The Experts below are selected from a list of 4215 Experts worldwide ranked by ideXlab platform
Subrata Mukherjee - One of the best experts on this subject based on the ideXlab platform.
-
The Boundary Node Method
Selected Topics in Boundary Integral Formulations for Solids and Fluids, 2020Co-Authors: Subrata MukherjeeAbstract:This chapter presents applications of the boundary Node Method (BNM) in three dimensional (3-D) linear elasticity. Following a brief introduction, and a section on surface approximants, derivations of the BNM and the hypersingular BNM (HBNM) are presented in Section 3. This is followed by a section describing error estimation and adaptivity with the BNM and the HBNM. Numerical results for selected examples are included throughout the chapter.
-
The extended boundary Node Method for three-dimensional potential theory
Computers & Structures, 2005Co-Authors: Srinivas Telukunta, Subrata MukherjeeAbstract:The boundary Node Method (BNM) [Mukherjee YX, Mukherjee S. The boundary Node Method for potential problems. Int J Numer Methods Eng 1997;40:797-815] is a boundary-only mesh-free Method that combines the moving least-squares (MLS) interpolation scheme with the standard boundary integral equations (BIEs). Curvilinear boundary co-ordinates were originally proposed and used in this Method-for both two [Mukherjee YX, Mukherjee S. The boundary Node Method for potential problems. Int J Numer Methods Eng 1997;40:797-815] and three-dimensional [Mukherjee S, Mukherjee YX. Boundary Methods-elements, contours and Nodes. Boca Raton, FL: CRC Press, in press] problems in potential theory and in linear elasticity. Li and Aluru [Li G, Aluru NR. Boundary cloud Method: a combined scattered point/boundary integral approach for boundary-only analysis. Comput Methods Appl Mech Eng 2002;191:2337-70; Li G. Aluru NR. A boundary cloud Method with a cloud-by-cloud polynomial basis. Eng Anal Boundary Elem 2003;27:57-71] have recently proposed an elegant improvement to the BNM (called the boundary cloud Method (BCM)) that allows the use of Cartesian co-ordinates. Their novel variable basis BCM [Li G. Aluru NR. A boundary cloud Method with a cloud-by-cloud polynomial basis. Eng Anal Boundary Elem 2003;27:57-71] has several advantages relative to the original BCM. It does, however, have a drawback in that continuous approximants are used for all boundary variables, even across corners. It is well known, for example, that the normal derivative of the potential function in potential theory, or the traction in linear elasticity, often suffers jump discontinuities across corners in two-dimensional (2-D) and across edges and corners in three-dimensional (3-D) problems. The present authors [Telukunta S, Mukherjee S. An extended boundary Node Method for modeling normal derivative discontinuities in potential theory across edges and corners. Eng Anal Boundary Elem 2004;28:1099-110] have recently proposed a further improvement to the BNM and the variable basis BCM. This new approach is called the extended BNM (EBNM). This Method employs Cartesian co-ordinates with variable bases, together with appropriate approximants for the normal derivative across edges and corners that can model discontinuities in this variable. Two-dimensional problems in potential theory are presented in [Telukunta S, Mukherjee S. An extended boundary Node Method for modeling normal derivative discontinuities in potential theory across edges and corners. Eng Anal Boundary Elem 2004;28:1099-110]. The present paper is concerned with far more challenging problems-3-D problems in potential theory.
-
A ‘pure’ boundary Node Method for potential theory
Communications in Numerical Methods in Engineering, 2002Co-Authors: Ramesh Gowrishankar, Subrata MukherjeeAbstract:The standard boundary Node Method (BNM) uses a (meshless) diffuse interpolation (in terms of neighbouring scattered boundary points) for the primary variables. The Method is not ‘truly meshless’, however, since cells on the boundary of a body are used for integration. This paper presents a ‘pure’ version of the BNM in which integration cells are dispensed with. Instead (overlapping), regions of influence (ROIs) of boundary Nodes are used for integration. Initial results for 2-D potential theory, presented here, are encouraging. Copyright © 2002 John Wiley & Sons, Ltd.
