Meshfree method offers high accuracy and computational capability and constructs the shape function without relying on predefined elements. We comparatively analyze the global weak form meshfree methods, such as eleme...Meshfree method offers high accuracy and computational capability and constructs the shape function without relying on predefined elements. We comparatively analyze the global weak form meshfree methods, such as element-free Galerkin method （EFGM）, the point interpolation method （PIM）, and the radial point interpolation method （RPIM）. Taking two dimensional Poisson equation as an example, we discuss the support-domain dimensionless size, the field nodes, and background element settings with respect to their effect on calculation accuracy of the meshfree method. RPIM and EFGM are applied to controlled- source two-dimensional electromagnetic modeling with fixed shape parameters. The accuracy of boundary conditions imposed directly and by a penalty function are discussed in the case of forward modeling of two-dimensional magnetotellurics in a homogeneous medium model. The coupling algorithm of EFG-PIM and EFG-RPIM are generated by integrating the PIM or RPIM and EFGM. The results of the numerical modeling suggest the following. First, the proposed meshfree method and corresponding coupled methods are well-suited for electromagnetic numerical modeling. The accuracy of the algorithm is the highest when the support-domain dimensionless size is 1.0 and the distribution of field nodes is consistent with the nodes of background elements. Second, the accuracy of PIM and RPIM are lower than that of EFGM for the Poisson equation but higher than EFGM for the homogeneous medium MT response. Third, RPIM overcomes the matrix inversion problem of PIM and has a wider selection of support-domain dimensionless sizes as compared to RPIM.展开更多
In this paper,a radial basis function method combined with the stochastic Galerkin method is considered to approximate elliptic optimal control problem with random coefficients.This radial basis function method is a m...In this paper,a radial basis function method combined with the stochastic Galerkin method is considered to approximate elliptic optimal control problem with random coefficients.This radial basis function method is a meshfree approach for solving high dimensional random problem.Firstly,the optimality system of the model problem is derived and represented as a set of deterministic equations in high-dimensional parameter space by finite-dimensional noise assumption.Secondly,the approximation scheme is established by using finite element method for the physical space,and compactly supported radial basis functions for the parameter space.The radial basis functions lead to the sparsity of the stiff matrix with lower condition number.A residual type a posteriori error estimates with lower and upper bounds are derived for the state,co-state and control variables.An adaptive algorithm is developed to deal with the physical and parameter space,respectively.Numerical examples are presented to illustrate the theoretical results.展开更多
An improved meshfree moving-Kriging(MK)formulation for free vibration analysis of functionally graded material-functionally graded carbon nanotube-reinforced composite(FGM-FGCNTRC)sandwich shells is first proposed in ...An improved meshfree moving-Kriging(MK)formulation for free vibration analysis of functionally graded material-functionally graded carbon nanotube-reinforced composite(FGM-FGCNTRC)sandwich shells is first proposed in this article.The proposed sandwich structure consists of skins of FGM layers and an FGCNTRC core.This structure possesses all the advantages of FGM and FGCNTRC,including high electrical or thermal insulating properties,high fatigue resistance,good corrosion resistance,high stiffness,low density,high strength,and high aspect ratios.Such sandwich structures can be used to replace conventional FGM structures.The present formulation has been established by using an improved meshfree MK method and the first-order shear deformation shell theory(FSDT).The effective material characteristics of the FGM-skin layers and the FGCNTRC core were calculated using the rule of mixture.Key parameters and factors such as the thickness-to-radius ratio,the length-to-radius ratio,layer-thickness ratios,CNT distributions,the volume fraction of CNTs,the power-law index,and various boundary conditions were rigorously investigated.A nonlinear CNT distribution that we term FG-nX is first proposed in this work,and many new results of FGM-FGCNTRC sandwich shells have been provided.展开更多
Standard finite element approaches are still ineffective in handling extreme material deformation, such as cases of large deformations and moving discontinuities due to severe mesh distortion. Among meshfree methods d...Standard finite element approaches are still ineffective in handling extreme material deformation, such as cases of large deformations and moving discontinuities due to severe mesh distortion. Among meshfree methods developed to overcome the ineffectiveness, Reproducing Kernel Particle Method (RKPM) has demonstrated its great suitability for structural analysis.This paper presents applications of RKPM in elasto-plastic problems after a review of meshfree methods and an introduction to RKPM. A slope stability problem in geotechnical engineering is analyzed as an illustrative case. The corresponding numerical simulations are carried out on an SGI Onyx3900 supercomputer. Comparison of the RKPM and the FEM under identical conditions showed that the RKPM is more suitable for problems where there exists extremely large strain such as in the case of slope sliding.展开更多
