In this paper, we first develop the far field asymptotic solutions of the second-order scattering waves for the vertical plane problem taking the second-order Stokes waves as the incident waves. The asymptotic solutio...In this paper, we first develop the far field asymptotic solutions of the second-order scattering waves for the vertical plane problem taking the second-order Stokes waves as the incident waves. The asymptotic solutions satisfy the Laplace equation, the sea bed and free surface boundary conditions and are the out-going waves. Then the radiation conditions of the second-order mattering waves are derived by using the asymptotic solutions. By using the two-dimensinal finite clement method with the radiation conditions imposed on the ar- tificial boundaries, the computer program, known as 'NWF2', for determining nonlinear wave forces on large submerged bodies has been written. As a numerical example, nonlinear wave forces on a semi-circu- lar cylinder lying on the sea bed arc presented.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
In this article, we consider a two-dimensional symmetric space-fractional diffusion equation in which the space fractional derivatives are defined in Riesz potential sense. The well-posed feature is guaranteed by ener...In this article, we consider a two-dimensional symmetric space-fractional diffusion equation in which the space fractional derivatives are defined in Riesz potential sense. The well-posed feature is guaranteed by energy inequality. To solve the diffusion equation, a fully discrete form is established by employing Crank-Nicolson technique in time and Galerkin finite element method in space. The stability and convergence are proved and the stiffness matrix is given analytically. Three numerical examples are given to confirm our theoretical analysis in which we find that even with the same initial condition, the classical and fractional diffusion equations perform differently but tend to be uniform diffusion at last.展开更多
The study of tidal circulation has a long history . The numerical simulation of tidal flow has been developed greatly with the development of computer techniques in the past two decades. The generalized wave equation ...The study of tidal circulation has a long history . The numerical simulation of tidal flow has been developed greatly with the development of computer techniques in the past two decades. The generalized wave equation finite-element method is a relatively new numerical model for studying shallow water flow . This method was used to simulate tidal waves of the Gulf of St. Lawrence in Canada . The very good agreement of the numerical results with the field data indicated that the model is an effective and promising numerical method for solving two-dimensional tidal wave problems .展开更多
In this paper,finite element method(FEM)is used to solve two-dimensional diffu-sion-reaction equations of boundary layer type.This kind of equations are usually too complicatedand diffcult to be solved by applying the...In this paper,finite element method(FEM)is used to solve two-dimensional diffu-sion-reaction equations of boundary layer type.This kind of equations are usually too complicatedand diffcult to be solved by applying the traditional methods used in chemical engineering becauseof the steep gradients of concentration and temperature.But,these difficulties are easy to be over-comed when the FEM is used.The integraded steps of solving this kind of problems by the FEMare presented in this paper.By applying the FEM to the two actual examples,the conclusion can bereached that the FEM has the advantages of simplicity and good accuracy.展开更多
Ceramic spheres,typically with a particle diameter of less than 0.8 mm,are frequently utilized as a critical proppant material in hydraulic fracturing for petroleum and natural gas extraction.Porous ceramic spheres wi...Ceramic spheres,typically with a particle diameter of less than 0.8 mm,are frequently utilized as a critical proppant material in hydraulic fracturing for petroleum and natural gas extraction.Porous ceramic spheres with artificial inherent pores are an important type of lightweight proppant,enabling their transport to distant fracture extremities and enhancing fracture conductivity.However,the focus frequently gravitates towards the low-density advantage,often overlooking the pore geometry impacts on compressive strength by traditional strength evaluation.This paper numerically bypasses such limitations by using a combined finite and discrete element method(FDEM)considering experimental results.The mesh size of the model undergoes validation,followed by the calibration of cohesive element parameters via the single particle compression test.The stimulation elucidates that proppants with a smaller pore size(40μm)manifest crack propagation evolution at a more rapid pace in comparison to their larger-pore counterparts,though the influence of pore diameter on overall strength is subtle.The inception of pores not only alters the trajectory of crack progression but also,with an increase in porosity,leads to a discernible decline in proppant compressive strength.Intriguingly,upon crossing a porosity threshold of 10%,the decrement in strength becomes more gradual.A denser congregation of pores accelerates crack propagation,undermining proppant robustness,suggesting that under analogous conditions,hollow proppants might not match the strength of their porous counterparts.This exploration elucidates the underlying mechanisms of proppant failure from a microstructural perspective,furnishing pivotal insights that may guide future refinements in the architectural design of porous proppant.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
