In this paper, we consider two methods, the Second order Central Difference Method (SCDM) and the Finite Element Method (FEM) with P1 triangular elements, for solving two dimensional general linear Elliptic Partial Di...In this paper, we consider two methods, the Second order Central Difference Method (SCDM) and the Finite Element Method (FEM) with P1 triangular elements, for solving two dimensional general linear Elliptic Partial Differential Equations (PDE) with mixed derivatives along with Dirichlet and Neumann boundary conditions. These two methods have almost the same accuracy from theoretical aspect with regular boundaries, but generally Finite Element Method produces better approximations when the boundaries are irregular. In order to investigate which method produces better results from numerical aspect, we apply these methods into specific examples with regular boundaries with constant step-size for both of them. The results which obtained confirm, in most of the cases, the theoretical results.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 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
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
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
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,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
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
Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained result...Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained results is verified by the finite difference method（FDM）and the finite element method（FEM）with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes（regular and non-regular）.The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.展开更多
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
A discontinuous Galerkin finite element method （DG-FEM） is developed for solving the axisymmetric Euler equations based on two-dimensional conservation laws. The method is used to simulate the unsteady-state underex...A discontinuous Galerkin finite element method （DG-FEM） is developed for solving the axisymmetric Euler equations based on two-dimensional conservation laws. The method is used to simulate the unsteady-state underexpanded axisymmetric jet. Several flow property distributions along the jet axis, including density, pres- sure and Mach number are obtained and the qualitative flowfield structures of interest are well captured using the proposed method, including shock waves, slipstreams, traveling vortex ring and multiple Mach disks. Two Mach disk locations agree well with computational and experimental measurement results. It indicates that the method is robust and efficient for solving the unsteady-state underexpanded axisymmetric jet.展开更多
The equilibrium equations and the functional for tubing buckling in arbitrary straight wells are derived. The entire buckling process of tubing in deviated wells is analyzed for the first time by utilizing the finite ...The equilibrium equations and the functional for tubing buckling in arbitrary straight wells are derived. The entire buckling process of tubing in deviated wells is analyzed for the first time by utilizing the finite element method. The effects of gravity and torques on the buckling are included in the analyses and the calculated results are well compared with existing solutions. It is shown that the buckling only occurs at the lower portion of the tubing where the axial load is the largest, and the contact force of the well, the bending moment of the tubing and the buckling displacement of this portion vary periodically. The buckling spreads upwards from the bit with the increase of axial load. There is no buckling at the upper portion of the tubing where the bending moment is zero. And the contact force of this section increases only slightly with the increase of the axial load. With the increase of the deviation angle, the length of buckling portion and buckling displacement amplitude decrease, the contact force increases with the increase of load at the upper portion and its amplitude decreases at the lower buckling section, the bending moment remains zero at the upper portion and its amplitude decreases at the lower buckling portion. The buckling displacement increases with the increase of the torque, but the increment is very small.展开更多
A mathematical model combined projection algorithm with phase-field method was applied. The adaptive finite element method was adopted to solve the model based on the non-uniform grid, and the behavior of dendritic gr...A mathematical model combined projection algorithm with phase-field method was applied. The adaptive finite element method was adopted to solve the model based on the non-uniform grid, and the behavior of dendritic growth was simulated from undercooled nickel melt under the forced flow. The simulation results show that the asymmetry behavior of the dendritic growth is caused by the forced flow. When the flow velocity is less than the critical value, the asymmetry of dendrite is little influenced by the forced flow. Once the flow velocity reaches or exceeds the critical value, the controlling factor of dendrite growth gradually changes from thermal diffusion to convection. With the increase of the flow velocity, the deflection angle towards upstream direction of the primary dendrite stem becomes larger. The effect of the dendrite growth on the flow field of the melt is apparent. With the increase of the dendrite size, the vortex is present in the downstream regions, and the vortex region is gradually enlarged. Dendrite tips appear to remelt. In addition, the adaptive finite element method can reduce CPU running time by one order of magnitude compared with uniform grid method, and the speed-up ratio is proportional to the size of computational domain.展开更多