We prove convergence for a meshfree first-order system least squares(FOSLS) partition of unity finite element method(PUFEM).Essentially,by virtue of the partition of unity,local approximation gives rise to global appr...We prove convergence for a meshfree first-order system least squares(FOSLS) partition of unity finite element method(PUFEM).Essentially,by virtue of the partition of unity,local approximation gives rise to global approximation in H(div)∩H(curl). The FOSLS formulation yields local a posteriori error estimates to guide the judicious allotment of new degrees of freedom to enrich the initial point set in a meshfree dis- cretization.Preliminary numerical results are provided and remaining challenges are discussed.展开更多
A size-dependent computational approach for bending,free vibration and buckling analyses of isotropic and sandwich functionally graded(FG)microplates is in this study presented.We consider both shear deformation and s...A size-dependent computational approach for bending,free vibration and buckling analyses of isotropic and sandwich functionally graded(FG)microplates is in this study presented.We consider both shear deformation and small scale effects through the generalized higher order shear deformation theory and modified couple stress theory(MCST).The present model only retains a single material length scale parameter for capturing properly size effects.A rule of mixture is used to model material properties varying through the thickness of plates.The principle of virtual work is used to derive the discrete system equations which are approximated by moving Kriging interpolation(MKI)meshfree method.Numerical examples consider the inclusions of geometrical parameters,volume fraction,boundary conditions and material length scale parameter.Reliability and effectiveness of the present method are confirmed through numerical results.展开更多
The collective cell migration behavior on a substrate was studied using RKPM meshfree method.The cells were modeled as nematic liquid crystal with hyperelastic cell nucleus.The cell-substrate and cell-cell interaction...The collective cell migration behavior on a substrate was studied using RKPM meshfree method.The cells were modeled as nematic liquid crystal with hyperelastic cell nucleus.The cell-substrate and cell-cell interactions were modeled by coarse-grained potential forces.Through this study,the pulling and pushing phenomenon during collective cell migration process was observed and it was found that the individual cell mobility significantly influenced the collective cell migratory behavior.More self-propelled cells are in the system along the same direction,the faster the collective group migrates toward coordinated direction.The parametric study on cell-cell adhesion strength indicated that as the adhesion strength increases,the collective cell migration speed increases.It also showed that the mechanical stress in leader cell is higher than stress in follower cells.展开更多
Condensation technique of degree of freedom is first proposed to improve the computational efficiency of meshfree method with Galerkin weak form for elastic dy- namic analysis. In the present method, scattered nodes w...Condensation technique of degree of freedom is first proposed to improve the computational efficiency of meshfree method with Galerkin weak form for elastic dy- namic analysis. In the present method, scattered nodes with- out connectivity are divided into several subsets by cells with arbitrary shape. Local discrete equation is established over each cell by using moving Kriging interpolation, in which the nodes that located in the cell are used for approxima- tion. Then local discrete equations can be simplified by con- densation of degree of freedom, which transfers equations of inner nodes to equations of boundary nodes based on cells. The global dynamic system equations are obtained by as- sembling all local discrete equations and are solved by using the standard implicit Newmark＇s time integration scheme. In the scheme of present method, the calculation of each cell is carried out by meshfree method, and local search is imple- mented in interpolation. Numerical examples show that the present method has high computational efficiency and good accuracy in solving elastic dynamic problems.展开更多
This paper proposes a geometrically nonlinear total Lagrangian Galerkin meshfree formulation based on the stabilized conforming nodal integration for efficient analysis of shear deformable beam.The present nonlinear a...This paper proposes a geometrically nonlinear total Lagrangian Galerkin meshfree formulation based on the stabilized conforming nodal integration for efficient analysis of shear deformable beam.The present nonlinear analysis encompasses the fully geometric nonlinearities due to large deflection,large deformation as well as finite rotation.The incremental equilibrium equation is obtained by the consistent linearization of the nonlinear variational equation.The Lagrangian meshfree shape function is utilized to discretize the variational equation.Subsequently to resolve the shear and membrane locking issues and accelerate the computation,the method of stabilized conforming nodal integration is systematically implemented through the Lagrangian gradient smoothing operation.Numerical results reveal that the present formulation is very effective.展开更多
