In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be r...In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin node.Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients.All the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element method.Four numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet method.The results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer.Compared with many other methods,the proposed method possesses satisfactory accuracy and efficiency.The theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5.展开更多
We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations ...We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations of nonlinear hyperbolic problems with properties that greatly simplify the design of invariant domain-preserving high-resolution schemes.Compared to many other continuous and discontinuous Galerkin method variants,a particular advantage of the LGL spectral operator is the availability of a natural decomposition into a compatible subcellflux discretization.Representing a highorder spatial semi-discretization in terms of intermediate states,we performflux limiting in a manner that keeps these states and the results of Runge-Kutta stages in convex invariant domains.In addition,local bounds may be imposed on scalar quantities of interest.In contrast to limiting approaches based on predictor-corrector algorithms,our MCL procedure for LGL-DGSEM yields nonlinearflux approximations that are independent of the time-step size and can be further modified to enforce entropy stability.To demonstrate the robustness of MCL/DGSEM schemes for the compressible Euler equations,we run simulations for challenging setups featuring strong shocks,steep density gradients,and vortex dominatedflows.展开更多
The quasi-static analysis method introduced by API RP 2P is well known and accepted as a very useful mooring analysis method. In the early design stage, this method is widely used for preliminary analysis and mooring ...The quasi-static analysis method introduced by API RP 2P is well known and accepted as a very useful mooring analysis method. In the early design stage, this method is widely used for preliminary analysis and mooring parameter selection. However, the quasi-static method of API RP 2P is developed for single-floating-body condition, i. e., only one floating body is considered in the computation procedure. Difficulties arise when it is used for the analysis of a CALM system, which is comprised of two floating bodies (tanker and buoy). This paper presents an analysis procedure for a two-floating-body system based on the quasi-static procedure of API RP 2P with some modifications reflecting special characteristics of the CALM system. Finally, the analysis results of a CALM system are given to illustrate the use of this procedure.展开更多
Thin structures are generally solved by the Finite Element Method(FEM), using plate or shell finite elements which have manylimitations in applications, such as numerical locking, edge effects,length scaling and the c...Thin structures are generally solved by the Finite Element Method(FEM), using plate or shell finite elements which have manylimitations in applications, such as numerical locking, edge effects,length scaling and the cnvergence problem. Recently, by proposing anew approach to tranting the nearly- singular integrals, Liu et al.developed a BEM to successfully solve thin structures with thethickness-to- length ratios in the micro-or nano-scales. On the otherhand, the meshless Regular Hybrid Boundary Node Method (RHBNM), whichis proposed by the current authors and based on a modified functionaland the Moving Least-Square (MLS) approximation, has very promisingapplications for engineering problems owing To its meshless natureand dimension-reduction advantage, and not involving any singular ornearly-singular Integrals. Test examples show that the RHBNM can alsobe applied readily to thin structures with high accu- Racy withoutany modification.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
This article analyzes the shift factors of the descending node local time for sun-synchronous satellites and proposes a shift control method to keep the local time shift within an allowance range. It is found that the...This article analyzes the shift factors of the descending node local time for sun-synchronous satellites and proposes a shift control method to keep the local time shift within an allowance range. It is found that the satellite orbit design and the orbit injection deviation are the causes for the initial shift velocity, whereas the atmospheric drag and the sun gravitational perturbation produce the shift acceleration. To deal with these shift factors, a shift control method is put forward, through such methods as orbit variation design, orbit altitude, and inclination keeping control. The simulation experiment and practical application have proved the effectiveness of this control method.展开更多
Node interpolation cell method(NICM)is a micromechanics method employing the virtual displacement principle and the representative volume element(RVE)scheme to obtain the relationship between the global and the lo...Node interpolation cell method(NICM)is a micromechanics method employing the virtual displacement principle and the representative volume element(RVE)scheme to obtain the relationship between the global and the local strain.Mechanical properties of 2-D textile fabric reinforced ceramic matrix composites are predicted by NICM.Microstructures of 2-D woven and braided fabric reinforced composite are modeled by two kinds of RVE scheme.NICM is used to predict the macroscopic mechanical properties.The fill and warp yarns are simulated with cubic B-spline and their undulating forms are approximated by sinusoid.The effect of porosity on the fiber and matrix are considered as a reduction of elastic module.The connection of microstructure parameters and fiber volume fraction is modeled to investigate the reflection on the mechanical properties.The results predicted by NICM are compared with that by the finite element method(FEM).The comparison shows that NICM is a valid and feasible method for predicting the mechanics properties of 2-D woven and braided fabric reinforced ceramic matrix composites.展开更多