-
The meshless hypersingular boundary Node Method for three-dimensional potential theory and linear elasticity problems
Engineering Analysis With Boundary Elements, 2001Co-Authors: Mandar K Chati, Subrata Mukherjee, Glaucio H. PaulinoAbstract:Abstract The Boundary Node Method (BNM) represents a coupling between Boundary Integral Equations (BIEs) and Moving Least Squares (MLS) approximants. The main idea here is to retain the dimensionality advantage of the former and the meshless attribute of the latter. The result is a ‘meshfree’ Method that decouples the mesh and the interpolation procedures. The BNM has been applied to solve 2-D and 3-D problems in potential theory and linear elasticity. The Hypersingular Boundary Element Method (HBEM) has diverse important applications in areas such as fracture mechanics, wave scattering, error analysis and adaptivity, and to obtain a symmetric Galerkin boundary element formulation. The present work presents a coupling of Hypersingular Boundary Integral Equations (HBIEs) with MLS approximants, to produce a new meshfree Method — the Hypersingular Boundary Node Method (HBNM). Numerical results from this new Method, for selected 3-D problems in potential theory and in linear elasticity, are presented and discussed in this paper.
-
The meshless standard and hypersingular boundary Node Methods—applications to error estimation and adaptivity in three‐dimensional problems
International Journal for Numerical Methods in Engineering, 2001Co-Authors: Mandar K Chati, Glaucio H. Paulino, Subrata MukherjeeAbstract:The standard (singular) boundary Node Method (BNM) and the novel hypersingular boundary Node Method (HBNM) are employed for the usual and adaptive solutions of three-dimensional potential and elasticity problems. These Methods couple boundary integral equations with moving least-squares interpolants while retaining the dimensionality advantage of the former and the meshless attribute of the latter. The ‘hypersingular residuals’, developed for error estimation in the mesh-based collocation boundary element Method (BEM) and symmetric Galerkin BEM by Paulino et al., are extended to the meshless BNM setting. A simple ‘a posteriori’ error estimation and an effective adaptive refinement procedure are presented. The implementation of all the techniques involved in this work are discussed, which includes aspects regarding parallel implementation of the BNM and HBNM codes. Several numerical examples are given and discussed in detail. Conclusions are inferred and relevant extensions of the Methodology introduced in this work are provided. Copyright © 2001 John Wiley & Sons, Ltd.
Yu Miao - One of the best experts on this subject based on the ideXlab platform.
-
Dual Hybrid Boundary Node Method for Transient Eddy Current Problem
2020Co-Authors: Bihai Liao, Yu MiaoAbstract:Dual hybrid boundary Node Method (DHBNM) is presented for solving transient eddy current problems in the paper. With difference to the traditional boundary element Method (BEM), the DHBNM combines dual reciprocity Method (DRM) and hybrid boundary Node Method (HBNM), which does not require the ‘boundary element mesh’, either for the purpose of interpolation of the solution variables, or for the integration of the ‘energy’. In this Method, the solution composes into two parts, i. e., the complementary solution and the particular solution. The complementary solution is solved by HBNM, and the particular one is obtained by DRM. Theoretical analysis in details is given and a transient eddy current example is also presented to prove the proposed theory.
-
Dual Reciprocity Hybrid Boundary Node Method for Solving Poisson Equations
Computational Mechanics, 2020Co-Authors: Yu Miao, Junhai Wang, Y. Z. Sima, Yuanhan WangAbstract:It has long been claimed that the boundary element Method (BEM) is a viable alternative to the domain-type finite element Method (FEM) and finite difference Method (FDM) due to its advantages in dimensional reducibility and suitability to infinite domain problems. However, it has a major difficulty in handling inhomogeneous terms such as time-dependent and nonlinear problems. It is over 18 years since the dual reciprocity Method (DRM) was first proposed by Nardini and Brebbia which provides a very general Methodology for obtaining a boundary element solution to wide range of problems. Another obstacle in BEM, just like the FEM, surface mesh or remesh requires costly computation, especially for moving boundary and nonlinear problems. The boundary-type meshless Methods such as the hybrid boundary Node Method (Hybrid-BNM) , the boundary Node Method (BNM) shown an emerging technique to alleviate these drawbacks.
