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
This study presents an effective hybrid simulation approach for simulating broadband ground motion in complex near-fault locations.The approach utilizes a deterministic approach based on the spectral element method(SE...This study presents an effective hybrid simulation approach for simulating broadband ground motion in complex near-fault locations.The approach utilizes a deterministic approach based on the spectral element method(SEM),which is used to simulate low-frequency ground motion(f<1 Hz)by incorporating an innovative efficient discontinuous Galerkin(DG)method for grid division to accurately model basin sedimentary layers at reduced costs.It also introduces a comprehensive hybrid source model for high-frequency random scattering and a nonlinear analysis module for basin sedimentary layers.Deterministic outcomes are combined with modified three-dimensional stochastic finite fault method(3D-EXSIM)simulations of high-frequency ground motion(f>1 Hz).A fourth-order Butterworth filter with zero phase shift is employed for time-domain filtering of low-and high-frequency time series at a crossover frequency of 1 Hz,merging the low and high-frequency ground motions into a broadband time series.Taking an Ms 6.8 Luding earthquake,as an example,this hybrid method was used for a rapid and efficient simulation analysis of broadband ground motion in the region.The accuracy and efficiency of this hybrid method were verified through comparisons with actually observed station data and empirical attenuation curves.Deterministic method simulation results revealed the effects of mountainous topography,basin effects,nonlinear effects within the basin’s sedimentary layers,and a coupling interaction between the basin and the mountains.The findings are consistent with similar studies,showing that near-fault sedimentary basins significantly focus and amplify strong ground motion,and the soil’s nonlinear behavior in the basin influences ground motion to varying extents at different distances from the fault.The mountainous topography impacts the basin’s response to ground motion,leading to barrier effects.This research provides a scientific foundation for seismic zoning,urban planning,and seismic design in nearfault mountain basin regions.展开更多
In this paper,a novel method for investigating the particle-crushing behavior of breeding particles in a fusion blanket is proposed.The fractal theory and Weibull distribution are combined to establish a theoretical m...In this paper,a novel method for investigating the particle-crushing behavior of breeding particles in a fusion blanket is proposed.The fractal theory and Weibull distribution are combined to establish a theoretical model,and its validity was verified using a simple impact test.A crushable discrete element method(DEM)framework is built based on the previously established theoretical model.The tensile strength,which considers the fractal theory,size effect,and Weibull variation,was assigned to each generated particle.The assigned strength is then used for crush detection by comparing it with its maximum tensile stress.Mass conservation is ensured by inserting a series of sub-particles whose total mass was equal to the quality loss.Based on the crushable DEM framework,a numerical simulation of the crushing behavior of a pebble bed with hollow cylindrical geometry under a uniaxial compression test was performed.The results of this investigation showed that the particle withstands the external load by contact and sliding at the beginning of the compression process,and the results confirmed that crushing can be considered an important method of resisting the increasing external load.A relatively regular particle arrangement aids in resisting the load and reduces the occurrence of particle crushing.However,a limit exists to the promotion of resistance.When the strain increases beyond this limit,the distribution of the crushing position tends to be isotropic over the entire pebble bed.The theoretical model and crushable DEM framework provide a new method for exploring the pebble bed in a fusion reactor,considering particle crushing.展开更多
A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue prob...A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).展开更多
Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The t...Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The traditional thermal elastic-plastic finite element method(TEP-FEM)can accurately predict welding deformation.However,its efficiency is low because of the complex nonlinear transient computation,making it difficult to meet the needs of rapid engineering evaluation.To address this challenge,this study proposes an efficient prediction method for welding deformation in marine thin plate butt welds.This method is based on the coupled temperature gradient-thermal strain method(TG-TSM)that integrates inherent strain theory with a shell element finite element model.The proposed method first extracts the distribution pattern and characteristic value of welding-induced inherent strain through TEP-FEM analysis.This strain is then converted into the equivalent thermal load applied to the shell element model for rapid computation.The proposed method-particularly,the gradual temperature gradient-thermal strain method(GTG-TSM)-achieved improved computational efficiency and consistent precision.Furthermore,the proposed method required much less computation time than the traditional TEP-FEM.Thus,this study lays the foundation for future prediction of welding deformation in more complex marine thin plates.展开更多