Seawater intrusion caused by groundwater over-exploitation from coastal aquifers poses a severe problem in many regions. Formulation of proper pumping strategy using a simulation model can assure sustainable supply of...Seawater intrusion caused by groundwater over-exploitation from coastal aquifers poses a severe problem in many regions. Formulation of proper pumping strategy using a simulation model can assure sustainable supply of fresh water from the coastal aquifers. The focus of the present study is on the development of a numerical model based on Meshfree (MFree) method to study the seawater intrusion problem. For the simulation of seawater intrusion problem, widely used models are based on Finite Difference (FDM) and Finite Element (FEM) Methods, which demand well defined grids/meshes and considerable pre-processing efforts. Here, MFree Point Collocation Method (PCM) based on the Radial Basis Function (RBF) is proposed for the simulation. Diffusive interface approach with density-dependent dispersion and solution of flow and solute transport is adopted. These equations are solved using PCM with appropriate boundary conditions. The developed model has been verified with Henry’s problem, and found to be satisfactory. Further the model has been applied to another established problem and an attempt is made to examine the influence of important system parameters including pumping and recharge on the seawater intrusion. The PCM based MFree model is found computationally efficient as preprocessing is avoided when compared to other numerical methods.展开更多
A meshfree method based on reproducing kernel approximation and point collocation is presented for analysis of metal ring compression. The point collocation method is a true meshfree method without the employment of a...A meshfree method based on reproducing kernel approximation and point collocation is presented for analysis of metal ring compression. The point collocation method is a true meshfree method without the employment of a background mesh. It is shown that, in a point collocation approach, the remesh problem because of the mesh distortion in FEM （finite element method） and the low efficiency in Galerkin-based meshfree method are avoided. The corrected kernel functions are introduced to the stabilization of free-surface boundary conditions. The solution of symmetric ring compression problem is compared with a conventional finite element solution, and reasonable results have been obtained.展开更多
Recently,the radial point interpolation meshfree method has gained popularity owing to its advantages in large deformation and discontinuity problems,however,the accuracy of this method depends on many factors and the...Recently,the radial point interpolation meshfree method has gained popularity owing to its advantages in large deformation and discontinuity problems,however,the accuracy of this method depends on many factors and their influences are not fully investigated yet.In this work,three main factors,i.e.,the shape parameters,the influence domain size,and the nodal distribution,on the accuracy of the radial point interpolation method(RPIM)are systematically studied and conclusive results are obtained.First,the effect of shape parameters(R,q)of the multi-quadric basis function on the accuracy of RPIM is examined via global search.A new interpolation error index,closely related to the accuracy of RPIM,is proposed.The distribution of various error indexes on the R q plane shows that shape parameters q[1.2,1.8]and R[0,1.5]can give good results for general 3-D analysis.This recommended range of shape parameters is examined by multiple benchmark examples in 3D solid mechanics.Second,through numerical experiments,an average of 30 40 nodes in the influence domain of a Gauss point is recommended for 3-D solid mechanics.Third,it is observed that the distribution of nodes has significant effect on the accuracy of RPIM although it has little effect on the accuracy of interpolation.Nodal distributions with better uniformity give better results.Furthermore,how the influence domain size and nodal distribution affect the selection of shape parameters and how the nodal distribution affects the choice of influence domain size are also discussed.展开更多
By introducing the radial basis functions(RBFs)into the reproducing kernel particle method(RKPM),the calculating accuracy and stability of the RKPM can be improved,and a novel meshfree method of the radial basis RKPM(...By introducing the radial basis functions(RBFs)into the reproducing kernel particle method(RKPM),the calculating accuracy and stability of the RKPM can be improved,and a novel meshfree method of the radial basis RKPM(meshfree RRKPM)is proposed.Meanwhile,the meshfree RRKPM is applied to transient heat conduction problems(THCP),and the corresponding equations of the meshfree RRKPM for the THCP are derived.The twopoint time difference scheme is selected to discretize the time of the THCP.Finally,the numerical results illustrate the effectiveness of the meshfree RRKPM for the THCP.展开更多
The independent continuous mapping（ICM） method is integrated into element free Galerkin method and a new implementation of topology optimization for continuum structure is presented.To facilitate the enforcement of ...The independent continuous mapping（ICM） method is integrated into element free Galerkin method and a new implementation of topology optimization for continuum structure is presented.To facilitate the enforcement of the essential boundary condition and derivative of various sensitivities,a singular weight function in element free Galerkin method is introduced.Material point variable is defined to illustrate the condition of material point and its vicinity instead of element or node.The topological variables field is constructed by moving least square approximation which inherits the continuity and smoothness of the weight function.Due to reciprocal relationships between the topological variables and design variables,various structural responses sensitivities are derived according to the method for calculating the partial derivatives of compound functions.Numerical examples indicate that checkerboard pattern and mesh-dependence phenomena are overcome without additional restriction methods.展开更多
