FE model.展开更多
This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practi...This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practical engineering fields,such as in short take-off and vertical landing(STOVL)aircraft.Nowadays many intricate phenomena associated with impinging jet flows remain inadequately elucidated,which limits the ability to optimize aircraft design.Given a boundary condition in the inlet,the impinging jet problem is transformed into a Bernoulli-type free boundary problem according to the stream function.Then the variational method is used to study the corresponding variational problem with one parameter,thereby the wellposedness is established.The main conclusion is as follows.For a 3D axisymmetric finitely long nozzle and an infinitely long vertical wall,given an axial velocity in the inlet of nozzle,there exists a unique smooth incom‑pressible impinging jet flow such that the free boundary initiates smoothly at the endpoint of the nozzle and extends to infinity along the vertical wall at far fields.The key point is to investigate the regularity of the corner where the nozzle and the vertical axis intersect.展开更多
Design a precision electroplating mechanical structure for automobiles based on finite element analysis method and analyze its mechanical properties.Taking the automobile steering knuckle as the research object,ABAQUS...Design a precision electroplating mechanical structure for automobiles based on finite element analysis method and analyze its mechanical properties.Taking the automobile steering knuckle as the research object,ABAQUS parametric modeling technology is used to construct its three-dimensional geometric model,and geometric simplification is carried out.Two surface treatment processes,HK-35 zinc nickel alloy electroplating and pure zinc electroplating,were designed,and the influence of different coatings on the mechanical properties of steering knuckles was compared and analyzed through numerical simulation.At the same time,standard specimens were prepared for salt spray corrosion testing and scratch method combined strength testing to verify the numerical simulation results.The results showed that under emergency braking and composite working conditions,the peak Von Mises stress of the zinc nickel alloy coating was 119.85 MPa,which was lower than that of the pure zinc coating and the alkaline electroplated zinc layer.Its equivalent strain value was 652×10^(-6),which was lower than that of the pure zinc coating and the alkaline electroplated zinc layer.Experimental data confirms that zinc nickel alloy coatings exhibit significant advantages in stress distribution uniformity,strain performance,and load-bearing capacity in high stress zones.The salt spray corrosion test further indicates that the coating has superior corrosion resistance and coating substrate interface bonding strength,which can significantly improve the mechanical stability and long-term reliability of automotive precision electroplating mechanical structures.展开更多
In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided int...In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided into,by the work of Amiot[Bull.Soc.Math.France,2007,135(3):435-474](see also[Adv.Math.,2008,217(6):2443-2484]and[J.Algebra,2016,446:426-449]),three classes:type A,type D and type E.展开更多
To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical c...To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%.展开更多
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.
基金The Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“RBF-Hermite difference scheme for the time-fractional kdv-Burgers equation”(2024D01C43)。
文摘In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is developed using the trigonometric scheme,which is based on zero,first,and second moments,and the direct discontinuous Galerkin(DDG)flux is used to discretize the diffusion term.Moreover,the DDG method directly applies the weak form of the parabolic equation to each computational cell,which can better capture the characteristics of the solution,especially the discontinuous solution.Meanwhile,the third-order TVD-Runge-Kutta method is applied for temporal discretization.Finally,the effectiveness and stability of the method constructed in this paper are evaluated through numerical tests.
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partly supported by the Beijing Natural Science Foundation(Grant No.Z200003)by the National Natural Science Foundation of China(Grant Nos.12331015,12301475,12301465)+1 种基金by the National Center for Mathematics and Interdisciplinary Science,Chinese Academy of Sciencesby the Research Foundation for the Beijing University of Technology New Faculty(Grant No.006000514122516).