In this work,the Hierarchical Quadrature Element Method(HQEM)formulation of geometrically exact shells is proposed and applied for geometrically nonlinear analyses of both isotropic and laminated shells.The stress res...In this work,the Hierarchical Quadrature Element Method(HQEM)formulation of geometrically exact shells is proposed and applied for geometrically nonlinear analyses of both isotropic and laminated shells.The stress resultant formulation is developed within the HQEM framework,consequently significantly simplifying the computations of residual force and stiffness matrix.The present formulation inherently avoids shear and membrane locking,benefiting from its high-order approximation property.Furthermore,HQEM’s independent nodal distribution capability conveniently supports local p-refinement and flexibly facilitates mesh generation in various structural configurations through the combination of quadrilateral and triangular elements.Remarkably,in lateral buckling analysis,the HQEM outperforms the weak-form quadrilateral element(QEM)in accuracy with identical nodal degrees of freedom(three displacements and two rotations).Under high-load nonlinear response,the QEM exhibits a maximum relative deviation of approximately 9.5%from the reference,while the HQEM remains closely aligned with the benchmark results.In addition,for the cantilever beam under tip moment,HQEM produces virtually no out-of-plane deviation,compared to a slight deviation of 0.00001 with QEM,confirming its superior numerical reliability.In summary,the method demonstrates high accuracy,superior convergence,and robustness in handling large rotations and complex post-buckling behaviors across a series of benchmark problems.展开更多
There are vast constraint equations in conventional dynamics analysis of deployable structures,which lead to differential-algebraic equations(DAEs)solved hard.To reduce the difficulty of solving and the amount of equa...There are vast constraint equations in conventional dynamics analysis of deployable structures,which lead to differential-algebraic equations(DAEs)solved hard.To reduce the difficulty of solving and the amount of equations,a new flexible multibody dynamics analysis methodology of deployable structures with scissor-like elements(SLEs)is presented.Firstly,a precise model of a flexible bar of SLE is established by the higher order shear deformable beam element based on the absolute nodal coordinate formulation(ANCF),and the master/slave freedom method is used to obtain the dynamics equations of SLEs without constraint equations.Secondly,according to features of deployable structures,the specification matrix method(SMM)is proposed to eliminate the constraint equations among SLEs in the frame of ANCF.With this method,the inner and the boundary nodal coordinates of element characteristic matrices can be separated simply and efficiently,especially on condition that there are vast nodal coordinates.So the element characteristic matrices can be added end to end circularly.Thus,the dynamic model of deployable structure reduces dimension and can be assembled without any constraint equation.Next,a new iteration procedure for the generalized-a algorithm is presented to solve the ordinary differential equations(ODEs)of deployable structure.Finally,the proposed methodology is used to analyze the flexible multi-body dynamics of a planar linear array deployable structure based on three scissor-like elements.The simulation results show that flexibility has a significant influence on the deployment motion of the deployable structure.The proposed methodology indeed reduce the difficulty of solving and the amount of equations by eliminating redundant degrees of freedom and the constraint equations in scissor-like elements and among scissor-like elements.展开更多
Heterogeneity is an inherent component of rock and may be present in different forms including mineralheterogeneity, geometrical heterogeneity, weak grain boundaries and micro-defects. Microcracks areusually observed ...Heterogeneity is an inherent component of rock and may be present in different forms including mineralheterogeneity, geometrical heterogeneity, weak grain boundaries and micro-defects. Microcracks areusually observed in crystalline rocks in two forms： natural and stress-induced; the amount of stressinducedmicrocracking increases with depth and in-situ stress. Laboratory results indicate that thephysical properties of rocks such as strength, deformability, P-wave velocity and permeability areinfluenced by increase in microcrack intensity. In this study, the finite-discrete element method （FDEM）is used to model microcrack heterogeneity by introducing into a model sample sets of microcracks usingthe proposed micro discrete fracture network （mDFN） approach. The characteristics of the microcracksrequired to create mDFN models are obtained through image analyses of thin sections of Lac du Bonnetgranite adopted from published literature. A suite of two-dimensional laboratory tests including uniaxial,triaxial compression and Brazilian tests is simulated and the results are compared with laboratory data.The FDEM-mDFN models indicate that micro-heterogeneity has a profound influence on both the mechanicalbehavior and resultant fracture pattern. An increase in the microcrack intensity leads to areduction in the strength of the sample and changes the character of the rock strength envelope. Spallingand axial splitting dominate the failure mode at low confinement while shear failure is the dominantfailure mode at high confinement. Numerical results from simulated compression tests show thatmicrocracking reduces the cohesive component of strength alone, and the frictional strength componentremains unaffected. Results from simulated Brazilian tests show that the tensile strength is influenced bythe presence of microcracks, with a reduction in tensile strength as microcrack intensity increases. Theimportance of microcrack heterogeneity in reproducing a bi-linear or S-shape failure envelope and itseffects on the mechanisms leading to spalling damage near an underground opening are also discussed.展开更多