A numerical simulation of the toroidal shock wave focusing in a co-axial cylindrical shock tube is inves- tigated by using discontinuous Galerkin （DG） finite element method to solve the axisymmetric Euler equations....A numerical simulation of the toroidal shock wave focusing in a co-axial cylindrical shock tube is inves- tigated by using discontinuous Galerkin （DG） finite element method to solve the axisymmetric Euler equations. For validating the numerical method, the shock-tube problem with exact solution is computed, and the computed results agree well with the exact cases. Then, several cases with higher incident Mach numbers varying from 2.0 to 5.0 are simulated. Simulation results show that complicated flow-field structures of toroidal shock wave diffraction, reflection, and focusing in a co-axial cylindrical shock tube can be obtained at different incident Mach numbers and the numerical solutions appear steep gradients near the focusing point, which illustrates the DG method has higher accuracy and better resolution near the discontinuous point. Moreover, the focusing peak pres- sure with different grid scales is compared.展开更多
This study investigates the complex heat transfer dynamics inmultilayer bifacial photovoltaic(bPV)solar modules under spectrally resolved solar irradiation.A novel numericalmodel is developed to incorporate internal h...This study investigates the complex heat transfer dynamics inmultilayer bifacial photovoltaic(bPV)solar modules under spectrally resolved solar irradiation.A novel numericalmodel is developed to incorporate internal heat generation resulting from optical absorption,grounded in the physical equations governing light-matter interactions within the module’smultilayer structure.The model accounts for reflection and transmission at each interface between adjacent layers,as well as absorption within individual layers,using the wavelength-dependent dielectric properties of constituent materials.These properties are used to calculate the spectral reflectance,transmittance,and absorption coefficients,enabling precise quantification of internal heat sources from irradiance incidents on both the front and rear surfaces of the module.The study further examines the influence of irradiance reflection on thermal behavior,evaluates the thermal impact of various supporting materials placed beneath the module,and analyzes the role of albedo in modifying heat distribution.By incorporating spectrally resolved heat generation across each layer often simplified or omitted in conventional models,the proposed approach enhances physical accuracy.The transient heat equation is solved using a one-dimensional finite difference(FD)method to produce detailed temperature profiles under multiple operating scenarios,including Standard Test Conditions(STC),Bifacial Standard Test Conditions(BSTC),Normal Operating Cell Temperature(NOCT),and Bifacial NOCT(BNOCT).The results offer valuable insights into the interplay between optical and thermal phenomena in bifacial systems,informing the design and optimization of more efficient photovoltaic technologies.展开更多
A method combining finite difference method(FDM)and k-means clustering algorithm which can determine the threshold of rock bridge generation is proposed.Jointed slope models with different joint coalescence coefficien...A method combining finite difference method(FDM)and k-means clustering algorithm which can determine the threshold of rock bridge generation is proposed.Jointed slope models with different joint coalescence coefficients(k)are constructed based on FDM.The rock bridge area was divided through k-means algorithm and the optimal number of clusters was determined by sum of squared errors(SSE)and elbow method.The influence of maximum principal stress and stress change rate as clustering indexes on the clustering results of rock bridges was compared by using Euclidean distance.The results show that using stress change rate as clustering index is more effective.When the joint coalescence coefficient is less than 0.6,there is no significant stress concentration in the middle area of adjacent joints,that is,no generation of rock bridge.In addition,the range of rock bridge is affected by the coalescence coefficient(k),the relative position of joints and the parameters of weak interlayer.展开更多
In this work, we first derive the one-point large deviations principle (LDP) for both the stochastic Cahn–Hilliard equation with small noise and its spatial finite difference method (FDM). Then, we focus on giving th...In this work, we first derive the one-point large deviations principle (LDP) for both the stochastic Cahn–Hilliard equation with small noise and its spatial finite difference method (FDM). Then, we focus on giving the convergence of the one-point large deviations rate function (LDRF) of the spatial FDM, which is about the asymptotical limit of a parametric variational problem. The main idea for proving the convergence of the LDRF of the spatial FDM is via the Γ-convergence of objective functions. This relies on the qualitative analysis of skeleton equations of the original equation and the numerical method. In order to overcome the difficulty that the drift coefficient is not one-sided Lipschitz continuous, we derive the equivalent characterization of the skeleton equation of the spatial FDM and the discrete interpolation inequality to obtain the uniform boundedness of the solution to the underlying skeleton equation. These play important roles in deriving the T-convergence of objective functions.展开更多
The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are...The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are asymptotically convergent. Both methods are considered in continnous time.展开更多
文摘In this paper, we consider two methods, the Second order Central Difference Method (SCDM) and the Finite Element Method (FEM) with P1 triangular elements, for solving two dimensional general linear Elliptic Partial Differential Equations (PDE) with mixed derivatives along with Dirichlet and Neumann boundary conditions. These two methods have almost the same accuracy from theoretical aspect with regular boundaries, but generally Finite Element Method produces better approximations when the boundaries are irregular. In order to investigate which method produces better results from numerical aspect, we apply these methods into specific examples with regular boundaries with constant step-size for both of them. The results which obtained confirm, in most of the cases, the theoretical results.