文摘This study proposes a class of augmented subspace schemes for the weak Galerkin(WG)finite element method used to solve eigenvalue problems.The augmented subspace is built with the conforming linear finite element space defined on the coarse mesh and the eigen-function approximations in the WG finite element space defined on the fine mesh.Based on this augmented subspace,solving the eigenvalue problem in the fine WG finite element space can be reduced to the solution of the linear boundary value problem in the same WG finite element space and a low dimensional eigenvalue problem in the augmented sub-space.The proposed augmented subspace techniques have the second order convergence rate with respect to the coarse mesh size,as demonstrated by the accompanying error esti-mates.Finally,a few numerical examples are provided to validate the proposed numerical techniques.
基金supported by the National Natural Science Foundation of China(Grant No.11571181)by the Natural Science Foundation of Jiangsu Province(Grant No.BK20171454).
文摘In this paper,we propose and analyze two second-order accurate finite difference schemes for the one-dimensional heat equation with concentrated capacity on a computa-tional domain=[a,b].We first transform the target equation into the standard heat equation on the domain excluding the singular point equipped with an inner interface matching(IIM)condition on the singular point x=ξ∈(a,b),then adopt Taylor’s ex-pansion to approximate the IIM condition at the singular point and apply second-order finite difference method to approximate the standard heat equation at the nonsingular points.This discrete procedure allows us to choose different grid sizes to partition the two sub-domains[a,ξ]and[ξ,b],which ensures that x=ξ is a grid point,and hence the pro-posed schemes can be generalized to the heat equation with more than one concentrated capacities.We prove that the two proposed schemes are uniquely solvable.And through in-depth analysis of the local truncation errors,we rigorously prove that the two schemes are second-order accurate both in temporal and spatial directions in the maximum norm without any constraint on the grid ratio.Numerical experiments are carried out to verify our theoretical conclusions.
文摘This paper presents a nonlinear micropolar nonclassical continuum theory (MPNCCT) for finite deformation, finite strain deformation physics of thermosviscoelastic solid medium with memory (polymeric micropolar solids) based on classical rotations cΘand their rates. Contravariant second Piola-Kirchhoff stress and moment tensors, in conjunction with finite deformation measures derived by the authors in recent paper, are utilized in deriving the conservation and balance laws and the constitutive theories based on conjugate pairs in entropy inequality and the representation theorem. This nonlinear MPNCCT for TVES with rheology: 1) incorporates nonlinear ordered rate dissipation mechanism based on Green’s strain rates up to order n;2) also incorporates an additional ordered rate dissipation mechanism due to microconstituents, the viscosity of the medium and the rates of the symmetric part of the rotation gradient (of cΘ) tensor up to order n, referred to as micropolar dissipation or micropolar viscous dissipation mechanism;3) incorporates the primary mechanism of memory or rheology due to long chain molecules of the polymer and the viscosity of the medium by using the contravaraint second Piola-Kirchhoff stress tensor and its rates up to order m, resulting in a relaxation spectrum;4) incorporates second mechanism of memory or rheology due to nonclassical physics, interaction of microconstituents with the viscous medium and long chain molecules by considering rates of the contravariant second Piola-Kirchhoff moment tensor up to order m, resulting in relaxation of second Piola-Kirchhoff moment tensor. This results in another relaxation spectrum for the second Piola-Kirchhoff moment tensor due to microconstituents, referred to as micropolar relaxation spectrum consisting of micropolar relaxation time constants of the material. This nonlinear MPNCCT for TVES with memory is thermodynamically and mathematically consistent, and the mathematical model consisting of conservation and balance laws and the constitutive theories has closure and naturally reduces to linear MPNCCT based on infinitesimal deformation assumption. BMM is the essential balance law for all MPNCCT and is used in the present work as well. In the absence of this balance law, a valid thermodynamically and mathematically consistent nonlinear MPNCCT is not possible. The nonlinear MPNCCT based on rotations (cΘ+αΘ) and αΘ(ignoring cΘ) is not considered due to the fact that even the linear MPNCCT based on these rotations is invalid and is thermodynamically and mathematically inconsistent MPNCCT.