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
This study presents a novel methodology to obtain an approximate analytical solution for an isotropic homo-geneous elastic medium with displacement and traction boundary conditions.The solution is derived through solv...This study presents a novel methodology to obtain an approximate analytical solution for an isotropic homo-geneous elastic medium with displacement and traction boundary conditions.The solution is derived through solving a specific numerical problem under the scope of the linear finite element method(LFEM),so the method is termed computational method for analytical solutions with finite elements(CMAS-FE).The primary objective of the CMAS-FE is to construct analytical expressions for displacements and reaction forces at nodes,as well as for strains and stresses at elemental quadrature points,all of which are formulated as infinite series solutions of various orders of Poisson’s ratios.Like the conventional LFEM,the CMAS-FE forms global sparse linear equations,but the Young’s modulus and Poisson’s ratio remain variables(or symbols).By employing a direct inverse method to solve these symbolic linear systems,an analytical expression of the displacement field can be constructed.The CMAS-FE is validated via patch and bending tests,which demonstrate convergence with mesh and term refine-ment.Furthermore,the CMAS-FE is applied to obtain the bending stiffness of a beam structure and to estimate an approximate stress intensity factor for a straight crack within a square-shaped plate.展开更多
Magneto-electro-elastic(MEE)materials are widely utilized across various fields due to their multi-field coupling effects.Consequently,investigating the coupling behavior of MEE composite materials is of significant i...Magneto-electro-elastic(MEE)materials are widely utilized across various fields due to their multi-field coupling effects.Consequently,investigating the coupling behavior of MEE composite materials is of significant importance.The traditional finite element method(FEM)remains one of the primary approaches for addressing such issues.However,the application of FEM typically necessitates the use of a fine finite element mesh to accurately capture the heterogeneous properties of the materials and meet the required computational precision,which inevitably leads to a reduction in computational efficiency.To enhance the computational accuracy and efficiency of the FEM for heterogeneous multi-field coupling problems,this study presents the coupling magneto-electro-elastic multiscale finite element method(CM-MsFEM)for heterogeneous MEE structures.Unlike the conventional multiscale FEM(MsFEM),the proposed algorithm simultaneously constructs displacement,electric,and magnetic potential multiscale basis functions to address the heterogeneity of the corresponding parameters.The macroscale formulation of CM-MsFEM was derived,and the macroscale/microscale responses of the problems were obtained through up/downscaling calculations.Evaluation using numerical examples analyzing the transient behavior of heterogeneous MEE structures demonstrated that the proposed method outperforms traditional FEM in terms of both accuracy and computational efficiency,making it an appropriate choice for numerically modeling the dynamics of heterogeneous MEE structures.展开更多
The microstructure and related property evolution induced by dynamic recrystallization(DRX)and static recrystallization(SRX)in thermo-mechanical process are two critical factors for the metal forming.The DRX and SRX a...The microstructure and related property evolution induced by dynamic recrystallization(DRX)and static recrystallization(SRX)in thermo-mechanical process are two critical factors for the metal forming.The DRX and SRX are determined by the grain level deformation and sequentially coupled.In order to fully capture the microstructure and mechanical property evolution,a crystal plasticity finite element based modelling method for DRX and SRX is proposed in the current work.The grain level deformation is calculated with crystal plasticity which is coupled with the recrystallization model straightforwardly,and both the grain deformation and microstructure evolution are updated simultaneously.The proposed method is validated with discontinuous DRX experiments and the effects of initial deformation conditions are well-captured.Two controversial mechanisms for recrystallization microstructure evolution,i.e.oriented nucleation and growth selection,are discussed in the current framework with the advantages of accurate grain level deformation and interaction predictions.Furthermore,the sequentially coupled DRX and SRX are modelled seamlessly in the current work which provides a critical method for fully integrated thermo-mechanical processes analysis.展开更多