-
Thermal analysis of 3D composites by a new fast multipole hybrid boundary Node Method
Computational Mechanics, 2013Co-Authors: Yu Miao, Qiao Wang, Yinping LiAbstract:This paper applies the hybrid boundary Node Method (Hybrid BNM) for the thermal analysis of 3D composites. A new formulation is derived for the inclusion-based composites. In the new formulation, the unknowns of the interfaces are assembled only once in the final system equation, which can reduce nearly one half of degrees of freedom (DOFs) compared with the conventional multi-domain solver when there are lots of inclusions. A new version of the fast multipole Method (FMM) is also coupled with the new formulation and the technique is applied to thermal analysis of composites with many inclusions. In the new fast multipole hybrid boundary Node Method (FM-HBNM), a diagonal form for translation operators is used and the Method presented can be applied to the computation of more than 1,000,000 DOFs on a personal computer. Numerical examples are presented to analyze the thermal behavior of composites with many inclusions.
-
Boundary Node Method based on parametric space for 2D elasticity
Engineering Analysis With Boundary Elements, 2013Co-Authors: J.h. Lv, Yu MiaoAbstract:Abstract This paper presents a new implementation of the boundary Node Method (BNM) for 2D elasticity based on the parametric space. The BNM couples the boundary integral equations (BIE) with the moving least square (MLS) approximation, which retains the dimensionality advantage and the meshless attribute. However, the BNM is performed on an approximate geometry by MLS fitting and geometry errors are inevitable. In this paper, the BNM is implemented directly on the boundary representation (B-rep) data structure used in most CAD packages for geometry modeling, which named the boundary line Method (BLM). The integration quantities, such as the coordinates of Gauss points, the outward normal and Jacobian are calculated directly from the lines represented in a parametric form which are the same as the real boundary, and thus no errors will be introduced. A new integration scheme has been developed to deal with weakly singular integrals easily. Numerical results presented in this paper show excellent accuracy and high convergence rate.
-
A fast multipole hybrid boundary Node Method for composite materials
Computational Mechanics, 2012Co-Authors: Qiao Wang, Yu MiaoAbstract:This article presents a multi-domain fast multipole hybrid boundary Node Method for composite materials in 3D elasticity. The hybrid boundary Node Method (hybrid BNM) is a meshless Method which only requires Nodes constructed on the surface of a domain. The Method is applied to 3D simulation of composite materials by a multi-domain solver and accelerated by the fast multipole Method (FMM) in this paper. The preconditioned GMRES is employed to solve the final system equation and precondition techniques are discussed. The matrix---vector multiplication in each iteration is divided into smaller scale ones at the sub-domain level and then accelerated by FMM within individual sub-domains. The computed matrix---vector products at the sub-domain level are then combined according to the continuity conditions on the interfaces. The algorithm is implemented on a computer code written in C + +. Numerical results show that the technique is accurate and efficient.
Yuanhan Wang - One of the best experts on this subject based on the ideXlab platform.
-
Dual Reciprocity Hybrid Boundary Node Method for Solving Poisson Equations
Computational Mechanics, 2020Co-Authors: Yu Miao, Junhai Wang, Y. Z. Sima, Yuanhan WangAbstract:It has long been claimed that the boundary element Method (BEM) is a viable alternative to the domain-type finite element Method (FEM) and finite difference Method (FDM) due to its advantages in dimensional reducibility and suitability to infinite domain problems. However, it has a major difficulty in handling inhomogeneous terms such as time-dependent and nonlinear problems. It is over 18 years since the dual reciprocity Method (DRM) was first proposed by Nardini and Brebbia which provides a very general Methodology for obtaining a boundary element solution to wide range of problems. Another obstacle in BEM, just like the FEM, surface mesh or remesh requires costly computation, especially for moving boundary and nonlinear problems. The boundary-type meshless Methods such as the hybrid boundary Node Method (Hybrid-BNM) , the boundary Node Method (BNM) shown an emerging technique to alleviate these drawbacks.
-
Solution of seepage problem with free surface by hybrid boundary Node Method
Rock and Soil Mechanics, 2010Co-Authors: Bang Deng, Dong-ming Zhang, Yuanhan WangAbstract:The seepage problem with a free surface is solved by combining the hybrid boundary Node Method(HBNM) and iterative Method.The HBNM is based on a hybrid displacement variational principle and moving least square(MLS) approximation.The domain variables are interpolated by fundamental solution,while the boundary variables are approximated by MLS.Therefore,the HBNM is a truly boundary-type meshless Method.Only Nodes on the boundary are required and any mesh is not required.At first,the initial position of free surface is assumed;then the solution is obtained by the iterative Method.The numerical example indicates that this Method has high precision,little computation work;and it is suitable for solving various seepage problems with free surfaces.