To overcome the difficulties of re-meshing and tracking the crack-tip in other computational methods for crack propagation simulations,the phase field method based on the minimum energy principle is introduced by defi...To overcome the difficulties of re-meshing and tracking the crack-tip in other computational methods for crack propagation simulations,the phase field method based on the minimum energy principle is introduced by defining a continuous phase field variable(x)∈[0,1]to characterize discontinuous cracks in brittle materials.This method can well describe the crack initiation and propagation without assuming the shape,size and orientation of the initial crack in advance.In this paper,a phase field method based on Miehe's approach[Miehe et al.,Comp.Meth.App.Mech.Eng.(2010)]is applied to simulate different crack propagation problems in twodimensional(2D),isotropic and linear elastic materials.The numerical implementation of the phase field method is realized within the framework of the finite element method(FEM).The validity,accuracy and efficiency of the present method are verified by comparing the numerical results with other reference results in literature.Several numerical examples are presented to show the effects of the loading type(tension and shear),boundary conditions,and initial crack location and orientation on the crack propagation path and force-displacement curve.Furthermore,for a single edge-cracked bi-material specimen,the influences of the loading type and the crack location on the crack propagation trajectory and force-displacement curve are also investigated and discussed.It is demonstrated that the phase field method is an efficient tool for the numerical simulation of the crack propagation problems in brittle elastic materials,and the corresponding results may have an important relevance for predicting and preventing possible crack propagations in engineering applications.展开更多
Recent developments in tunneling have stimulated design practitioners to more effectively utilize the underground spaces.However,tunneling at shallow depth in soft grounds gives rise to concerns associated with tunnel...Recent developments in tunneling have stimulated design practitioners to more effectively utilize the underground spaces.However,tunneling at shallow depth in soft grounds gives rise to concerns associated with tunnel instability.Umbrella arch method(UAM),as a pre-reinforcement approach of tunnels in complex geological conditions,is widely used to maintain the tunnel stability.Quantitative assessment of the impacts of the entire approach and forepoling pipe features on tunnel stability remains challenging due to the complex nature of the UAM application.This study aimed to assess the effect of pipe design parameters on reinforcing the tunnels excavated in soft grounds.This practical investigation considered the actual field conditions attributed to the tunneling procedure and UAM deployment.Then,the tunneling process was modeled and the tunnel excavation-induced settlements were calculated.The post-processed results confirmed that deploying the UAM substantially reduced the tunnel crown and ground surface settlements by 76%and 42%,respectively.Investigation of various design parameters of pipes underscored the significance of incorporating the optimum value for each individual parameter into design schemes to more effectively control the settlements.Additionally,contrasting the settlement reduction rates(SRRs)for pipe design variables showed that the tunnel stability is more sensitive to the changes in the values of diameter and length,compared to values of the installation angle and center-tocenter distance of the pipes.展开更多
As a force-based finite element method (FEM), large increment method (LIM) has been developed in recent years. It has been shown that LIM provided prominent advantage of parallel computation with high efficiency and l...As a force-based finite element method (FEM), large increment method (LIM) has been developed in recent years. It has been shown that LIM provided prominent advantage of parallel computation with high efficiency and low time consumption for member structural system. To fully utilize its advantage in parallel computation, it is the time to extend LIM to 2D and 3D continua analysis. In this paper, a 2D finite element library with the capability of modeling arbitrary configurations is developed. Some illustrative numerical examples are solved by using the proposed library; the obtained results are compared with those obtained from both traditional displacement-based FEM and analytical solutions, which has clearly shown the advantages of LIM.展开更多
An improved analytical method to determine the content of 52 major, minor and trace elements in marine geological samples, using a HF-HCl-HNO_3 acid system with a high-pressure closed digestion method（HPCD）, is stud...An improved analytical method to determine the content of 52 major, minor and trace elements in marine geological samples, using a HF-HCl-HNO_3 acid system with a high-pressure closed digestion method（HPCD）, is studied by an inductively coupled plasma optical emission spectrometry（ICP-OES） and an inductively coupled plasma mass spectrometry（ICP-MS）. The operating parameters of the instruments are optimized, and the optimal analytical parameters are determined. The influences of optical spectrum and mass spectrum interferences, digestion methods and acid systems on the analytical results are investigated. The optimal spectral lines and isotopes are chosen, and internal standard element of rhodium is selected to compensate for matrix effects and analytical signals drifting. Compared with the methods of an electric heating plate digestion and a microwave digestion, a high-pressure closed digestion method is optimized with less acid, complete digestion,less damage for digestion process. The marine geological samples are dissolved completely by a HF-HCl-HNO_3 system, the relative error（RE） for the analytical results are all less than 6.0%. The method detection limits are 2–40μg/g by the ICP-OES, and 6–80 ng/g by ICP-MS. The methods are used to determine the marine sediment reference materials（GBW07309, GBW07311, GBW07313）, rock reference materials（GBW07103, GBW07104,GBW07105）, and cobalt-rich crust reference materials（GBW07337, GBW07338, GBW07339）, the obtained analytical results are in agreement with the certified values, and both of the relative standard deviation（RSD） and the relative error（RE） are less than 6.0%. The analytical method meets the requirements for determining 52 elements contents of bulk marine geological samples.展开更多