In this paper,we propose a multiphysics finite element method for a nonlinear poroelasticity model with nonlinear stress-strain relation.Firstly,we reformulate the original problem into a new coupled fluid system-a ge...In this paper,we propose a multiphysics finite element method for a nonlinear poroelasticity model with nonlinear stress-strain relation.Firstly,we reformulate the original problem into a new coupled fluid system-a generalized nonlinear Stokes problem of displacement vector field related to pseudo pressure and a diffusion problem of other pseudo pressure fields.Secondly,a fully discrete multiphysics finite element method is performed to solve the reformulated system numerically.Thirdly,existence and uniqueness of the weak solution of the reformulated model and stability analysis and optimal convergence order for the multiphysics finite element method are proven theoretically.Lastly,numerical tests are given to verify the theoretical results.展开更多
Skin panels on supersonic vehicles are subjected to aero-thermo-acoustic loads,resulting in a well-known multi-physics dynamic problem.The high-frequency dynamic response of these panels significantly impacts the stru...Skin panels on supersonic vehicles are subjected to aero-thermo-acoustic loads,resulting in a well-known multi-physics dynamic problem.The high-frequency dynamic response of these panels significantly impacts the structural safety of supersonic vehicles,but it has been rarely investigated.Given that existing methods are inefficient for high-frequency dynamic analysis in multi-physics fields,the present work addresses this challenge by proposing a Stochastic Energy Finite Element Method(SEFEM).SEFEM uses energy density instead of displacement to describe the dynamic response,thereby significantly enhancing its efficiency.In SEFEM,the effects of aerodynamic and thermal loads on the energy propagation characteristics are studied analytically and incorporated into the energy density governing equation.These effects are also considered when calculating the input power generated by the acoustic load,and two effective approaches named Frequency Response Function Method(FRFM)and Mechanical Impedance Method(MIM)are developed accordingly and integrated into SEFEM.The good accuracy,applicability,and high efficiency of the proposed SEFEM are demonstrated through numerical simulations performed on a two-dimensional panel under aero-thermoacoustic loads.Additionally,the effects and underlying mechanisms of aero-thermo-acoustic loads on the high-frequency response are explored.This work not only presents an efficient approach for predicting high-frequency dynamic response of panels subjected to aero-thermo-acoustic loads,but also provides insights into the high-frequency dynamic characteristics in multi-physics fields.展开更多
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
The application of carbon capture systems on ships is technically constrained by limited onboard space and the weight of the conventional absorption tower.The rotating packed bed(RPB)has emerged as a promising alterna...The application of carbon capture systems on ships is technically constrained by limited onboard space and the weight of the conventional absorption tower.The rotating packed bed(RPB)has emerged as a promising alternative due to its small footprint and high mass transfer performance.However,despite its advantages,the structural and vibration stability of RPBs at high rotational speed remains insufficiently studied,and no international design standards currently exist for RPBs.To address this gap,this study performed a comprehensive finite element analysis(FEA)using ANSYS to investigate the structural and dynamic characteristics of an RPB.A three-dimensional model was developed to evaluate the effects of material selection(316 stainless steel,aluminum alloy,titanium alloy),bearing stiffness,and unbalanced mass on deformation,stress,and natural frequencies.In the structural analysis,316 stainless steel exhibited the highest von Mises stress and deformation.However,it was confirmed that all three materials did not exceed their yield strengths at the maximum rotating speed.Modal analysis and Campbell diagrams showed no resonance risk within the rated speed range,and increased bearing stiffness led to higher natural frequencies and improved stability.The findings provide quantitative design guidance for material selection,bearing stiffness optimization,and vibration control in high-rotational-speed RPB systems.This study contributes to establishing a foundational framework for the mechanical reliability and standardization of marine carbon capture units.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
Controlled nuclear fusion represents a significant solution for future clean energy,with ion cyclotron range of frequency(ICRF)heating emerging as one of the most promising technologies for heating the fusion plasma.T...Controlled nuclear fusion represents a significant solution for future clean energy,with ion cyclotron range of frequency(ICRF)heating emerging as one of the most promising technologies for heating the fusion plasma.This study primarily presents a self-developed 2D ion cyclotron resonance antenna electromagnetic field solver(ICRAEMS)code implemented on the MATLAB platform,which solves the electric field wave equation by using the finite element method,establishing perfectly matched layer(PML)boundary conditions,and post-processing the electromagnetic field data.This code can be utilized to facilitate the design and optimization processes of antennas for ICRF heating technology.Furthermore,this study examines the electric field distribution and power spectrum associated with various antenna phases to investigate how different antenna configurations affect the electromagnetic field propagation and coupling characteristics.展开更多