-
Regular hybrid boundary Node Method for biharmonic problems
Engineering Analysis With Boundary Elements, 2010Co-Authors: Yuanhan Wang, Yu MiaoAbstract:Abstract The regular hybrid boundary Node Method (RHBNM) is a new technique for the numerical solutions of the boundary value problems. By coupling the moving least squares (MLS) approximation with a modified functional, the RHBNM retains the meshless attribute and the reduced dimensionality advantage. Besides, since the source points of the fundamental solutions are located outside the domain, ‘boundary layer effect’ is also avoided. However, an initial restriction of the present Method is that it is only suitable for the problems which the governing differential equation is in second order. Now, a new variational formulation for the RHBNM is presented further to solve the biharmonic problems, in which the governing differential equation is in fourth order. The modified variational functional is applied to form the discrete equations of the RHBNM. The MLS is employed to approximate the boundary variables, while the domain variables are interpolated by a linear combination of fundamental solutions of both the biharmonic equation and Laplace’s equation. Numerical examples for some biharmonic problems show that the high accuracy with a small Node number is achievable. Furthermore, the computation parameters have been studied. They can be chosen in a wide range and have little influence on the results. It is shown that the present Method is effective and can be widely applied in practical engineering.
-
Multiple reciprocity hybrid boundary Node Method for potential problems
Engineering Analysis With Boundary Elements, 2010Co-Authors: Yuanhan WangAbstract:Abstract Meshless Methods have some obvious advantages such as they do not require meshes in the domain and on the boundary, only some Nodes are needed in the computation. Furthermore, for the boundary-type meshless Methods, the Nodes are even not needed in the domain and only distributed on the boundary. Practice shows that boundary-type meshless Methods are effective for homogeneous problems. But for inhomogeneous problems, the application of these boundary-type meshless Methods has some difficulties and need to be studied further. The hybrid boundary Node Method (HBNM) is a boundary-only meshless Method, which is based on the moving least squares (MLS) approximation and the hybrid displacement variational principle. No cell is required either for the interpolation of solution variables or for numerical integration. It has a drawback of ‘boundary layer effect’, so a new regular hybrid boundary Node Method (RHBNM) has been proposed to avoid this pitfall, in which the source points of the fundamental solutions are located outside the domain. These two Methods, however, can only be used for solving homogeneous problems. Combining the dual reciprocity Method (DRM) and the HBNM, the dual reciprocity hybrid boundary Node Method (DRHBNM) has been proposed for the inhomogeneous terms. The DRHBNM requires a substantial number of internal points to interpolate the particular solution by the radial basis function, where approximation based only on boundary Nodes may not guarantee sufficient accuracy. Now a further improvement to the RHBNM, i.e., a combination of the RHBNM and the multiple reciprocity Method (MRM), is presented and called the multiple reciprocity hybrid boundary Node Method (MRHBNM). The solution comprises two parts, i.e., the complementary and particular solutions. The complementary solution is solved by the RHBNM. The particular solution is solved by the MRM, i.e., a sum of high-order homogeneous solutions, which can be approximated by the same-order fundamental solutions. Compared with the DRHBNM, the MRHBNM does not require internal points to obtain the particular solution for inhomogeneous problems. Therefore, the present Method is a real boundary-only meshless Method, and can be used to deal with inhomogeneous problems conveniently. The validity and efficiency of the present Method are demonstrated by a series of numerical examples of inhomogeneous potential problems.