The newly proposed element energy projection(EEP) method has been applied to the computation of super_convergent nodal stresses of Timoshenko beam elements.General formulas based on element projection theorem were der...The newly proposed element energy projection(EEP) method has been applied to the computation of super_convergent nodal stresses of Timoshenko beam elements.General formulas based on element projection theorem were derived and illustrative numerical examples using two typical elements were given.Both the analysis and examples show that EEP method also works very well for the problems with vector function solutions.The EEP method gives super_convergent nodal stresses,which are well comparable to the nodal displacements in terms of both convergence rate and error magnitude.And in addition,it can overcome the “shear locking” difficulty for stresses even when the displacements are badly affected.This research paves the way for application of the EEP method to general one_dimensional systems of ordinary differential equations.展开更多
Isoparametric quadrilateral elements are widely used in the finite element method, but the accuracy of the isoparametric quadrilateral elements will drop obviously deteriorate due to mesh distortions. Spline functions...Isoparametric quadrilateral elements are widely used in the finite element method, but the accuracy of the isoparametric quadrilateral elements will drop obviously deteriorate due to mesh distortions. Spline functions have some properties of simplicity and conformality. Two 8-node quadrilateral elements have been developed using the trian- gular area coordinates and the B-net method, which can ex- actly model the quadratic field for both convex and concave quadrangles. Some appropriate examples are employed to evaluate the performance of the proposed elements. The nu- merical results show that the two spline elements can obtain solutions which are highly accurate and insensitive to mesh distortions.展开更多
A unified analysis is presented for the stabilized methods including the pres- sure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements f...A unified analysis is presented for the stabilized methods including the pres- sure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements for the stationary Navier-Stokes equa- tions. The existence and uniqueness of the solution and the optimal error estimates are proved.展开更多
A novel polygonal finite element method （PFEM） based on partition of unity is proposed, termed the virtual node method （VNM）. To test the performance of the present method, numerical examples are given for solid m...A novel polygonal finite element method （PFEM） based on partition of unity is proposed, termed the virtual node method （VNM）. To test the performance of the present method, numerical examples are given for solid mechanics problems. With a polynomial form, the VNM achieves better results than those of traditional PFEMs, including the Wachspress method and the mean value method in standard patch tests. Compared with the standard triangular FEM, the VNM can achieve better accuracy. With the ability to construct shape functions on polygonal elements, the VNM provides greater flexibility in mesh generation. Therefore, several fracture problems are studied to demonstrate the potential implementation. With the advantage of the VNM, the convenient refinement and remeshing strategy are applied.展开更多
The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh disto...The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh distortions. In a previous work, we constructed an 8-node quadrilateral spline element L8 using the triangular area coordinates and the B- net method, which can be insensitive to mesh distortions and possess the second order completeness in the Cartesian co- ordinates. In this paper, a thin plate spline element is devel- oped based on the spline element L8 and the refined tech- nique. Numerical examples show that the present element indeed possesses higher accuracy than the DKQ element for distorted meshes.展开更多
Two-Line Element(TLE)datasets are the only orbital data source of Earth-orbiting space objects for many civil users for their research and applications.The datasets have uneven qualities that may affect the reliabilit...Two-Line Element(TLE)datasets are the only orbital data source of Earth-orbiting space objects for many civil users for their research and applications.The datasets have uneven qualities that may affect the reliability of the propagated positions of space objects using a single TLE.The least squares approach to use multiple TLEs also suffers from the poor quality of some TLEs,and reliable error information cannot be available.This paper proposes a simplex algorithm to estimate an optimal TLE from multiple TLEs and obtain the uncertainty of each element.It is a derivative-free technique that can deal with various orbit types.Experiments have demonstrated that using the TLE estimated from the simplex method is more reliable,stable,and effective than those from the batch least squares method.As an application example,the optimal TLE and its uncertainty are used for predicting the fallen area,keeping the actual fallen site in the prediction areas.展开更多
In this paper, an optimal V-cycle multigrid method for some conforming and nonconforming plate elements are constructed. A new method dealing with nonnested multigrid methods is presented.