This study adapts the flexible characteristic of meshfree method in analyzing three-dimensional(3D)complex geometry structures,which are the interlocking concrete blocks of step seawall.The elastostatic behavior of th...This study adapts the flexible characteristic of meshfree method in analyzing three-dimensional(3D)complex geometry structures,which are the interlocking concrete blocks of step seawall.The elastostatic behavior of the block is analysed by solving the Galerkin weak form formulation over local support domain.The 3D moving least square(MLS)approximation is applied to build the interpolation functions of unknowns.The pre-defined number of nodes in an integration domain ranging from 10 to 60 nodes is also investigated for their effect on the studied results.The accuracy and efficiency of the studied method on 3D elastostatic responses are validated through the comparison with the solutions of standard finite element method(FEM)using linear shape functions on tetrahedral elements and the well-known commercial software,ANSYS.The results show that elastostatic responses of studied concrete block obtained by meshfree method converge faster and are more accurate than those of standard FEM.The studied meshfree method is effective in the analysis of static responses of complex geometry structures.The amount of discretised nodes within the integration domain used in building MLS shape functions should be in the range from 30 to 60 nodes and should not be less than 20 nodes.展开更多
In this paper,we investigate a stochastic meshfree finite volume element method for an optimal control problem governed by the convection diffusion equations with random coefficients.There are two contributions of thi...In this paper,we investigate a stochastic meshfree finite volume element method for an optimal control problem governed by the convection diffusion equations with random coefficients.There are two contributions of this paper.Firstly,we establish a scheme to approximate the optimality system by using the finite volume element method in the physical space and the meshfree method in the probability space,which is competitive for high-dimensional random inputs.Secondly,the a priori error estimates are derived for the state,the co-state and the control variables.Some numerical tests are carried out to confirm the theoretical results and demonstrate the efficiency of the proposed method.展开更多
In this work, we further extended the face-based smoothed finite element method （FS-FEM） for modal analysis of three-dimensional solids using four-node tetrahedron elements. The FS-FEM is formulated based on the smo...In this work, we further extended the face-based smoothed finite element method （FS-FEM） for modal analysis of three-dimensional solids using four-node tetrahedron elements. The FS-FEM is formulated based on the smoothed Calerkin weak form which employs smoothed strains obtained using the gradient smoothing operation on face-based smoothing domains. This strain smoothing operation can provide softening effect to the system stiffness and make the FSFEM provide more accurate eigenfrequency prediction than the FEM does. Numerical studies have verified this attractive property of FS-FEM as well as its ability and effectiveness on providing reliable eigenfrequency and eigenmode prediction in practical engineering application.展开更多
An h-adaptivity analysis scheme based on multiple scale reproducing kernel particle method was proposed, and two node refinement strategies were constructed using searching-neighbor-nodes（SNN） and local-Delaunay-tri...An h-adaptivity analysis scheme based on multiple scale reproducing kernel particle method was proposed, and two node refinement strategies were constructed using searching-neighbor-nodes（SNN） and local-Delaunay-triangulation（LDT） techniques, which were suitable and effective for h-adaptivity analysis on 2-D problems with the regular or irregular distribution of the nodes. The results of multiresolution and h- adaptivity analyses on 2-D linear elastostatics and bending plate problems demonstrate that the improper high-gradient indicator will reduce the convergence property of the h- adaptivity analysis, and that the efficiency of the LDT node refinement strategy is better than SNN, and that the presented h-adaptivity analysis scheme is provided with the validity, stability and good convergence property.展开更多
In this paper, a meshfree boundary integral equation （BIE） method, called the moving Kriging interpolation- based boundary node method （MKIBNM）, is developed for solving two-dimensional potential problems. This st...In this paper, a meshfree boundary integral equation （BIE） method, called the moving Kriging interpolation- based boundary node method （MKIBNM）, is developed for solving two-dimensional potential problems. This study combines the DIE method with the moving Kriging interpolation to present a boundary-type meshfree method, and the corresponding formulae of the MKIBNM are derived. In the present method, the moving Kriging interpolation is applied instead of the traditional moving least-square approximation to overcome Kronecker＇s delta property, then the boundary conditions can be imposed directly and easily. To verify the accuracy and stability of the present formulation, three selected numerical examples are presented to demonstrate the efficiency of MKIBNM numerically.展开更多
We proposed a mesh-free method, the called node-based smoothed point interpolation method(NS-PIM),for dynamic analysis of rotating beams. A gradient smoothing technique is used, and the requirements on the consistence...We proposed a mesh-free method, the called node-based smoothed point interpolation method(NS-PIM),for dynamic analysis of rotating beams. A gradient smoothing technique is used, and the requirements on the consistence of the displacement functions are further weakened. In static problems, the beams with three types of boundary conditions are analyzed, and the results are compared with the exact solution, which shows the effectiveness of this method and can provide an upper bound solution for the deflection.This means that the NS-PIM makes the system soften. The NS-PIM is then further extended for solving a rigid-flexible coupled system dynamics problem, considering a rotating flexible cantilever beam. In this case, the rotating flexible cantilever beam considers not only the transverse deformations,but also the longitudinal deformations. The rigid-flexible coupled dynamic equations of the system are derived via employing Lagrange’s equations of the second type. Simulation results of the NS-PIM are compared with those obtained using finite element method(FEM) and assumed mode method. It is found that compared with FEM, the NS-PIM has anti-ill solving ability under the same calculation conditions.展开更多