-
Dual reciprocity hybrid boundary Node Method for free vibration analysis
Journal of Sound and Vibration, 2009Co-Authors: Yuanhan Wang, Yu Miao, Y.k. CheungAbstract:Abstract As a truly meshless Method of boundary-type, the hybrid boundary Node Method (HBNM) has the advantages of both boundary element Method (BEM) and meshless Method. The main problem is that it is only suitable for the homogeneous problems. Now, the dual reciprocity Method (DRM) is introduced into HBNM to deal with the integral for the inhomogeneous terms of the governing equations, and the rigid body motion approach is employed to solve the hyper-singular integrations. A new meshless Method named dual reciprocity hybrid boundary Node Method (DRHBNM) is proposed and applied to solve free vibration problems. In this Method, the solution composes into two parts, i.e., the general solution and the particular solution. The general solution is solved by HBNM and the particular one is obtained by DRM. DRHBNM is a true boundary-type meshless Method. It does not require the ‘boundary element mesh’, either for the purpose of interpolation of the variables, or for the integration of ‘energy’. The points in the domain are only used to interpolate particular solution by the radial basis function. Finally, the boundary variables are interpolated by the independent smooth boundary segments. The Q–R algorithm and Householder algorithm are applied to solve the eigenvalues and eigenvectors of the transformed matrix. Numerical examples for free vibration problems show that a good convergence with mesh refinement is achievable and the computational results for the natural circular frequencies and free vibration modes are very accurate. Furthermore, the computation parameters have little influence on the results and can be chosen in a wide range. It is shown that the present Method is effective and can be widely applied in practical engineering.
Xiaolin Li - One of the best experts on this subject based on the ideXlab platform.
-
A meshless complex variable Galerkin boundary Node Method for potential and Stokes problems
Engineering Analysis With Boundary Elements, 2017Co-Authors: Yaozong Tang, Xiaolin LiAbstract:Abstract In this study, combining the boundary integral equations (BIEs) with the complex variable moving least squares (CVMLS) approximation, a symmetric and boundary-only meshless Method, the complex variable Galerkin boundary Node Method (CVGBNM), is developed. Numerical applications and theoretical error estimates of the CVGBNM are derived for BIEs, potential problems and Stokes problems. Finally, numerical examples are given to demonstrate the efficacy of the Method.
-
A meshless interpolating Galerkin boundary Node Method for Stokes flows
Engineering Analysis With Boundary Elements, 2015Co-Authors: Xiaolin LiAbstract:Abstract Combining an improved interpolating moving least-square (IIMLS) scheme and a variational formulation of boundary integral equations, a symmetric and boundary-only meshless Method, which is called the interpolating Galerkin boundary Node Method (IGBNM), is developed in this paper for 2D and 3D Stokes flow problems. The IIMLS is used to form shape functions with delta function property. So unlike the Galerkin boundary Node Method (GBNM), the IGBNM is a direct numerical Method in which the basic unknown quantity is the real solution of nodal variables. Besides, to obtain uniqueness of unknown boundary functions and to retain symmetry of system matrices, a Lagrange multiplier is introduced and then a variational formulation with side conditions is gained. Consequently, in the IGBNM, boundary conditions can be applied directly and easily, and the resulting system matrices are symmetric. Thus, the IGBNM gives greater computational precision than the GBNM. The numerical formulae are valid for 2D and 3D Stokes flows and also valid for both interior and exterior problems simultaneously. The capability of the IGBNM is illustrated and assessed by some numerical examples.
-
Implementation of boundary conditions in BIEs-based meshless Methods: A dual boundary Node Method
Engineering Analysis With Boundary Elements, 2014Co-Authors: Xiaolin LiAbstract:Abstract A new implementation of the boundary Node Method (BNM) is developed in this paper for two- and three-dimensional potential problems. In our implementation, here called the dual boundary Node Method (DBNM), the conventional BIE is applied on the Dirichlet boundary and the hypersingular BIE is applied on the Neumann boundary. The DBNM can apply the boundary conditions directly and easily. And the number of both unknowns and system equations in the DBNM is only half of that in the BNM, thus the computing speed and efficiency are higher. The present Method is applicable to other BIEs-based meshless Methods, such as the boundary cloud Method, the boundary element-free Method and the boundary face Method, in which the used shape functions lack the delta function property. Some numerical examples are given to demonstrate the Method.
-
THE MESHLESS GALERKIN BOUNDARY Node Method FOR TWO-DIMENSIONAL SOLIDS
International Journal of Computational Methods, 2013Co-Authors: Xiaolin LiAbstract:The Galerkin boundary Node Method (GBNM) is developed for two-dimensional solid mechanics problems. The GBNM is a boundary only meshless Method that combines an equivalent variational form of boundary integral formulations for governing equations with the moving least-squares (MLS) approximations for construction of the trial and test functions. In this Method, boundary conditions can be implemented directly and easily despite the MLS shape functions lack the delta function property, and the resulting formulation inherits the symmetry and positive definiteness of the variational problems. The optimal asymptotic error estimates of this approach for displacements and stresses are derived in detail in Sobolev spaces. Numerical tests are also given to demonstrate the developed algorithms.