In this paper we study the theoretical properties of multigrid algorithm for discretization of the Poisson equation in 2D using a mortar element method under the assumption that the triangulations on every subdomain a...In this paper we study the theoretical properties of multigrid algorithm for discretization of the Poisson equation in 2D using a mortar element method under the assumption that the triangulations on every subdomain are uniform.We prove the convergence of the W-cycle with a sufficiently large number of smoothing steps.The variable V-cycle multigrid preconditioner are also available.展开更多
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National Natural Science Foundation of China under Grant Nos.U2139208 and 52278516Key Laboratory of Earthquake Engineering and Engineering Vibration,China Earthquake Administration under Grant No.2024D15Key Laboratory of Soft Soil Characteristic and Engineering Environment,Tianjin Chengjian University under Grant No.2022SCEEKL003。
文摘This study presents an effective hybrid simulation approach for simulating broadband ground motion in complex near-fault locations.The approach utilizes a deterministic approach based on the spectral element method(SEM),which is used to simulate low-frequency ground motion(f<1 Hz)by incorporating an innovative efficient discontinuous Galerkin(DG)method for grid division to accurately model basin sedimentary layers at reduced costs.It also introduces a comprehensive hybrid source model for high-frequency random scattering and a nonlinear analysis module for basin sedimentary layers.Deterministic outcomes are combined with modified three-dimensional stochastic finite fault method(3D-EXSIM)simulations of high-frequency ground motion(f>1 Hz).A fourth-order Butterworth filter with zero phase shift is employed for time-domain filtering of low-and high-frequency time series at a crossover frequency of 1 Hz,merging the low and high-frequency ground motions into a broadband time series.Taking an Ms 6.8 Luding earthquake,as an example,this hybrid method was used for a rapid and efficient simulation analysis of broadband ground motion in the region.The accuracy and efficiency of this hybrid method were verified through comparisons with actually observed station data and empirical attenuation curves.Deterministic method simulation results revealed the effects of mountainous topography,basin effects,nonlinear effects within the basin’s sedimentary layers,and a coupling interaction between the basin and the mountains.The findings are consistent with similar studies,showing that near-fault sedimentary basins significantly focus and amplify strong ground motion,and the soil’s nonlinear behavior in the basin influences ground motion to varying extents at different distances from the fault.The mountainous topography impacts the basin’s response to ground motion,leading to barrier effects.This research provides a scientific foundation for seismic zoning,urban planning,and seismic design in nearfault mountain basin regions.
基金supported by Anhui Provincial Natural Science Foundation(2408085QA030)Natural Science Research Project of Anhui Educational Committee,China(2022AH050825)+3 种基金Medical Special Cultivation Project of Anhui University of Science and Technology(YZ2023H2C008)the Excellent Research and Innovation Team of Anhui Province,China(2022AH010052)the Scientific Research Foundation for High-level Talents of Anhui University of Science and Technology,China(2021yjrc51)Collaborative Innovation Program of Hefei Science Center,CAS,China(2019HSC-CIP006).
文摘In this paper,a novel method for investigating the particle-crushing behavior of breeding particles in a fusion blanket is proposed.The fractal theory and Weibull distribution are combined to establish a theoretical model,and its validity was verified using a simple impact test.A crushable discrete element method(DEM)framework is built based on the previously established theoretical model.The tensile strength,which considers the fractal theory,size effect,and Weibull variation,was assigned to each generated particle.The assigned strength is then used for crush detection by comparing it with its maximum tensile stress.Mass conservation is ensured by inserting a series of sub-particles whose total mass was equal to the quality loss.Based on the crushable DEM framework,a numerical simulation of the crushing behavior of a pebble bed with hollow cylindrical geometry under a uniaxial compression test was performed.The results of this investigation showed that the particle withstands the external load by contact and sliding at the beginning of the compression process,and the results confirmed that crushing can be considered an important method of resisting the increasing external load.A relatively regular particle arrangement aids in resisting the load and reduces the occurrence of particle crushing.However,a limit exists to the promotion of resistance.When the strain increases beyond this limit,the distribution of the crushing position tends to be isotropic over the entire pebble bed.The theoretical model and crushable DEM framework provide a new method for exploring the pebble bed in a fusion reactor,considering particle crushing.
基金supported by the National Natural Science Foundation of China(12401482)the second author was supported by the National Natural Science Foundation of China(12371371,12261160361,11971366)supported by the Open Research Fund of Hubei Key Laboratory of Computational Science,Wuhan University.
文摘A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).
基金Supported by the National Natural Science Foundation of China under Grant No.51975138the High-Tech Ship Scientific Research Project from the Ministry of Industry and Information Technology under Grant No.CJ05N20the National Defense Basic Research Project under Grant No.JCKY2023604C006.
文摘Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The traditional thermal elastic-plastic finite element method(TEP-FEM)can accurately predict welding deformation.However,its efficiency is low because of the complex nonlinear transient computation,making it difficult to meet the needs of rapid engineering evaluation.To address this challenge,this study proposes an efficient prediction method for welding deformation in marine thin plate butt welds.This method is based on the coupled temperature gradient-thermal strain method(TG-TSM)that integrates inherent strain theory with a shell element finite element model.The proposed method first extracts the distribution pattern and characteristic value of welding-induced inherent strain through TEP-FEM analysis.This strain is then converted into the equivalent thermal load applied to the shell element model for rapid computation.The proposed method-particularly,the gradual temperature gradient-thermal strain method(GTG-TSM)-achieved improved computational efficiency and consistent precision.Furthermore,the proposed method required much less computation time than the traditional TEP-FEM.Thus,this study lays the foundation for future prediction of welding deformation in more complex marine thin plates.