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(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 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 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.
文摘Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained results is verified by the finite difference method（FDM）and the finite element method（FEM）with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes（regular and non-regular）.The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.
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%.
文摘A discontinuous Galerkin finite element method （DG-FEM） is developed for solving the axisymmetric Euler equations based on two-dimensional conservation laws. The method is used to simulate the unsteady-state underexpanded axisymmetric jet. Several flow property distributions along the jet axis, including density, pres- sure and Mach number are obtained and the qualitative flowfield structures of interest are well captured using the proposed method, including shock waves, slipstreams, traveling vortex ring and multiple Mach disks. Two Mach disk locations agree well with computational and experimental measurement results. It indicates that the method is robust and efficient for solving the unsteady-state underexpanded axisymmetric jet.
文摘The equilibrium equations and the functional for tubing buckling in arbitrary straight wells are derived. The entire buckling process of tubing in deviated wells is analyzed for the first time by utilizing the finite element method. The effects of gravity and torques on the buckling are included in the analyses and the calculated results are well compared with existing solutions. It is shown that the buckling only occurs at the lower portion of the tubing where the axial load is the largest, and the contact force of the well, the bending moment of the tubing and the buckling displacement of this portion vary periodically. The buckling spreads upwards from the bit with the increase of axial load. There is no buckling at the upper portion of the tubing where the bending moment is zero. And the contact force of this section increases only slightly with the increase of the axial load. With the increase of the deviation angle, the length of buckling portion and buckling displacement amplitude decrease, the contact force increases with the increase of load at the upper portion and its amplitude decreases at the lower buckling section, the bending moment remains zero at the upper portion and its amplitude decreases at the lower buckling portion. The buckling displacement increases with the increase of the torque, but the increment is very small.
基金Projects(51161011,11364024)supported by the National Natural Science Foundation of ChinaProject(1204GKCA065)supported by the Key Technology R&D Program of Gansu Province,China+1 种基金Project(201210)supported by the Fundamental Research Funds for the Universities of Gansu Province,ChinaProject(J201304)supported by the Funds for Distinguished Young Scientists of Lanzhou University of Technology,China
文摘A mathematical model combined projection algorithm with phase-field method was applied. The adaptive finite element method was adopted to solve the model based on the non-uniform grid, and the behavior of dendritic growth was simulated from undercooled nickel melt under the forced flow. The simulation results show that the asymmetry behavior of the dendritic growth is caused by the forced flow. When the flow velocity is less than the critical value, the asymmetry of dendrite is little influenced by the forced flow. Once the flow velocity reaches or exceeds the critical value, the controlling factor of dendrite growth gradually changes from thermal diffusion to convection. With the increase of the flow velocity, the deflection angle towards upstream direction of the primary dendrite stem becomes larger. The effect of the dendrite growth on the flow field of the melt is apparent. With the increase of the dendrite size, the vortex is present in the downstream regions, and the vortex region is gradually enlarged. Dendrite tips appear to remelt. In addition, the adaptive finite element method can reduce CPU running time by one order of magnitude compared with uniform grid method, and the speed-up ratio is proportional to the size of computational domain.