基金supported by the National Nature Science Foundation of China(Grant No.40874055)the Natural Science Foundation of the Hunan Province,China(Grant No.14JJ2012)
文摘Meshfree method offers high accuracy and computational capability and constructs the shape function without relying on predefined elements. We comparatively analyze the global weak form meshfree methods, such as element-free Galerkin method （EFGM）, the point interpolation method （PIM）, and the radial point interpolation method （RPIM）. Taking two dimensional Poisson equation as an example, we discuss the support-domain dimensionless size, the field nodes, and background element settings with respect to their effect on calculation accuracy of the meshfree method. RPIM and EFGM are applied to controlled- source two-dimensional electromagnetic modeling with fixed shape parameters. The accuracy of boundary conditions imposed directly and by a penalty function are discussed in the case of forward modeling of two-dimensional magnetotellurics in a homogeneous medium model. The coupling algorithm of EFG-PIM and EFG-RPIM are generated by integrating the PIM or RPIM and EFGM. The results of the numerical modeling suggest the following. First, the proposed meshfree method and corresponding coupled methods are well-suited for electromagnetic numerical modeling. The accuracy of the algorithm is the highest when the support-domain dimensionless size is 1.0 and the distribution of field nodes is consistent with the nodes of background elements. Second, the accuracy of PIM and RPIM are lower than that of EFGM for the Poisson equation but higher than EFGM for the homogeneous medium MT response. Third, RPIM overcomes the matrix inversion problem of PIM and has a wider selection of support-domain dimensionless sizes as compared to RPIM.
基金supported by the National Natural Science Foundation of China(Grant Nos.11701253,11871312,12171042,11971259)by the Higher Education Key Platform and Research Project of Guangdong Province(The Key Project on the New Generation of Information Technology,No.2020zdzx3067)by the Natural Science Foundation of Shandong Province,China(Grant Nos.ZR2018MA007,ZR2023MA086,ZR2022MA005).
文摘In this paper,a radial basis function method combined with the stochastic Galerkin method is considered to approximate elliptic optimal control problem with random coefficients.This radial basis function method is a meshfree approach for solving high dimensional random problem.Firstly,the optimality system of the model problem is derived and represented as a set of deterministic equations in high-dimensional parameter space by finite-dimensional noise assumption.Secondly,the approximation scheme is established by using finite element method for the physical space,and compactly supported radial basis functions for the parameter space.The radial basis functions lead to the sparsity of the stiff matrix with lower condition number.A residual type a posteriori error estimates with lower and upper bounds are derived for the state,co-state and control variables.An adaptive algorithm is developed to deal with the physical and parameter space,respectively.Numerical examples are presented to illustrate the theoretical results.
文摘An improved meshfree moving-Kriging(MK)formulation for free vibration analysis of functionally graded material-functionally graded carbon nanotube-reinforced composite(FGM-FGCNTRC)sandwich shells is first proposed in this article.The proposed sandwich structure consists of skins of FGM layers and an FGCNTRC core.This structure possesses all the advantages of FGM and FGCNTRC,including high electrical or thermal insulating properties,high fatigue resistance,good corrosion resistance,high stiffness,low density,high strength,and high aspect ratios.Such sandwich structures can be used to replace conventional FGM structures.The present formulation has been established by using an improved meshfree MK method and the first-order shear deformation shell theory(FSDT).The effective material characteristics of the FGM-skin layers and the FGCNTRC core were calculated using the rule of mixture.Key parameters and factors such as the thickness-to-radius ratio,the length-to-radius ratio,layer-thickness ratios,CNT distributions,the volume fraction of CNTs,the power-law index,and various boundary conditions were rigorously investigated.A nonlinear CNT distribution that we term FG-nX is first proposed in this work,and many new results of FGM-FGCNTRC sandwich shells have been provided.
文摘Standard finite element approaches are still ineffective in handling extreme material deformation, such as cases of large deformations and moving discontinuities due to severe mesh distortion. Among meshfree methods developed to overcome the ineffectiveness, Reproducing Kernel Particle Method (RKPM) has demonstrated its great suitability for structural analysis.This paper presents applications of RKPM in elasto-plastic problems after a review of meshfree methods and an introduction to RKPM. A slope stability problem in geotechnical engineering is analyzed as an illustrative case. The corresponding numerical simulations are carried out on an SGI Onyx3900 supercomputer. Comparison of the RKPM and the FEM under identical conditions showed that the RKPM is more suitable for problems where there exists extremely large strain such as in the case of slope sliding.