基金supported by the National Natural Science Foundation of China(Grant Nos.12472194,12002018,11972004,11772031,11402015).
文摘In this work,the Hierarchical Quadrature Element Method(HQEM)formulation of geometrically exact shells is proposed and applied for geometrically nonlinear analyses of both isotropic and laminated shells.The stress resultant formulation is developed within the HQEM framework,consequently significantly simplifying the computations of residual force and stiffness matrix.The present formulation inherently avoids shear and membrane locking,benefiting from its high-order approximation property.Furthermore,HQEM’s independent nodal distribution capability conveniently supports local p-refinement and flexibly facilitates mesh generation in various structural configurations through the combination of quadrilateral and triangular elements.Remarkably,in lateral buckling analysis,the HQEM outperforms the weak-form quadrilateral element(QEM)in accuracy with identical nodal degrees of freedom(three displacements and two rotations).Under high-load nonlinear response,the QEM exhibits a maximum relative deviation of approximately 9.5%from the reference,while the HQEM remains closely aligned with the benchmark results.In addition,for the cantilever beam under tip moment,HQEM produces virtually no out-of-plane deviation,compared to a slight deviation of 0.00001 with QEM,confirming its superior numerical reliability.In summary,the method demonstrates high accuracy,superior convergence,and robustness in handling large rotations and complex post-buckling behaviors across a series of benchmark problems.
基金Supported by National Natural Science Foundation of China(Grant No.51175422)
文摘There are vast constraint equations in conventional dynamics analysis of deployable structures,which lead to differential-algebraic equations(DAEs)solved hard.To reduce the difficulty of solving and the amount of equations,a new flexible multibody dynamics analysis methodology of deployable structures with scissor-like elements(SLEs)is presented.Firstly,a precise model of a flexible bar of SLE is established by the higher order shear deformable beam element based on the absolute nodal coordinate formulation(ANCF),and the master/slave freedom method is used to obtain the dynamics equations of SLEs without constraint equations.Secondly,according to features of deployable structures,the specification matrix method(SMM)is proposed to eliminate the constraint equations among SLEs in the frame of ANCF.With this method,the inner and the boundary nodal coordinates of element characteristic matrices can be separated simply and efficiently,especially on condition that there are vast nodal coordinates.So the element characteristic matrices can be added end to end circularly.Thus,the dynamic model of deployable structure reduces dimension and can be assembled without any constraint equation.Next,a new iteration procedure for the generalized-a algorithm is presented to solve the ordinary differential equations(ODEs)of deployable structure.Finally,the proposed methodology is used to analyze the flexible multi-body dynamics of a planar linear array deployable structure based on three scissor-like elements.The simulation results show that flexibility has a significant influence on the deployment motion of the deployable structure.The proposed methodology indeed reduce the difficulty of solving and the amount of equations by eliminating redundant degrees of freedom and the constraint equations in scissor-like elements and among scissor-like elements.
文摘Heterogeneity is an inherent component of rock and may be present in different forms including mineralheterogeneity, geometrical heterogeneity, weak grain boundaries and micro-defects. Microcracks areusually observed in crystalline rocks in two forms： natural and stress-induced; the amount of stressinducedmicrocracking increases with depth and in-situ stress. Laboratory results indicate that thephysical properties of rocks such as strength, deformability, P-wave velocity and permeability areinfluenced by increase in microcrack intensity. In this study, the finite-discrete element method （FDEM）is used to model microcrack heterogeneity by introducing into a model sample sets of microcracks usingthe proposed micro discrete fracture network （mDFN） approach. The characteristics of the microcracksrequired to create mDFN models are obtained through image analyses of thin sections of Lac du Bonnetgranite adopted from published literature. A suite of two-dimensional laboratory tests including uniaxial,triaxial compression and Brazilian tests is simulated and the results are compared with laboratory data.The FDEM-mDFN models indicate that micro-heterogeneity has a profound influence on both the mechanicalbehavior and resultant fracture pattern. An increase in the microcrack intensity leads to areduction in the strength of the sample and changes the character of the rock strength envelope. Spallingand axial splitting dominate the failure mode at low confinement while shear failure is the dominantfailure mode at high confinement. Numerical results from simulated compression tests show thatmicrocracking reduces the cohesive component of strength alone, and the frictional strength componentremains unaffected. Results from simulated Brazilian tests show that the tensile strength is influenced bythe presence of microcracks, with a reduction in tensile strength as microcrack intensity increases. Theimportance of microcrack heterogeneity in reproducing a bi-linear or S-shape failure envelope and itseffects on the mechanisms leading to spalling damage near an underground opening are also discussed.