基金supported by the National Natural Science Foundation of China(No.42372287 and No.U24A20178)the Fundamental Research Funds for the Central Universities CHD(No.2024SHEEAR002)+3 种基金the Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shaanxi Province(No.2020024)the China Postdoctoral Science Foundation(GZC20232955,2024M753472,and 2024MD763937)the Science-Technology Foundation for Young Scientists of Gansu Province,China(No.24JRRA097)the Study of biodiversity survey and limiting factor analysis of Yinkentala(2023ZL01).
文摘Accurately simulating water flow movement in vadose zone is crucial for effective water resources assessment.Richards'equation,which describes the movement of water flow in the vadose zone,is highly nonlinear and challenging to solve.Existing numerical methods often face issues such as numerical dispersion,oscillation,and mass non-conservation when spatial and temporal discretization conditions are not appropriately configured.To address these problems and achieve accurate and stable numerical solutions,a finite analytic method based on water content-based Richards'equation(FAM-W)is proposed.The performance of the FAM-W is compared with analytical solutions,Finite Difference Method(FDM),and Finite Analytic Method based on the pressure Head-based Richards'equation(FAM-H).Compared to analytical solution and other numerical methods(FDM and FAM-H),FAM-W demonstrates superior accuracy and efficiency in controlling mass balance errors,regardless of spatial step sizes.This study introduces a novel approach for modelling water flow in the vadose zone,offering significant benefits for water resources management.
基金the National Natural Science Foundation of China(No.11672238)the 111 Project(No.BP0719007)the Shaanxi Province Natural Science Foundation(No.2020JZ-06)for the financial support.
文摘A modified inner-element edge-based smoothed finite element method(IES-FEM)is developed and integrated with ABAQUS using a user-defined element(UEL)in this study.Initially,the smoothing domain discretization of IES-FEM is described and compared with ES-FEM.A practical modification of IES-FEM is then introduced that used the technique employed by ES-FEM for the nodal strain calculation.The differences in the strain computation among ES-FEM,IES-FEM,and FEM are then discussed.The modified IES-FEM exhibited superior performance in displacement and a slight advantage in stress compared to FEM using the same mesh according to the results obtained from both the regular and irregular elements.The robustness of the IES-FEM to severely deformed meshes was also verified.
基金supported by the National Natural Science Foundation of China(No.12002290)。
文摘In the field of discretization-based meshfree/meshless methods,the improvements in the higher-order consistency,stability,and computational efficiency are of great concerns in computational science and numerical solutions to partial differential equations.Various alternative numerical methods of the finite particle method(FPM)frame have been extended from mathematical theories to numerical applications separately.As a comprehensive numerical scheme,this study suggests a unified resolved program for numerically investigating their accuracy,stability,consistency,computational efficiency,and practical applicability in industrial engineering contexts.The high-order finite particle method(HFPM)and corrected methods based on the multivariate Taylor series expansion are constructed and analyzed to investigate the whole applicability in different benchmarks of computational fluid dynamics.Specifically,four benchmarks are designed purposefully from statical exact solutions to multifaceted hydrodynamic tests,which possess different numerical performances on the particle consistency,numerical discretized forms,particle distributions,and transient time evolutional stabilities.This study offers a numerical reference for the current unified resolved program.
基金supported by the National Natural Science Foundation of China(Grant Nos.11874270 and 12174228)the Shenzhen Basic Research Special Project(Grant No.JCYJ20240813141606009)。
文摘A theory based on the superposition principle is developed to uncover the basic physics of wave behavior in a finite grating of N unit cells.The theory reveals that bound states in the continuum(BICs)of infinite quality factor(Q-factor)can be supported by such a grating when perfect reflection is introduced at its boundaries.If geometrical perturbations are introduced into the structure,the dark BICs transform into bright quasi-BICs with finite Q-factor,maintaining spectral characteristics nearly identical to those of quasi-BICs supported by infinite gratings.When the boundaries are replaced with high-reflectivity metallic mirrors,the Q-factor of the resonant mode is reduced to be finite;however,it can be much larger than that in the corresponding nanostructure with open boundaries and can be tuned over a large range by varying the number of unit cells or boundary conditions.