文摘We prove convergence for a meshfree first-order system least squares(FOSLS) partition of unity finite element method(PUFEM).Essentially,by virtue of the partition of unity,local approximation gives rise to global approximation in H(div)∩H(curl). The FOSLS formulation yields local a posteriori error estimates to guide the judicious allotment of new degrees of freedom to enrich the initial point set in a meshfree dis- cretization.Preliminary numerical results are provided and remaining challenges are discussed.
文摘A size-dependent computational approach for bending,free vibration and buckling analyses of isotropic and sandwich functionally graded(FG)microplates is in this study presented.We consider both shear deformation and small scale effects through the generalized higher order shear deformation theory and modified couple stress theory(MCST).The present model only retains a single material length scale parameter for capturing properly size effects.A rule of mixture is used to model material properties varying through the thickness of plates.The principle of virtual work is used to derive the discrete system equations which are approximated by moving Kriging interpolation(MKI)meshfree method.Numerical examples consider the inclusions of geometrical parameters,volume fraction,boundary conditions and material length scale parameter.Reliability and effectiveness of the present method are confirmed through numerical results.
基金This work is supported by a grant from National Institutes of Health(Grant No.SC2GM112575)a grant from the John L.Santikos Charitable Foundation of the San Antonio Area Foundation.
文摘The collective cell migration behavior on a substrate was studied using RKPM meshfree method.The cells were modeled as nematic liquid crystal with hyperelastic cell nucleus.The cell-substrate and cell-cell interactions were modeled by coarse-grained potential forces.Through this study,the pulling and pushing phenomenon during collective cell migration process was observed and it was found that the individual cell mobility significantly influenced the collective cell migratory behavior.More self-propelled cells are in the system along the same direction,the faster the collective group migrates toward coordinated direction.The parametric study on cell-cell adhesion strength indicated that as the adhesion strength increases,the collective cell migration speed increases.It also showed that the mechanical stress in leader cell is higher than stress in follower cells.
基金supported by the National Natural Science Founda-tion of China(11272118)Open Found of State Key Laboratory of Explosion Science and Technology(KFJJ12-5M)
文摘Condensation technique of degree of freedom is first proposed to improve the computational efficiency of meshfree method with Galerkin weak form for elastic dy- namic analysis. In the present method, scattered nodes with- out connectivity are divided into several subsets by cells with arbitrary shape. Local discrete equation is established over each cell by using moving Kriging interpolation, in which the nodes that located in the cell are used for approxima- tion. Then local discrete equations can be simplified by con- densation of degree of freedom, which transfers equations of inner nodes to equations of boundary nodes based on cells. The global dynamic system equations are obtained by as- sembling all local discrete equations and are solved by using the standard implicit Newmark＇s time integration scheme. In the scheme of present method, the calculation of each cell is carried out by meshfree method, and local search is imple- mented in interpolation. Numerical examples show that the present method has high computational efficiency and good accuracy in solving elastic dynamic problems.
基金supported by the National Natural Science Foundation of China (10972188)the Program for New Century Excellent Talents in University from China Education Ministry (NCET-09-0678)
文摘This paper proposes a geometrically nonlinear total Lagrangian Galerkin meshfree formulation based on the stabilized conforming nodal integration for efficient analysis of shear deformable beam.The present nonlinear analysis encompasses the fully geometric nonlinearities due to large deflection,large deformation as well as finite rotation.The incremental equilibrium equation is obtained by the consistent linearization of the nonlinear variational equation.The Lagrangian meshfree shape function is utilized to discretize the variational equation.Subsequently to resolve the shear and membrane locking issues and accelerate the computation,the method of stabilized conforming nodal integration is systematically implemented through the Lagrangian gradient smoothing operation.Numerical results reveal that the present formulation is very effective.
文摘Seawater intrusion caused by groundwater over-exploitation from coastal aquifers poses a severe problem in many regions. Formulation of proper pumping strategy using a simulation model can assure sustainable supply of fresh water from the coastal aquifers. The focus of the present study is on the development of a numerical model based on Meshfree (MFree) method to study the seawater intrusion problem. For the simulation of seawater intrusion problem, widely used models are based on Finite Difference (FDM) and Finite Element (FEM) Methods, which demand well defined grids/meshes and considerable pre-processing efforts. Here, MFree Point Collocation Method (PCM) based on the Radial Basis Function (RBF) is proposed for the simulation. Diffusive interface approach with density-dependent dispersion and solution of flow and solute transport is adopted. These equations are solved using PCM with appropriate boundary conditions. The developed model has been verified with Henry’s problem, and found to be satisfactory. Further the model has been applied to another established problem and an attempt is made to examine the influence of important system parameters including pumping and recharge on the seawater intrusion. The PCM based MFree model is found computationally efficient as preprocessing is avoided when compared to other numerical methods.