基金supported by the National Natural Science Foundation of China (Grant U1833116)the financial support by the China Scholarship Council (CSC)
文摘To overcome the difficulties of re-meshing and tracking the crack-tip in other computational methods for crack propagation simulations,the phase field method based on the minimum energy principle is introduced by defining a continuous phase field variable(x)∈[0,1]to characterize discontinuous cracks in brittle materials.This method can well describe the crack initiation and propagation without assuming the shape,size and orientation of the initial crack in advance.In this paper,a phase field method based on Miehe's approach[Miehe et al.,Comp.Meth.App.Mech.Eng.(2010)]is applied to simulate different crack propagation problems in twodimensional(2D),isotropic and linear elastic materials.The numerical implementation of the phase field method is realized within the framework of the finite element method(FEM).The validity,accuracy and efficiency of the present method are verified by comparing the numerical results with other reference results in literature.Several numerical examples are presented to show the effects of the loading type(tension and shear),boundary conditions,and initial crack location and orientation on the crack propagation path and force-displacement curve.Furthermore,for a single edge-cracked bi-material specimen,the influences of the loading type and the crack location on the crack propagation trajectory and force-displacement curve are also investigated and discussed.It is demonstrated that the phase field method is an efficient tool for the numerical simulation of the crack propagation problems in brittle elastic materials,and the corresponding results may have an important relevance for predicting and preventing possible crack propagations in engineering applications.
文摘Recent developments in tunneling have stimulated design practitioners to more effectively utilize the underground spaces.However,tunneling at shallow depth in soft grounds gives rise to concerns associated with tunnel instability.Umbrella arch method(UAM),as a pre-reinforcement approach of tunnels in complex geological conditions,is widely used to maintain the tunnel stability.Quantitative assessment of the impacts of the entire approach and forepoling pipe features on tunnel stability remains challenging due to the complex nature of the UAM application.This study aimed to assess the effect of pipe design parameters on reinforcing the tunnels excavated in soft grounds.This practical investigation considered the actual field conditions attributed to the tunneling procedure and UAM deployment.Then,the tunneling process was modeled and the tunnel excavation-induced settlements were calculated.The post-processed results confirmed that deploying the UAM substantially reduced the tunnel crown and ground surface settlements by 76%and 42%,respectively.Investigation of various design parameters of pipes underscored the significance of incorporating the optimum value for each individual parameter into design schemes to more effectively control the settlements.Additionally,contrasting the settlement reduction rates(SRRs)for pipe design variables showed that the tunnel stability is more sensitive to the changes in the values of diameter and length,compared to values of the installation angle and center-tocenter distance of the pipes.
基金the National Natural Science Foundation of China (No. 10872128)
文摘As a force-based finite element method (FEM), large increment method (LIM) has been developed in recent years. It has been shown that LIM provided prominent advantage of parallel computation with high efficiency and low time consumption for member structural system. To fully utilize its advantage in parallel computation, it is the time to extend LIM to 2D and 3D continua analysis. In this paper, a 2D finite element library with the capability of modeling arbitrary configurations is developed. Some illustrative numerical examples are solved by using the proposed library; the obtained results are compared with those obtained from both traditional displacement-based FEM and analytical solutions, which has clearly shown the advantages of LIM.
基金The China Ocean Mineral Resources Research and Development Association Research Program of the State Oceanic Administration of China under contract No.DY125-13-R-07the National Natural Science Foundation of China under contract Nos 41322036 and 41230960+1 种基金the Shandong Provincial Natural Science Foundation of China under contract No.ZR2014DP009the Special Basic Research Funds for Central Public Research Institutes for The First Institute of Oceanography,State Oceanic Administration of China under contract Nos GY0213G06 and GY02-2012G35
文摘An improved analytical method to determine the content of 52 major, minor and trace elements in marine geological samples, using a HF-HCl-HNO_3 acid system with a high-pressure closed digestion method（HPCD）, is studied by an inductively coupled plasma optical emission spectrometry（ICP-OES） and an inductively coupled plasma mass spectrometry（ICP-MS）. The operating parameters of the instruments are optimized, and the optimal analytical parameters are determined. The influences of optical spectrum and mass spectrum interferences, digestion methods and acid systems on the analytical results are investigated. The optimal spectral lines and isotopes are chosen, and internal standard element of rhodium is selected to compensate for matrix effects and analytical signals drifting. Compared with the methods of an electric heating plate digestion and a microwave digestion, a high-pressure closed digestion method is optimized with less acid, complete digestion,less damage for digestion process. The marine geological samples are dissolved completely by a HF-HCl-HNO_3 system, the relative error（RE） for the analytical results are all less than 6.0%. The method detection limits are 2–40μg/g by the ICP-OES, and 6–80 ng/g by ICP-MS. The methods are used to determine the marine sediment reference materials（GBW07309, GBW07311, GBW07313）, rock reference materials（GBW07103, GBW07104,GBW07105）, and cobalt-rich crust reference materials（GBW07337, GBW07338, GBW07339）, the obtained analytical results are in agreement with the certified values, and both of the relative standard deviation（RSD） and the relative error（RE） are less than 6.0%. The analytical method meets the requirements for determining 52 elements contents of bulk marine geological samples.