In this work, the two-dimensional convective Brinkman-Forchheimer equa- tions are considered. The well-posedness for the variational problem and its mixed finite element approximation is established, and the error est...In this work, the two-dimensional convective Brinkman-Forchheimer equa- tions are considered. The well-posedness for the variational problem and its mixed finite element approximation is established, and the error estimates based on the conforming approximation are obtained. For the computation, a one-step Newton (or semi-Newton) iteration algorithm initialized using a fixed-point iteration is proposed. Finally, numerical experiments using a Taylor-Hood mixed element built on a structured or unstructured triangular mesh are implemented. The numerical results obtained using the algorithm are compared with the analytic data, and are shown to be in very good agreement. Moreover, the lid-driven problem at Reynolds numbers of 100 and 400 is considered and analyzed.展开更多
Fines migration along with rainfall infiltration is a possible cause of failures of slopes composed of loose deposits.To investigate the intrinsic mechanisms,a rigid mathematical model which can fully capture the mult...Fines migration along with rainfall infiltration is a possible cause of failures of slopes composed of loose deposits.To investigate the intrinsic mechanisms,a rigid mathematical model which can fully capture the multi-phasic and multiphysical process is necessary.In this research,the macro and micro physical phenomena of fines migration process within deposited soil slopes under rainfall infiltration were summarized.Based on the mixture theory,a seepage-erosion model for unsaturated erodible soils capable to capture these phenomena mathematically was built based on a rigid theoretical framework.The model was used to simulate a set of rainfall flume tests involving fines migration phenomena with the finite element method.Two distinct slope failure modes observed experimentally,which were induced by the soil erosion-deposition properties,can be well reproduced by our numerical model.The seepage-erosion coupled process during the rainfall infiltration,as well as the intrinsic mechanism responsible for the slope failures,was illustrated in detail based on the numerical results.It was shown that the fines migration process can affect the hydro-mechanical response within unsaturated slopes significantly,and therefore special attention should be paid to those soil slopes susceptible to internal erosion.展开更多
文摘In this paper, we first develop the far field asymptotic solutions of the second-order scattering waves for the vertical plane problem taking the second-order Stokes waves as the incident waves. The asymptotic solutions satisfy the Laplace equation, the sea bed and free surface boundary conditions and are the out-going waves. Then the radiation conditions of the second-order mattering waves are derived by using the asymptotic solutions. By using the two-dimensinal finite clement method with the radiation conditions imposed on the ar- tificial boundaries, the computer program, known as 'NWF2', for determining nonlinear wave forces on large submerged bodies has been written. As a numerical example, nonlinear wave forces on a semi-circu- lar cylinder lying on the sea bed arc presented.
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.
文摘In this article, we consider a two-dimensional symmetric space-fractional diffusion equation in which the space fractional derivatives are defined in Riesz potential sense. The well-posed feature is guaranteed by energy inequality. To solve the diffusion equation, a fully discrete form is established by employing Crank-Nicolson technique in time and Galerkin finite element method in space. The stability and convergence are proved and the stiffness matrix is given analytically. Three numerical examples are given to confirm our theoretical analysis in which we find that even with the same initial condition, the classical and fractional diffusion equations perform differently but tend to be uniform diffusion at last.
文摘The study of tidal circulation has a long history . The numerical simulation of tidal flow has been developed greatly with the development of computer techniques in the past two decades. The generalized wave equation finite-element method is a relatively new numerical model for studying shallow water flow . This method was used to simulate tidal waves of the Gulf of St. Lawrence in Canada . The very good agreement of the numerical results with the field data indicated that the model is an effective and promising numerical method for solving two-dimensional tidal wave problems .
基金Project financially supported by scientific research foundation coferring to Ph.D.