基金the National Natural Science Foundation of China （No. 50275059）.
文摘A meshfree method based on reproducing kernel approximation and point collocation is presented for analysis of metal ring compression. The point collocation method is a true meshfree method without the employment of a background mesh. It is shown that, in a point collocation approach, the remesh problem because of the mesh distortion in FEM （finite element method） and the low efficiency in Galerkin-based meshfree method are avoided. The corrected kernel functions are introduced to the stabilization of free-surface boundary conditions. The solution of symmetric ring compression problem is compared with a conventional finite element solution, and reasonable results have been obtained.
基金Project(2010CB732103)supported by the National Basic Research Program of ChinaProject(51179092)supported by the National Natural Science Foundation of ChinaProject(2012-KY-02)supported by the State Key Laboratory of Hydroscience and Engineering,China
文摘Recently,the radial point interpolation meshfree method has gained popularity owing to its advantages in large deformation and discontinuity problems,however,the accuracy of this method depends on many factors and their influences are not fully investigated yet.In this work,three main factors,i.e.,the shape parameters,the influence domain size,and the nodal distribution,on the accuracy of the radial point interpolation method(RPIM)are systematically studied and conclusive results are obtained.First,the effect of shape parameters(R,q)of the multi-quadric basis function on the accuracy of RPIM is examined via global search.A new interpolation error index,closely related to the accuracy of RPIM,is proposed.The distribution of various error indexes on the R q plane shows that shape parameters q[1.2,1.8]and R[0,1.5]can give good results for general 3-D analysis.This recommended range of shape parameters is examined by multiple benchmark examples in 3D solid mechanics.Second,through numerical experiments,an average of 30 40 nodes in the influence domain of a Gauss point is recommended for 3-D solid mechanics.Third,it is observed that the distribution of nodes has significant effect on the accuracy of RPIM although it has little effect on the accuracy of interpolation.Nodal distributions with better uniformity give better results.Furthermore,how the influence domain size and nodal distribution affect the selection of shape parameters and how the nodal distribution affects the choice of influence domain size are also discussed.
基金supported by the Natural Science Foundation of Shandong Province(Grant No.ZR2017MA028)supported by the Natural Science Foundation of Shandong Province(Grant No.ZR2020MA059).
文摘By introducing the radial basis functions(RBFs)into the reproducing kernel particle method(RKPM),the calculating accuracy and stability of the RKPM can be improved,and a novel meshfree method of the radial basis RKPM(meshfree RRKPM)is proposed.Meanwhile,the meshfree RRKPM is applied to transient heat conduction problems(THCP),and the corresponding equations of the meshfree RRKPM for the THCP are derived.The twopoint time difference scheme is selected to discretize the time of the THCP.Finally,the numerical results illustrate the effectiveness of the meshfree RRKPM for the THCP.
基金Sponsored by the Ministerial Level Advanced Research Foundation (010896367)
文摘The independent continuous mapping（ICM） method is integrated into element free Galerkin method and a new implementation of topology optimization for continuum structure is presented.To facilitate the enforcement of the essential boundary condition and derivative of various sensitivities,a singular weight function in element free Galerkin method is introduced.Material point variable is defined to illustrate the condition of material point and its vicinity instead of element or node.The topological variables field is constructed by moving least square approximation which inherits the continuity and smoothness of the weight function.Due to reciprocal relationships between the topological variables and design variables,various structural responses sensitivities are derived according to the method for calculating the partial derivatives of compound functions.Numerical examples indicate that checkerboard pattern and mesh-dependence phenomena are overcome without additional restriction methods.
基金the VLIR-UOS TEAM Project,VN2017TEA454A103,‘An innovative solution to protect Vietnamese coastal riverbanks from floods and erosion’,funded by the Flemish Government.https://www.vliruos.be/en/projects/project/22?pid=3251.
文摘This study adapts the flexible characteristic of meshfree method in analyzing three-dimensional(3D)complex geometry structures,which are the interlocking concrete blocks of step seawall.The elastostatic behavior of the block is analysed by solving the Galerkin weak form formulation over local support domain.The 3D moving least square(MLS)approximation is applied to build the interpolation functions of unknowns.The pre-defined number of nodes in an integration domain ranging from 10 to 60 nodes is also investigated for their effect on the studied results.The accuracy and efficiency of the studied method on 3D elastostatic responses are validated through the comparison with the solutions of standard finite element method(FEM)using linear shape functions on tetrahedral elements and the well-known commercial software,ANSYS.The results show that elastostatic responses of studied concrete block obtained by meshfree method converge faster and are more accurate than those of standard FEM.The studied meshfree method is effective in the analysis of static responses of complex geometry structures.The amount of discretised nodes within the integration domain used in building MLS shape functions should be in the range from 30 to 60 nodes and should not be less than 20 nodes.