文摘The newly proposed element energy projection(EEP) method has been applied to the computation of super_convergent nodal stresses of Timoshenko beam elements.General formulas based on element projection theorem were derived and illustrative numerical examples using two typical elements were given.Both the analysis and examples show that EEP method also works very well for the problems with vector function solutions.The EEP method gives super_convergent nodal stresses,which are well comparable to the nodal displacements in terms of both convergence rate and error magnitude.And in addition,it can overcome the “shear locking” difficulty for stresses even when the displacements are badly affected.This research paves the way for application of the EEP method to general one_dimensional systems of ordinary differential equations.
基金supported by the National Natural Science Foundation of China(11001037,11102037 and 11290143)the Fundamental Research Funds for the Central Universities
文摘Isoparametric quadrilateral elements are widely used in the finite element method, but the accuracy of the isoparametric quadrilateral elements will drop obviously deteriorate due to mesh distortions. Spline functions have some properties of simplicity and conformality. Two 8-node quadrilateral elements have been developed using the trian- gular area coordinates and the B-net method, which can ex- actly model the quadratic field for both convex and concave quadrangles. Some appropriate examples are employed to evaluate the performance of the proposed elements. The nu- merical results show that the two spline elements can obtain solutions which are highly accurate and insensitive to mesh distortions.
基金supported by the National Natural Science Foundation of China(Nos.11271273 and 11271298)
文摘A unified analysis is presented for the stabilized methods including the pres- sure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements for the stationary Navier-Stokes equa- tions. The existence and uniqueness of the solution and the optimal error estimates are proved.
文摘A novel polygonal finite element method （PFEM） based on partition of unity is proposed, termed the virtual node method （VNM）. To test the performance of the present method, numerical examples are given for solid mechanics problems. With a polynomial form, the VNM achieves better results than those of traditional PFEMs, including the Wachspress method and the mean value method in standard patch tests. Compared with the standard triangular FEM, the VNM can achieve better accuracy. With the ability to construct shape functions on polygonal elements, the VNM provides greater flexibility in mesh generation. Therefore, several fracture problems are studied to demonstrate the potential implementation. With the advantage of the VNM, the convenient refinement and remeshing strategy are applied.
基金supported by the National Natural Science Foundation of China(11001037,11102037,11290143)the Fundamental Research Funds for the Central Universities(DUT13LK07)
文摘The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh distortions. In a previous work, we constructed an 8-node quadrilateral spline element L8 using the triangular area coordinates and the B- net method, which can be insensitive to mesh distortions and possess the second order completeness in the Cartesian co- ordinates. In this paper, a thin plate spline element is devel- oped based on the spline element L8 and the refined tech- nique. Numerical examples show that the present element indeed possesses higher accuracy than the DKQ element for distorted meshes.
基金supported by Chongqing Municipal Natural Science Foundation of General Program(CSTB2022NSCQMSX1093)the Science and Technology Research Program of Chongqing Municipal Education Commission(Grant No.KJQN202200701)China Postdoctoral Science Foundation(2021M703487).
文摘Two-Line Element(TLE)datasets are the only orbital data source of Earth-orbiting space objects for many civil users for their research and applications.The datasets have uneven qualities that may affect the reliability of the propagated positions of space objects using a single TLE.The least squares approach to use multiple TLEs also suffers from the poor quality of some TLEs,and reliable error information cannot be available.This paper proposes a simplex algorithm to estimate an optimal TLE from multiple TLEs and obtain the uncertainty of each element.It is a derivative-free technique that can deal with various orbit types.Experiments have demonstrated that using the TLE estimated from the simplex method is more reliable,stable,and effective than those from the batch least squares method.As an application example,the optimal TLE and its uncertainty are used for predicting the fallen area,keeping the actual fallen site in the prediction areas.
基金The rescarch was supported by the Doctoral Point Foundation of chinese Universities and NSF
文摘In this paper, an optimal V-cycle multigrid method for some conforming and nonconforming plate elements are constructed. A new method dealing with nonnested multigrid methods is presented.
基金This research was supported by the National Natural Science Foundation of China under grant 10071015
文摘In this paper we study the theoretical properties of multigrid algorithm for discretization of the Poisson equation in 2D using a mortar element method under the assumption that the triangulations on every subdomain are uniform.We prove the convergence of the W-cycle with a sufficiently large number of smoothing steps.The variable V-cycle multigrid preconditioner are also available.