基金supported by the Natural Science Foundation of Shandong Province(ZR2021MA019)the National Natural Science Foundation of China(11871312)。
文摘In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow equation.The velocity and pressure are computed simultaneously.The accuracy of velocity is improved one order.The concentration equation is solved by using mixed finite element,multi-step difference and upwind approximation.A multi-step method is used to approximate time derivative for improving the accuracy.The upwind approximation and an expanded mixed finite element are adopted to solve the convection and diffusion,respectively.The composite method could compute the diffusion flux and its gradient.It possibly becomes an eficient tool for solving convection-dominated diffusion problems.Firstly,the conservation of mass holds.Secondly,the multi-step method has high accuracy.Thirdly,the upwind approximation could avoid numerical dispersion.Using numerical analysis of a priori estimates and special techniques of differential equations,we give an error estimates for a positive definite problem.Numerical experiments illustrate its computational efficiency and feasibility of application.
文摘1-way multihead quantum finite state automata (1QFA(k)) can be thought of modified version of 1-way quantum finite state automata (1QFA) and k-letter quantum finite state automata (k-letter QFA) respectively. It has been shown by Moore and Crutchfield as well as Konadacs and Watrous that 1QFA can’t accept all regular language. In this paper, we show different language recognizing capabilities of our model 1-way multihead QFAs. New results presented in this paper are the following ones: 1) We show that newly introduced 1-way 2-head quantum finite state automaton (1QFA(2)) structure can accept all unary regular languages. 2) A language which can’t be accepted by 1-way deterministic 2-head finite state automaton (1DFA((2)) can be accepted by 1QFA(2) with bounded error. 3) 1QFA(2) is more powerful than 1-way reversible 2-head finite state automaton (1RMFA(2)) with respect to recognition of language.
基金supported by the Science and Technology Research and Development Plan of the China State Railway Group Company Limited(No.Q2023J012).
文摘Purpose–The brake pipe system was an essential braking component of the railway freight trains,but the existing E-type sealing rings had problems such as insufficient low-temperature resistance,poor heat stability and short service life.To address these issues,low-phenyl silicone rubber was prepared and tested,and the finite element analysis and experimental studies on the sealing performance of its sealing rings were carried out.Design/methodology/approach–The low-temperature resistance and thermal stability of the prepared lowphenyl silicone rubber were studied using low-temperature tensile testing,differential scanning calorimetry,dynamic thermomechanical analysis and thermogravimetric analysis.The sealing performance of the lowphenyl silicone rubber sealing ring was studied by using finite element analysis software abaqus and experiments.Findings–The prepared low-phenyl silicone rubber sealing ring possessed excellent low-temperature resistance and thermal stability.According to the finite element analysis results,the finish of the flange sealing surface and groove outer edge should be ensured,and extrusion damage should be avoided.The sealing rings were more susceptible to damage in high compression ratio and/or low-temperature environments.When the sealing effect was ensured,a small compression ratio should be selected,and rubbers with hardness and elasticity less affected by temperature should be selected.The prepared low-phenyl silicone rubber sealing ring had zero leakage at both room temperature(RT)and�508C.Originality/value–The innovation of this study is that it provides valuable data and experience for the future development of the sealing rings used in the brake pipe flange joints of the railway freight cars in China.
文摘Total hip arthroplasty for adults with sequelae from childhood hip disorders poses significant challenges due to altered anatomy.The paper published by Oommen et al reviews the essential management strategies for these complex cases.This article explores the integration of finite element analysis(FEA)to enhance surgical precision and outcomes.FEA provides detailed biomechanical insights,aiding in preoperative planning,implant design,and surgical technique optimization.By simulating implant configurations and assessing bone quality,FEA helps in customizing implants and evaluating surgical techniques like subtrochanteric shortening osteotomy.Advanced imaging techniques,such as 3D printing,virtual reality,and augmented reality,further enhance total hip arthroplasty precision.Future research should focus on validating FEA models,developing patient-specific simulations,and promoting multidisciplinary collaboration.Integrating FEA and advanced technologies in total hip arthroplasty can improve functional outcomes,reduce complications,and enhance quality of life for patients with childhood hip disorder sequelae.