基金supported by the National Natural Science Foundation of China(Nos.11701253,11971259,11801216)Natural Science Foundation of Shandong Province(No.ZR2017BA010)。
文摘In this paper,we investigate a stochastic meshfree finite volume element method for an optimal control problem governed by the convection diffusion equations with random coefficients.There are two contributions of this paper.Firstly,we establish a scheme to approximate the optimality system by using the finite volume element method in the physical space and the meshfree method in the probability space,which is competitive for high-dimensional random inputs.Secondly,the a priori error estimates are derived for the state,the co-state and the control variables.Some numerical tests are carried out to confirm the theoretical results and demonstrate the efficiency of the proposed method.
基金Project supported by the National Project 973 (No. 2010CB328005)the National Natural Science Foundation of China (No. 11202074)+2 种基金partially supported by the Open Research Fund Program of the State Key Laboratory of Advanced Technology of Design and Manufacturing for Vehicle Body, Hunan University, P. R. China (No. 31175002)the support of Centre for ACES, Singapore-MIT Alliance (SMA)National University of Singapore for the work
文摘In this work, we further extended the face-based smoothed finite element method （FS-FEM） for modal analysis of three-dimensional solids using four-node tetrahedron elements. The FS-FEM is formulated based on the smoothed Calerkin weak form which employs smoothed strains obtained using the gradient smoothing operation on face-based smoothing domains. This strain smoothing operation can provide softening effect to the system stiffness and make the FSFEM provide more accurate eigenfrequency prediction than the FEM does. Numerical studies have verified this attractive property of FS-FEM as well as its ability and effectiveness on providing reliable eigenfrequency and eigenmode prediction in practical engineering application.
文摘An h-adaptivity analysis scheme based on multiple scale reproducing kernel particle method was proposed, and two node refinement strategies were constructed using searching-neighbor-nodes（SNN） and local-Delaunay-triangulation（LDT） techniques, which were suitable and effective for h-adaptivity analysis on 2-D problems with the regular or irregular distribution of the nodes. The results of multiresolution and h- adaptivity analyses on 2-D linear elastostatics and bending plate problems demonstrate that the improper high-gradient indicator will reduce the convergence property of the h- adaptivity analysis, and that the efficiency of the LDT node refinement strategy is better than SNN, and that the presented h-adaptivity analysis scheme is provided with the validity, stability and good convergence property.
基金Project supported by the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.10902076)the Natural Science Foundation of Shanxi Province of China(Grant No.2007011009)+1 种基金the Scientific Research and Development Program of the Shanxi Higher Education Institutions(Grant No.20091131)the Doctoral Startup Foundation of Taiyuan University of Science and Technology(Grant No.200708)
文摘In this paper, a meshfree boundary integral equation （BIE） method, called the moving Kriging interpolation- based boundary node method （MKIBNM）, is developed for solving two-dimensional potential problems. This study combines the DIE method with the moving Kriging interpolation to present a boundary-type meshfree method, and the corresponding formulae of the MKIBNM are derived. In the present method, the moving Kriging interpolation is applied instead of the traditional moving least-square approximation to overcome Kronecker＇s delta property, then the boundary conditions can be imposed directly and easily. To verify the accuracy and stability of the present formulation, three selected numerical examples are presented to demonstrate the efficiency of MKIBNM numerically.
基金the support from the National Natural Science Foundation of China (Grants 11272155, 11132007, and 11502113)the Fundamental Research Funds for Central Universities (Grant 30917011103)the China Scholarship Council for one year study at the University of Cincinnati
文摘We proposed a mesh-free method, the called node-based smoothed point interpolation method(NS-PIM),for dynamic analysis of rotating beams. A gradient smoothing technique is used, and the requirements on the consistence of the displacement functions are further weakened. In static problems, the beams with three types of boundary conditions are analyzed, and the results are compared with the exact solution, which shows the effectiveness of this method and can provide an upper bound solution for the deflection.This means that the NS-PIM makes the system soften. The NS-PIM is then further extended for solving a rigid-flexible coupled system dynamics problem, considering a rotating flexible cantilever beam. In this case, the rotating flexible cantilever beam considers not only the transverse deformations,but also the longitudinal deformations. The rigid-flexible coupled dynamic equations of the system are derived via employing Lagrange’s equations of the second type. Simulation results of the NS-PIM are compared with those obtained using finite element method(FEM) and assumed mode method. It is found that compared with FEM, the NS-PIM has anti-ill solving ability under the same calculation conditions.