基金Supported by the National Natural Science Foundation of China(50976072,51106099,10902070)the Leading Academic Discipline Project of Shanghai Municipal Education Commission(J50501)the Science Foundation for the Excellent Youth Scholar of Higher Education of Shanghai(slg09003)~~
文摘A numerical simulation of the toroidal shock wave focusing in a co-axial cylindrical shock tube is inves- tigated by using discontinuous Galerkin （DG） finite element method to solve the axisymmetric Euler equations. For validating the numerical method, the shock-tube problem with exact solution is computed, and the computed results agree well with the exact cases. Then, several cases with higher incident Mach numbers varying from 2.0 to 5.0 are simulated. Simulation results show that complicated flow-field structures of toroidal shock wave diffraction, reflection, and focusing in a co-axial cylindrical shock tube can be obtained at different incident Mach numbers and the numerical solutions appear steep gradients near the focusing point, which illustrates the DG method has higher accuracy and better resolution near the discontinuous point. Moreover, the focusing peak pres- sure with different grid scales is compared.
文摘This study investigates the complex heat transfer dynamics inmultilayer bifacial photovoltaic(bPV)solar modules under spectrally resolved solar irradiation.A novel numericalmodel is developed to incorporate internal heat generation resulting from optical absorption,grounded in the physical equations governing light-matter interactions within the module’smultilayer structure.The model accounts for reflection and transmission at each interface between adjacent layers,as well as absorption within individual layers,using the wavelength-dependent dielectric properties of constituent materials.These properties are used to calculate the spectral reflectance,transmittance,and absorption coefficients,enabling precise quantification of internal heat sources from irradiance incidents on both the front and rear surfaces of the module.The study further examines the influence of irradiance reflection on thermal behavior,evaluates the thermal impact of various supporting materials placed beneath the module,and analyzes the role of albedo in modifying heat distribution.By incorporating spectrally resolved heat generation across each layer often simplified or omitted in conventional models,the proposed approach enhances physical accuracy.The transient heat equation is solved using a one-dimensional finite difference(FD)method to produce detailed temperature profiles under multiple operating scenarios,including Standard Test Conditions(STC),Bifacial Standard Test Conditions(BSTC),Normal Operating Cell Temperature(NOCT),and Bifacial NOCT(BNOCT).The results offer valuable insights into the interplay between optical and thermal phenomena in bifacial systems,informing the design and optimization of more efficient photovoltaic technologies.
基金supported by the National Natural Science Foundation of China(No.42277175)Guangxi Emergency Management Department 2024 Innovation and Technology Research Project,China(No.2024GXYJ006)+2 种基金Hunan Provincial Department of Natural Resources Geological Exploration Project,China(No.2023ZRBSHZ056)The First National Natural Disaster Comprehensive Risk Survey in Hunan Province,China(No.2022-70)Guizhou Provincial Major Scientific and Technological Program,China(No.2023-425).
文摘A method combining finite difference method(FDM)and k-means clustering algorithm which can determine the threshold of rock bridge generation is proposed.Jointed slope models with different joint coalescence coefficients(k)are constructed based on FDM.The rock bridge area was divided through k-means algorithm and the optimal number of clusters was determined by sum of squared errors(SSE)and elbow method.The influence of maximum principal stress and stress change rate as clustering indexes on the clustering results of rock bridges was compared by using Euclidean distance.The results show that using stress change rate as clustering index is more effective.When the joint coalescence coefficient is less than 0.6,there is no significant stress concentration in the middle area of adjacent joints,that is,no generation of rock bridge.In addition,the range of rock bridge is affected by the coalescence coefficient(k),the relative position of joints and the parameters of weak interlayer.
基金supported by the National Natural Science Foundation of China(12201228,12171047)the Fundamental Research Funds for the Central Universities(3034011102)supported by National Key R&D Program of China(2020YFA0713701).
文摘In this work, we first derive the one-point large deviations principle (LDP) for both the stochastic Cahn–Hilliard equation with small noise and its spatial finite difference method (FDM). Then, we focus on giving the convergence of the one-point large deviations rate function (LDRF) of the spatial FDM, which is about the asymptotical limit of a parametric variational problem. The main idea for proving the convergence of the LDRF of the spatial FDM is via the Γ-convergence of objective functions. This relies on the qualitative analysis of skeleton equations of the original equation and the numerical method. In order to overcome the difficulty that the drift coefficient is not one-sided Lipschitz continuous, we derive the equivalent characterization of the skeleton equation of the spatial FDM and the discrete interpolation inequality to obtain the uniform boundedness of the solution to the underlying skeleton equation. These play important roles in deriving the T-convergence of objective functions.
文摘The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are asymptotically convergent. Both methods are considered in continnous time.