基金supported by the National Natural Science Foundation of China(Grant Nos.51890912,51979025 and 52011530189).
文摘This article presents a micro-structure tensor enhanced elasto-plastic finite element(FE)method to address strength anisotropy in three-dimensional(3D)soil slope stability analysis.The gravity increase method(GIM)is employed to analyze the stability of 3D anisotropic soil slopes.The accuracy of the proposed method is first verified against the data in the literature.We then simulate the 3D soil slope with a straight slope surface and the convex and concave slope surfaces with a 90turning corner to study the 3D effect on slope stability and the failure mechanism under anisotropy conditions.Based on our numerical results,the end effect significantly impacts the failure mechanism and safety factor.Anisotropy degree notably affects the safety factor,with higher degrees leading to deeper landslides.For concave slopes,they can be approximated by straight slopes with suitable boundary conditions to assess their stability.Furthermore,a case study of the Saint-Alban test embankment A in Quebec,Canada,is provided to demonstrate the applicability of the proposed FE model.
文摘This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practical engineering fields,such as in short take-off and vertical landing(STOVL)aircraft.Nowadays many intricate phenomena associated with impinging jet flows remain inadequately elucidated,which limits the ability to optimize aircraft design.Given a boundary condition in the inlet,the impinging jet problem is transformed into a Bernoulli-type free boundary problem according to the stream function.Then the variational method is used to study the corresponding variational problem with one parameter,thereby the wellposedness is established.The main conclusion is as follows.For a 3D axisymmetric finitely long nozzle and an infinitely long vertical wall,given an axial velocity in the inlet of nozzle,there exists a unique smooth incom‑pressible impinging jet flow such that the free boundary initiates smoothly at the endpoint of the nozzle and extends to infinity along the vertical wall at far fields.The key point is to investigate the regularity of the corner where the nozzle and the vertical axis intersect.
文摘Design a precision electroplating mechanical structure for automobiles based on finite element analysis method and analyze its mechanical properties.Taking the automobile steering knuckle as the research object,ABAQUS parametric modeling technology is used to construct its three-dimensional geometric model,and geometric simplification is carried out.Two surface treatment processes,HK-35 zinc nickel alloy electroplating and pure zinc electroplating,were designed,and the influence of different coatings on the mechanical properties of steering knuckles was compared and analyzed through numerical simulation.At the same time,standard specimens were prepared for salt spray corrosion testing and scratch method combined strength testing to verify the numerical simulation results.The results showed that under emergency braking and composite working conditions,the peak Von Mises stress of the zinc nickel alloy coating was 119.85 MPa,which was lower than that of the pure zinc coating and the alkaline electroplated zinc layer.Its equivalent strain value was 652×10^(-6),which was lower than that of the pure zinc coating and the alkaline electroplated zinc layer.Experimental data confirms that zinc nickel alloy coatings exhibit significant advantages in stress distribution uniformity,strain performance,and load-bearing capacity in high stress zones.The salt spray corrosion test further indicates that the coating has superior corrosion resistance and coating substrate interface bonding strength,which can significantly improve the mechanical stability and long-term reliability of automotive precision electroplating mechanical structures.
文摘In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided into,by the work of Amiot[Bull.Soc.Math.France,2007,135(3):435-474](see also[Adv.Math.,2008,217(6):2443-2484]and[J.Algebra,2016,446:426-449]),three classes:type A,type D and type E.
基金Supported by Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)+3 种基金National Natural Science Foundation of China(12301556)Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)Basic Research Plan of Shanxi Province(202203021211129)。
文摘To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%.