文摘In this paper,finite element method(FEM)is used to solve two-dimensional diffu-sion-reaction equations of boundary layer type.This kind of equations are usually too complicatedand diffcult to be solved by applying the traditional methods used in chemical engineering becauseof the steep gradients of concentration and temperature.But,these difficulties are easy to be over-comed when the FEM is used.The integraded steps of solving this kind of problems by the FEMare presented in this paper.By applying the FEM to the two actual examples,the conclusion can bereached that the FEM has the advantages of simplicity and good accuracy.
基金the financial support provided by Tianfu Yongxing Laboratory Organized Research Project Funding(No.2023CXXM01)the ARC linkage program(No.LP200100420).
文摘Ceramic spheres,typically with a particle diameter of less than 0.8 mm,are frequently utilized as a critical proppant material in hydraulic fracturing for petroleum and natural gas extraction.Porous ceramic spheres with artificial inherent pores are an important type of lightweight proppant,enabling their transport to distant fracture extremities and enhancing fracture conductivity.However,the focus frequently gravitates towards the low-density advantage,often overlooking the pore geometry impacts on compressive strength by traditional strength evaluation.This paper numerically bypasses such limitations by using a combined finite and discrete element method(FDEM)considering experimental results.The mesh size of the model undergoes validation,followed by the calibration of cohesive element parameters via the single particle compression test.The stimulation elucidates that proppants with a smaller pore size(40μm)manifest crack propagation evolution at a more rapid pace in comparison to their larger-pore counterparts,though the influence of pore diameter on overall strength is subtle.The inception of pores not only alters the trajectory of crack progression but also,with an increase in porosity,leads to a discernible decline in proppant compressive strength.Intriguingly,upon crossing a porosity threshold of 10%,the decrement in strength becomes more gradual.A denser congregation of pores accelerates crack propagation,undermining proppant robustness,suggesting that under analogous conditions,hollow proppants might not match the strength of their porous counterparts.This exploration elucidates the underlying mechanisms of proppant failure from a microstructural perspective,furnishing pivotal insights that may guide future refinements in the architectural design of porous proppant.
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.
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 Excellence Research Group Program for“Multiscale Problems in Nonlinear Mechanics”(Grant No.12588201)the National Key R&D Program of China(Grant No.2023YFA1008901)+1 种基金the National Nat-ural Science Foundation of China(Grant No.12172009)supported by“The Fundamental Research Funds for the Central Universities,Peking University”.
文摘This study presents a novel methodology to obtain an approximate analytical solution for an isotropic homo-geneous elastic medium with displacement and traction boundary conditions.The solution is derived through solving a specific numerical problem under the scope of the linear finite element method(LFEM),so the method is termed computational method for analytical solutions with finite elements(CMAS-FE).The primary objective of the CMAS-FE is to construct analytical expressions for displacements and reaction forces at nodes,as well as for strains and stresses at elemental quadrature points,all of which are formulated as infinite series solutions of various orders of Poisson’s ratios.Like the conventional LFEM,the CMAS-FE forms global sparse linear equations,but the Young’s modulus and Poisson’s ratio remain variables(or symbols).By employing a direct inverse method to solve these symbolic linear systems,an analytical expression of the displacement field can be constructed.The CMAS-FE is validated via patch and bending tests,which demonstrate convergence with mesh and term refine-ment.Furthermore,the CMAS-FE is applied to obtain the bending stiffness of a beam structure and to estimate an approximate stress intensity factor for a straight crack within a square-shaped plate.
基金supported by the National Natural Science Foundation of China(Grant Nos.42102346,42172301).
文摘Magneto-electro-elastic(MEE)materials are widely utilized across various fields due to their multi-field coupling effects.Consequently,investigating the coupling behavior of MEE composite materials is of significant importance.The traditional finite element method(FEM)remains one of the primary approaches for addressing such issues.However,the application of FEM typically necessitates the use of a fine finite element mesh to accurately capture the heterogeneous properties of the materials and meet the required computational precision,which inevitably leads to a reduction in computational efficiency.To enhance the computational accuracy and efficiency of the FEM for heterogeneous multi-field coupling problems,this study presents the coupling magneto-electro-elastic multiscale finite element method(CM-MsFEM)for heterogeneous MEE structures.Unlike the conventional multiscale FEM(MsFEM),the proposed algorithm simultaneously constructs displacement,electric,and magnetic potential multiscale basis functions to address the heterogeneity of the corresponding parameters.The macroscale formulation of CM-MsFEM was derived,and the macroscale/microscale responses of the problems were obtained through up/downscaling calculations.Evaluation using numerical examples analyzing the transient behavior of heterogeneous MEE structures demonstrated that the proposed method outperforms traditional FEM in terms of both accuracy and computational efficiency,making it an appropriate choice for numerically modeling the dynamics of heterogeneous MEE structures.