Combining Dual Reciprocity Method (DRM) with Hybrid Boundary Node Method (HBNM), the Dual Reciprocity Hybrid Boundary Node Method (DRHBNM) is developed for three-dimensional linear elasticity problems with body ...Combining Dual Reciprocity Method (DRM) with Hybrid Boundary Node Method (HBNM), the Dual Reciprocity Hybrid Boundary Node Method (DRHBNM) is developed for three-dimensional linear elasticity problems with body force. This method can be used to solve the elasticity problems with body force without domain integral, which is inevitable by HBNM. To demonstrate the versatility and the fast convergence of this method, some numerical examples of 3-D elasticity problems with body forces are examined. The computational results show that the present method is effective and can be widely applied in solving practical engineering problems.展开更多
A boundary-type meshless method called the scaled boundary node method (SBNM) is developed to directly evaluate mixed mode stress intensity factors (SIFs) without extra post-processing. The SBNM combines the scale...A boundary-type meshless method called the scaled boundary node method (SBNM) is developed to directly evaluate mixed mode stress intensity factors (SIFs) without extra post-processing. The SBNM combines the scaled boundary equations with the moving Kriging (MK) interpolation to retain the dimensionality advantage of the former and the meshless attribute of the latter. As a result, the SBNM requires only a set of scattered nodes on the boundary, and the displacement field is approximated by using the MK interpolation technique, which possesses the 5 function property. This makes the developed method efficient and straightforward in imposing the essential boundary conditions, and no special treatment techniques are required. Besides, the SBNM works by weakening the governing differential equations in the circumferential direction and then solving the weakened equations analytically in the radial direction. Therefore, the SBNM permits an accurate representation of the singularities in the radial direction when the scaling center is located at the crack tip. Numerical examples using the SBNM for computing the SIFs are presented. Good agreements with available results in the literature are obtained.展开更多
The identification of key nodes plays an important role in improving the robustness of the transportation network.For different types of transportation networks,the effect of the same identification method may be diff...The identification of key nodes plays an important role in improving the robustness of the transportation network.For different types of transportation networks,the effect of the same identification method may be different.It is of practical significance to study the key nodes identification methods corresponding to various types of transportation networks.Based on the knowledge of complex networks,the metro networks and the bus networks are selected as the objects,and the key nodes are identified by the node degree identification method,the neighbor node degree identification method,the weighted k-shell degree neighborhood identification method(KSD),the degree k-shell identification method(DKS),and the degree k-shell neighborhood identification method(DKSN).Take the network efficiency and the largest connected subgraph as the effective indicators.The results show that the KSD identification method that comprehensively considers the elements has the best recognition effect and has certain practical significance.展开更多
The singular hybrid boundary node method (SHBNM) is proposed for solving three-dimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and ...The singular hybrid boundary node method (SHBNM) is proposed for solving three-dimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and moving least squares (MLS) approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the later. The rigid movement method was employed to solve the hyper-singular integrations. The 'boundary layer effect', which is the main drawback of the original Hybrid BNM, was overcome by an adaptive integration scheme. The source points of the fundamental solution were arranged directly on the boundary. Thus the uncertain scale factor taken in the regular hybrid boundary node method (RHBNM) can be avoided. Numerical examples for some 3D elastic problems were given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method were studied through the numerical examples.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
In this paper,general interpolating isogeometric boundary node method(IIBNM)and isogeometric boundary element method(IBEM)based on parameter space are proposed for 2D elasticity problems.In both methods,the integral c...In this paper,general interpolating isogeometric boundary node method(IIBNM)and isogeometric boundary element method(IBEM)based on parameter space are proposed for 2D elasticity problems.In both methods,the integral cells and elements are defined in parameter space,which can reproduce the geometry exactly at all the stages.In IIBNM,the improved interpolating moving leastsquare method(IIMLS)is applied for field approximation and the shape functions have the delta function property.The Lagrangian basis functions are used for field approximation in IBEM.Thus,the boundary conditions can be imposed directly in both methods.The shape functions are defined in 1D parameter space and no curve length needs to be computed.Besides,most methods for the treatment of the singular integrals in the boundary element method can be applied in IIBNM and IBEM directly.Numerical examples have demonstrated the accuracy of the proposed methods.展开更多
