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
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
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
Combining moving least square approximations and boundary integral equations, a meshless Galerkin method, which is the Galerkin boundary node method （GBNM）, for twoand three-dimensional infinite elastic solid mechan...Combining moving least square approximations and boundary integral equations, a meshless Galerkin method, which is the Galerkin boundary node method （GBNM）, for twoand three-dimensional infinite elastic solid mechanics problems with traction boundary conditions is discussed. In this numerical method, the resulting formulation inherits the symmetry and positive definiteness of variational problems, and boundary conditions can be applied directly and easily. A rigorous error analysis and convergence study for both displacement and stress is presented in Sobolev spaces. The capability of this method is illustrated and assessed by some numerical examples.展开更多
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supported by the National Natural Science Foundation of China(Grant No.11101454)the Natural Science Foundation of Chongqing CSTC(GrantNo.cstc2011jjA30003)
文摘Combining moving least square approximations and boundary integral equations, a meshless Galerkin method, which is the Galerkin boundary node method （GBNM）, for twoand three-dimensional infinite elastic solid mechanics problems with traction boundary conditions is discussed. In this numerical method, the resulting formulation inherits the symmetry and positive definiteness of variational problems, and boundary conditions can be applied directly and easily. A rigorous error analysis and convergence study for both displacement and stress is presented in Sobolev spaces. The capability of this method is illustrated and assessed by some numerical examples.