基金supported by the National Natural Science Foundation of China(Nos.52105384 and U2141215).
文摘The microstructure and related property evolution induced by dynamic recrystallization(DRX)and static recrystallization(SRX)in thermo-mechanical process are two critical factors for the metal forming.The DRX and SRX are determined by the grain level deformation and sequentially coupled.In order to fully capture the microstructure and mechanical property evolution,a crystal plasticity finite element based modelling method for DRX and SRX is proposed in the current work.The grain level deformation is calculated with crystal plasticity which is coupled with the recrystallization model straightforwardly,and both the grain deformation and microstructure evolution are updated simultaneously.The proposed method is validated with discontinuous DRX experiments and the effects of initial deformation conditions are well-captured.Two controversial mechanisms for recrystallization microstructure evolution,i.e.oriented nucleation and growth selection,are discussed in the current framework with the advantages of accurate grain level deformation and interaction predictions.Furthermore,the sequentially coupled DRX and SRX are modelled seamlessly in the current work which provides a critical method for fully integrated thermo-mechanical processes analysis.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12371393,11971150 and 11801143)Natural Science Foundation of Henan Province(Grant No.242300421047).
文摘In this paper,we propose a multiphysics finite element method for a nonlinear poroelasticity model with nonlinear stress-strain relation.Firstly,we reformulate the original problem into a new coupled fluid system-a generalized nonlinear Stokes problem of displacement vector field related to pseudo pressure and a diffusion problem of other pseudo pressure fields.Secondly,a fully discrete multiphysics finite element method is performed to solve the reformulated system numerically.Thirdly,existence and uniqueness of the weak solution of the reformulated model and stability analysis and optimal convergence order for the multiphysics finite element method are proven theoretically.Lastly,numerical tests are given to verify the theoretical results.
基金financially supported by the National Natural Science Foundation of China(Nos.12302228 and 12372170)。
文摘Skin panels on supersonic vehicles are subjected to aero-thermo-acoustic loads,resulting in a well-known multi-physics dynamic problem.The high-frequency dynamic response of these panels significantly impacts the structural safety of supersonic vehicles,but it has been rarely investigated.Given that existing methods are inefficient for high-frequency dynamic analysis in multi-physics fields,the present work addresses this challenge by proposing a Stochastic Energy Finite Element Method(SEFEM).SEFEM uses energy density instead of displacement to describe the dynamic response,thereby significantly enhancing its efficiency.In SEFEM,the effects of aerodynamic and thermal loads on the energy propagation characteristics are studied analytically and incorporated into the energy density governing equation.These effects are also considered when calculating the input power generated by the acoustic load,and two effective approaches named Frequency Response Function Method(FRFM)and Mechanical Impedance Method(MIM)are developed accordingly and integrated into SEFEM.The good accuracy,applicability,and high efficiency of the proposed SEFEM are demonstrated through numerical simulations performed on a two-dimensional panel under aero-thermoacoustic loads.Additionally,the effects and underlying mechanisms of aero-thermo-acoustic loads on the high-frequency response are explored.This work not only presents an efficient approach for predicting high-frequency dynamic response of panels subjected to aero-thermo-acoustic loads,but also provides insights into the high-frequency dynamic characteristics in multi-physics fields.
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.
基金support of the Korea Institute of Industrial Technology and Promotion,with the financial resources of the government(Ministry of Trade,Industry,and Energy)in 2024.(RS-2024-00424595,project to train high-quality researchers for the next generation of marine mobility industry innovation).