In this paper,the node based smoothed-strain Abaqus user element(UEL)in the framework of finite element method is introduced.The basic idea behind of the node based smoothed finite element(NSFEM)is that finite element...In this paper,the node based smoothed-strain Abaqus user element(UEL)in the framework of finite element method is introduced.The basic idea behind of the node based smoothed finite element(NSFEM)is that finite element cells are divided into subcells and subcells construct the smoothing domain associated with each node of a finite element cell[Liu,Dai and Nguyen-Thoi(2007)].Therefore,the numerical integration is globally performed over smoothing domains.It is demonstrated that the proposed UEL retains all the advantages of the NSFEM,i.e.,upper bound solution,overly soft stiffness and free from locking in compressible and nearly-incompressible media.In this work,the constant strain triangular(CST)elements are used to construct node based smoothing domains,since any complex two dimensional domains can be discretized using CST elements.This additional challenge is successfully addressed in this paper.The efficacy and robustness of the proposed work is obtained by several benchmark problems in both linear and nonlinear elasticity.The developed UEL and the associated files can be downloaded from https://github.com/nsundar/NSFEM.展开更多
In the conventional differential quadrature (DQ) method the functional values along a mesh line are used to approximate derivatives and its application is limited to regular regions. In this paper, a local different...In the conventional differential quadrature (DQ) method the functional values along a mesh line are used to approximate derivatives and its application is limited to regular regions. In this paper, a local differential quadrature (LDQ) method was developed by using irregular distributed nodes, where any spatial derivative at a nodal point is approximated by a linear weighted sum of the functional values of nodes in the local physical domain. The weighting coefficients in the new approach are determined by the quadrature rule with the aid of nodal interpolation. Since the proposed method directly approximates the derivative, it can be consistently well applied to linear and nonlinear problems and the mesh-free feature is still kept. Numerical examples are provided to validate the LDQ method.展开更多
As a boundary-type meshless method, the singular hybrid boundary node method(SHBNM) is based on the modified variational principle and the moving least square(MLS) approximation, so it has the advantages of both b...As a boundary-type meshless method, the singular hybrid boundary node method(SHBNM) is based on the modified variational principle and the moving least square(MLS) approximation, so it has the advantages of both boundary element method(BEM) and meshless method. In this paper, the dual reciprocity method(DRM) is combined with SHBNM to solve Poisson equation in which the solution is divided into particular solution and general solution. The general solution is achieved by means of SHBNM, and the particular solution is approximated by using the radial basis function(RBF). Only randomly distributed nodes on the bounding surface of the domain are required and it doesn't need extra equations to compute internal parameters in the domain. The postprocess is very simple. Numerical examples for the solution of Poisson equation show that high convergence rates and high accuracy with a small node number are achievable.展开更多
How to automatically generate three-dimensional finite element Delaunay mesh by a peifected node connection method is introduced, where nodes are generated based on existing elements, instead of independence of node c...How to automatically generate three-dimensional finite element Delaunay mesh by a peifected node connection method is introduced, where nodes are generated based on existing elements, instead of independence of node creation and elements generation in traditional node connection method. Therefore, Ihe the difficulty about how to automatically create nodes in the traditional method is overcome.展开更多
In this paper we propose a collocation method for solving Lane-Emden type equation which is nonlinear or-dinary differential equation on the semi-infinite domain. This equation is categorized as singular initial value...In this paper we propose a collocation method for solving Lane-Emden type equation which is nonlinear or-dinary differential equation on the semi-infinite domain. This equation is categorized as singular initial value problems. We solve this equation by the generalized Laguerre polynomial collocation method based on Her-mite-Gauss nodes. This method solves the problem on the semi-infinite domain without truncating it to a fi-nite domain and transforming domain of the problem to a finite domain. In addition, this method reduces so-lution of the problem to solution of a system of algebraic equations.展开更多
基金supported by the National Natural Science Foundation of China (No.12172154)the 111 Project (No.B14044)+1 种基金the Natural Science Foundation of Gansu Province (No.23JRRA1035)the Natural Science Foundation of Anhui University of Finance and Economics (No.ACKYC20043).
文摘In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin node.Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients.All the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element method.Four numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet method.The results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer.Compared with many other methods,the proposed method possesses satisfactory accuracy and efficiency.The theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5.
文摘We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations of nonlinear hyperbolic problems with properties that greatly simplify the design of invariant domain-preserving high-resolution schemes.Compared to many other continuous and discontinuous Galerkin method variants,a particular advantage of the LGL spectral operator is the availability of a natural decomposition into a compatible subcellflux discretization.Representing a highorder spatial semi-discretization in terms of intermediate states,we performflux limiting in a manner that keeps these states and the results of Runge-Kutta stages in convex invariant domains.In addition,local bounds may be imposed on scalar quantities of interest.In contrast to limiting approaches based on predictor-corrector algorithms,our MCL procedure for LGL-DGSEM yields nonlinearflux approximations that are independent of the time-step size and can be further modified to enforce entropy stability.To demonstrate the robustness of MCL/DGSEM schemes for the compressible Euler equations,we run simulations for challenging setups featuring strong shocks,steep density gradients,and vortex dominatedflows.
文摘The quasi-static analysis method introduced by API RP 2P is well known and accepted as a very useful mooring analysis method. In the early design stage, this method is widely used for preliminary analysis and mooring parameter selection. However, the quasi-static method of API RP 2P is developed for single-floating-body condition, i. e., only one floating body is considered in the computation procedure. Difficulties arise when it is used for the analysis of a CALM system, which is comprised of two floating bodies (tanker and buoy). This paper presents an analysis procedure for a two-floating-body system based on the quasi-static procedure of API RP 2P with some modifications reflecting special characteristics of the CALM system. Finally, the analysis results of a CALM system are given to illustrate the use of this procedure.
文摘Thin structures are generally solved by the Finite Element Method(FEM), using plate or shell finite elements which have manylimitations in applications, such as numerical locking, edge effects,length scaling and the cnvergence problem. Recently, by proposing anew approach to tranting the nearly- singular integrals, Liu et al.developed a BEM to successfully solve thin structures with thethickness-to- length ratios in the micro-or nano-scales. On the otherhand, the meshless Regular Hybrid Boundary Node Method (RHBNM), whichis proposed by the current authors and based on a modified functionaland the Moving Least-Square (MLS) approximation, has very promisingapplications for engineering problems owing To its meshless natureand dimension-reduction advantage, and not involving any singular ornearly-singular Integrals. Test examples show that the RHBNM can alsobe applied readily to thin structures with high accu- Racy withoutany modification.
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supported by the China Postdotoral Science Foundation(20060401004)
文摘This article analyzes the shift factors of the descending node local time for sun-synchronous satellites and proposes a shift control method to keep the local time shift within an allowance range. It is found that the satellite orbit design and the orbit injection deviation are the causes for the initial shift velocity, whereas the atmospheric drag and the sun gravitational perturbation produce the shift acceleration. To deal with these shift factors, a shift control method is put forward, through such methods as orbit variation design, orbit altitude, and inclination keeping control. The simulation experiment and practical application have proved the effectiveness of this control method.
基金Supported by the Aviation Science Foundationof China(2009ZB5052)the Specialized Research Foundation for the Doctor Program of Higher Education(20070287039)~~
文摘Node interpolation cell method(NICM)is a micromechanics method employing the virtual displacement principle and the representative volume element(RVE)scheme to obtain the relationship between the global and the local strain.Mechanical properties of 2-D textile fabric reinforced ceramic matrix composites are predicted by NICM.Microstructures of 2-D woven and braided fabric reinforced composite are modeled by two kinds of RVE scheme.NICM is used to predict the macroscopic mechanical properties.The fill and warp yarns are simulated with cubic B-spline and their undulating forms are approximated by sinusoid.The effect of porosity on the fiber and matrix are considered as a reduction of elastic module.The connection of microstructure parameters and fiber volume fraction is modeled to investigate the reflection on the mechanical properties.The results predicted by NICM are compared with that by the finite element method(FEM).The comparison shows that NICM is a valid and feasible method for predicting the mechanics properties of 2-D woven and braided fabric reinforced ceramic matrix composites.
文摘Combining Dual Reciprocity Method (DRM) with Hybrid Boundary Node Method (HBNM), the Dual Reciprocity Hybrid Boundary Node Method (DRHBNM) is developed for three-dimensional linear elasticity problems with body force. This method can be used to solve the elasticity problems with body force without domain integral, which is inevitable by HBNM. To demonstrate the versatility and the fast convergence of this method, some numerical examples of 3-D elasticity problems with body forces are examined. The computational results show that the present method is effective and can be widely applied in solving practical engineering problems.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11002054)
文摘A boundary-type meshless method called the scaled boundary node method (SBNM) is developed to directly evaluate mixed mode stress intensity factors (SIFs) without extra post-processing. The SBNM combines the scaled boundary equations with the moving Kriging (MK) interpolation to retain the dimensionality advantage of the former and the meshless attribute of the latter. As a result, the SBNM requires only a set of scattered nodes on the boundary, and the displacement field is approximated by using the MK interpolation technique, which possesses the 5 function property. This makes the developed method efficient and straightforward in imposing the essential boundary conditions, and no special treatment techniques are required. Besides, the SBNM works by weakening the governing differential equations in the circumferential direction and then solving the weakened equations analytically in the radial direction. Therefore, the SBNM permits an accurate representation of the singularities in the radial direction when the scaling center is located at the crack tip. Numerical examples using the SBNM for computing the SIFs are presented. Good agreements with available results in the literature are obtained.
基金supported by the National Natural Science Foundation of China(Grant No.61961019)the Youth Key Project of the Natural Science Foundation of Jiangxi Province of China(Grant No.20202ACBL212003).
文摘The identification of key nodes plays an important role in improving the robustness of the transportation network.For different types of transportation networks,the effect of the same identification method may be different.It is of practical significance to study the key nodes identification methods corresponding to various types of transportation networks.Based on the knowledge of complex networks,the metro networks and the bus networks are selected as the objects,and the key nodes are identified by the node degree identification method,the neighbor node degree identification method,the weighted k-shell degree neighborhood identification method(KSD),the degree k-shell identification method(DKS),and the degree k-shell neighborhood identification method(DKSN).Take the network efficiency and the largest connected subgraph as the effective indicators.The results show that the KSD identification method that comprehensively considers the elements has the best recognition effect and has certain practical significance.
基金Project supported by the Program of the Key Laboratory of Rock and Soil Mechanics of Chinese Academy of Sciences (No.Z110507)
文摘The singular hybrid boundary node method (SHBNM) is proposed for solving three-dimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and moving least squares (MLS) approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the later. The rigid movement method was employed to solve the hyper-singular integrations. The 'boundary layer effect', which is the main drawback of the original Hybrid BNM, was overcome by an adaptive integration scheme. The source points of the fundamental solution were arranged directly on the boundary. Thus the uncertain scale factor taken in the regular hybrid boundary node method (RHBNM) can be avoided. Numerical examples for some 3D elastic problems were given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method were studied through the numerical examples.
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The research for this paper was supported by(1)the National Natural Science Foundation of China(Grants Nos.51708429,51708428)the Open Projects Foundation(Grant No.2017-04-GF)of State Key Laboratory for Health and Safety of Bridge Structures+1 种基金Wuhan Institute of Technology Science Found(Grant No.K201734)the science and technology projects of Wuhan Urban and Rural Construction Bureau(Grants Nos.201831,201919).
文摘In this paper,general interpolating isogeometric boundary node method(IIBNM)and isogeometric boundary element method(IBEM)based on parameter space are proposed for 2D elasticity problems.In both methods,the integral cells and elements are defined in parameter space,which can reproduce the geometry exactly at all the stages.In IIBNM,the improved interpolating moving leastsquare method(IIMLS)is applied for field approximation and the shape functions have the delta function property.The Lagrangian basis functions are used for field approximation in IBEM.Thus,the boundary conditions can be imposed directly in both methods.The shape functions are defined in 1D parameter space and no curve length needs to be computed.Besides,most methods for the treatment of the singular integrals in the boundary element method can be applied in IIBNM and IBEM directly.Numerical examples have demonstrated the accuracy of the proposed methods.
文摘In this paper,the node based smoothed-strain Abaqus user element(UEL)in the framework of finite element method is introduced.The basic idea behind of the node based smoothed finite element(NSFEM)is that finite element cells are divided into subcells and subcells construct the smoothing domain associated with each node of a finite element cell[Liu,Dai and Nguyen-Thoi(2007)].Therefore,the numerical integration is globally performed over smoothing domains.It is demonstrated that the proposed UEL retains all the advantages of the NSFEM,i.e.,upper bound solution,overly soft stiffness and free from locking in compressible and nearly-incompressible media.In this work,the constant strain triangular(CST)elements are used to construct node based smoothing domains,since any complex two dimensional domains can be discretized using CST elements.This additional challenge is successfully addressed in this paper.The efficacy and robustness of the proposed work is obtained by several benchmark problems in both linear and nonlinear elasticity.The developed UEL and the associated files can be downloaded from https://github.com/nsundar/NSFEM.
文摘In the conventional differential quadrature (DQ) method the functional values along a mesh line are used to approximate derivatives and its application is limited to regular regions. In this paper, a local differential quadrature (LDQ) method was developed by using irregular distributed nodes, where any spatial derivative at a nodal point is approximated by a linear weighted sum of the functional values of nodes in the local physical domain. The weighting coefficients in the new approach are determined by the quadrature rule with the aid of nodal interpolation. Since the proposed method directly approximates the derivative, it can be consistently well applied to linear and nonlinear problems and the mesh-free feature is still kept. Numerical examples are provided to validate the LDQ method.
基金Foundation item: Supported by the National Natural Science Foundation of China(50608036)
文摘As a boundary-type meshless method, the singular hybrid boundary node method(SHBNM) is based on the modified variational principle and the moving least square(MLS) approximation, so it has the advantages of both boundary element method(BEM) and meshless method. In this paper, the dual reciprocity method(DRM) is combined with SHBNM to solve Poisson equation in which the solution is divided into particular solution and general solution. The general solution is achieved by means of SHBNM, and the particular solution is approximated by using the radial basis function(RBF). Only randomly distributed nodes on the bounding surface of the domain are required and it doesn't need extra equations to compute internal parameters in the domain. The postprocess is very simple. Numerical examples for the solution of Poisson equation show that high convergence rates and high accuracy with a small node number are achievable.
基金This project is supported by Provincial Natural Science foundation of Guangdong!(970516)
文摘How to automatically generate three-dimensional finite element Delaunay mesh by a peifected node connection method is introduced, where nodes are generated based on existing elements, instead of independence of node creation and elements generation in traditional node connection method. Therefore, Ihe the difficulty about how to automatically create nodes in the traditional method is overcome.
文摘In this paper we propose a collocation method for solving Lane-Emden type equation which is nonlinear or-dinary differential equation on the semi-infinite domain. This equation is categorized as singular initial value problems. We solve this equation by the generalized Laguerre polynomial collocation method based on Her-mite-Gauss nodes. This method solves the problem on the semi-infinite domain without truncating it to a fi-nite domain and transforming domain of the problem to a finite domain. In addition, this method reduces so-lution of the problem to solution of a system of algebraic equations.