-
Application of the meshless Galerkin boundary Node Method to potential problems with mixed boundary conditions
Engineering Analysis With Boundary Elements, 2012Co-Authors: Xiaolin LiAbstract:Abstract In this paper, the meshless Galerkin boundary Node Method is developed for boundary-only analysis of two- and three-dimensional potential problems with mixed boundary conditions of Dirichlet and Neumann type. This meshless algorithm leads to a symmetric and positive definite system of linear equations. Additionally, boundary conditions can be implemented directly and easily despite the fact that the employed meshless shape functions lack the delta function property. Theoretical error analysis and numerical results indicate that it is an efficient and accurate numerical Method.
Miao Yu - One of the best experts on this subject based on the ideXlab platform.
-
Singular Hybrid Boundary Node Method in Solving Torsion Problems
Journal of Huazhong University of Science and Technology, 2020Co-Authors: Miao YuAbstract:A new boundary type meshless Method,which is called singular hybrid boundary Node Method(SHBNM),is presented for solving torsion problems.It is based on a modified variational principle and moving least squares(MLS) approximation,and exploiting the localization idea from MLBIE,Only randomly distributed nodal points on the bounding surface of the domain are required in computation,so it has the advantages of both BEM and meshless Methods.The dual reciprocity Method(DRM) is combined with SHBNM to solve torsion problems.The solution of the problem is devided into particular solution and homogeneous solution.The homogeneous solution is solved by means of SHBNM,and the particular solution is approximated by using radial basis functions.And the interior integrals can be avoided.The rigid movement Method is employed to solve the hyper-singular integrations.The boundary layer effect,which is the main drawback of the boundary type mothods,has been overcome by an adaptive integration scheme.Numerical examples show high accuracy and high convergence rates of the presented scheme.
-
Title Dual Reciprocity Hybrid Boundary Node Method for Helmholtz Equation
Journal of Hunan University, 2020Co-Authors: Miao YuAbstract:This paper presented a new boundary-type meshless Method,Dual Hybrid Boundary Node Method(DHBNM),which combines the Hybrid BNM with the Dual Reciprocity Method(DRM),to solve Helmholtz equation.In this Method,the solution of Helmholtz problem was divided into two parts,namely,the general solution and the particular solution.The general solution was solved by means of Hybrid BNM and the particular one was obtained with DRM.The proposed Method retains the characteristics of the meshless Method and BEM,which only requires discrete Nodes constructed on the boundary of a domain,and several Nodes in the domain are needed just for the RBF interpolation.The parameters that influence the performance of this Method were studied with numerical examples.Numerical results for the solution of Helmholtz equation have shown that high convergence rates and high accuracy can be achieved.
-
APPLICATION OF DUAL RECIPROCITY HYBRID BOUNDARY Node Method IN POTENTIAL PROBLEMS
Mechanics in Engineering, 2020Co-Authors: Sima Yuzhou, Zhu Hongping, Miao YuAbstract:The hybrid boundary Node Method (HBNM) and the dual reciprocity Method (DRM) are combined for solving potential problems in this paper.As a boundary-type meshless Method,the HBNM is based on a modified variational principle and moving least squares (MLS) approximation,with the advantages of both BEM and meshless Methods.The solution of potential problems is expressed as the sum of a particular solution and a homogeneous solution.The homogeneous solution is solved by means of HBNM,and the particular solution is approximated by using radial base functions.Only for discretely distributed nodal points on the boundary surface of the domain input data are required and without other extra equations to compute internal parameters in the domain.The postprocessing is very simple.Numerical examples show high accuracy and high convergence rates of the presented scheme.
-
Meshless Analysis for Three-Dimensional Elasticity With Singular Hybrid Boundary Node Method
Applied Mathematics and Mechanics-english Edition, 2006Co-Authors: Miao Yu, Wang Yuan-hanAbstract: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.