文摘The application of carbon capture systems on ships is technically constrained by limited onboard space and the weight of the conventional absorption tower.The rotating packed bed(RPB)has emerged as a promising alternative due to its small footprint and high mass transfer performance.However,despite its advantages,the structural and vibration stability of RPBs at high rotational speed remains insufficiently studied,and no international design standards currently exist for RPBs.To address this gap,this study performed a comprehensive finite element analysis(FEA)using ANSYS to investigate the structural and dynamic characteristics of an RPB.A three-dimensional model was developed to evaluate the effects of material selection(316 stainless steel,aluminum alloy,titanium alloy),bearing stiffness,and unbalanced mass on deformation,stress,and natural frequencies.In the structural analysis,316 stainless steel exhibited the highest von Mises stress and deformation.However,it was confirmed that all three materials did not exceed their yield strengths at the maximum rotating speed.Modal analysis and Campbell diagrams showed no resonance risk within the rated speed range,and increased bearing stiffness led to higher natural frequencies and improved stability.The findings provide quantitative design guidance for material selection,bearing stiffness optimization,and vibration control in high-rotational-speed RPB systems.This study contributes to establishing a foundational framework for the mechanical reliability and standardization of marine carbon capture units.
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.
基金Project supported by the National MCF Energy R&D Program(Grant No.2022YFE03190100)the National Natural Science Foundation of China(Grant Nos.12422513,12105035,and U21A20438)the Xiaomi Young Talents Program.
文摘Controlled nuclear fusion represents a significant solution for future clean energy,with ion cyclotron range of frequency(ICRF)heating emerging as one of the most promising technologies for heating the fusion plasma.This study primarily presents a self-developed 2D ion cyclotron resonance antenna electromagnetic field solver(ICRAEMS)code implemented on the MATLAB platform,which solves the electric field wave equation by using the finite element method,establishing perfectly matched layer(PML)boundary conditions,and post-processing the electromagnetic field data.This code can be utilized to facilitate the design and optimization processes of antennas for ICRF heating technology.Furthermore,this study examines the electric field distribution and power spectrum associated with various antenna phases to investigate how different antenna configurations affect the electromagnetic field propagation and coupling characteristics.
基金supported by the National Natural Science Foundation of China(Nos.11461068,11362021,and 11401511)the Doctoral Foundation of Xinjiang Uygur Autonomous Region of China(No.BS110101)
文摘In this work, the two-dimensional convective Brinkman-Forchheimer equa- tions are considered. The well-posedness for the variational problem and its mixed finite element approximation is established, and the error estimates based on the conforming approximation are obtained. For the computation, a one-step Newton (or semi-Newton) iteration algorithm initialized using a fixed-point iteration is proposed. Finally, numerical experiments using a Taylor-Hood mixed element built on a structured or unstructured triangular mesh are implemented. The numerical results obtained using the algorithm are compared with the analytic data, and are shown to be in very good agreement. Moreover, the lid-driven problem at Reynolds numbers of 100 and 400 is considered and analyzed.
基金supported by the NSFC(41925030,42072315,41790433)Scientific Foundation of CAS(KFJ-STS-QYZD-172)+2 种基金the Hundred Young Talents Program of IMHE(E0K2130130)the Youth Innovation Promotion Association fund of CAS(2020368)the Open fund of SKLGP(SKLGP2018K013)。
文摘Fines migration along with rainfall infiltration is a possible cause of failures of slopes composed of loose deposits.To investigate the intrinsic mechanisms,a rigid mathematical model which can fully capture the multi-phasic and multiphysical process is necessary.In this research,the macro and micro physical phenomena of fines migration process within deposited soil slopes under rainfall infiltration were summarized.Based on the mixture theory,a seepage-erosion model for unsaturated erodible soils capable to capture these phenomena mathematically was built based on a rigid theoretical framework.The model was used to simulate a set of rainfall flume tests involving fines migration phenomena with the finite element method.Two distinct slope failure modes observed experimentally,which were induced by the soil erosion-deposition properties,can be well reproduced by our numerical model.The seepage-erosion coupled process during the rainfall infiltration,as well as the intrinsic mechanism responsible for the slope failures,was illustrated in detail based on the numerical results.It was shown that the fines migration process can affect the hydro-mechanical response within unsaturated slopes significantly,and therefore special attention should be paid to those soil slopes susceptible to internal erosion.
