Y. Miao¹, T.G. HE¹, H. Luo^1,2, H.P. Zhu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.6, pp. 481-498, 2012, DOI:10.3970/cmes.2012.085.481

Abstract Combined the hybrid boundary node method (Hybrid BNM) and the dual reciprocity principle, a truly boundary-type meshless method, namely, dual hybrid boundary node method (Dual Hybrid BNM) is presented for solving transient dynamic fracture problems. The enriched basis functions in moving least squares (MLS) approximation is presented for simulating the singularity of the stress field on the tip of the fracture. The solution in Dual Hybrid BNM is divided into particular solution and complementary solution. The complementary solution is solved by means of Hybrid BNM, and the particular solution is approximated by using radial basis More >

F. Tan^1,2, Y.L. Zhang¹, Y.H. Wang³, Y. Miao³

CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.1, pp. 1-32, 2011, DOI:10.3970/cmes.2011.075.001

Abstract The meshless hybrid boundary node method (HBNM) for solving the bending problem of the Kirchhoff thin plate is presented and discussed in the present paper. In this method, the solution is divided into two parts, i.e. the complementary solution and the particular solution. The particular solution is approximated by the radial basis function (RBF) via dual reciprocity method (DRM), while the complementary one is solved by means of HBNM. The discrete equations of HBNM are obtained from a variational principle using a modified hybrid functional, in which the independent variables are the generalized displacements and… More >

Chia-Cheng Tsai ¹

CMC-Computers, Materials & Continua, Vol.22, No.3, pp. 197-218, 2011, DOI:10.3970/cmc.2011.022.197

Abstract This paper describes the combination of the method of fundamental solutions (MFS) and the dual reciprocity method (DRM) as a meshless numerical method to solve problems of Kirchhoff plates under arbitrary loadings. In the solution procedure, a arbitrary distributed loading is first approximated by either the multiquadrics (MQ) or the augmented polyharmonic splines (APS), which are constructed by splines and monomials. The particular solutions of multiquadrics, splines and monomials are all derived analytically and explicitly. Then, the complementary solutions are solved formally by the MFS. Furthermore, the boundary conditions of lateral displacement, slope, normal moment,… More >

Yu Miao¹, Qiao Wang¹, Bihai Liao^1,2, Junjie Zheng¹

CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.1, pp. 1-22, 2009, DOI:10.3970/cmes.2009.053.001

Abstract As a truly meshless method, the Hybrid Boundary Node method (Hybrid BNM) does not require a `boundary element mesh', either for the purpose of interpolation of the solution variables or for the integration of `energy'. This paper presents a further development of the Hybrid BNM to the 2D elastodynamics. Based on the radial basis function (RBF) and the Hybrid BNM, it presents an inherently meshless, boundary-only technique, which named dual hybrid boundary node method (DHBNM), for solving 2D elastodynamics. In this study, the RBFs are employed to approximate the inhomogeneous terms via dual reciprocity method More >

F. Yan^1,2, Y. Miao^2,3, Q. N. Yang²

CMES-Computer Modeling in Engineering & Sciences, Vol.46, No.1, pp. 21-50, 2009, DOI:10.3970/cmes.2009.046.021

Abstract A novel boundary type meshless method called Quasilinear Hybrid Boundary Node Method (QHBNM), which combines quasilinearization method, dual reciprocity method (DRM) and hybrid boundary node method (HBNM), is developed to solving a class of nonlinear problems. The nonlinear term of the governing equation is linearized by the generated quasilinearization method, in which the solution of the linearized equation can exactly converge to the solution of original equation at a very wide range initial value, and the convergence rate is quadratic. Then dual hybrid boundary node method is applied to solving the linearized equation, in which… More >

G. Dziatkiewicz¹ and P. Fedelinski¹

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.1, pp. 35-46, 2007, DOI:10.3970/cmes.2007.017.035

Abstract The aim of the present work is to show the formulation and application of the dual reciprocity boundary element method (BEM) to free vibrations of two-dimensional piezoelectric structures. The piezoelectric materials are modelled as homogenous, linear -- elastic, transversal isotropic and dielectric. Displacements and electric potentials are treated as generalized displacements and tractions and electric charge flux densities are treated as generalized tractions. The static fundamental solutions, which are required in the proposed approach, are derived using the Stroh formalism. The domain inertial integral is transformed to the equivalent boundary integral using the dual reciprocity More >

C.C. Tsai¹, D.L. Young², A.H.-D. Cheng³

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.1, pp. 117-128, 2002, DOI:10.3970/cmes.2002.003.117

Abstract This paper describes a combination of the dual reciprocity method (DRM) and the method of fundamental solution (MFS) as a meshless BEM (DRM-MFS) to solve three-dimensional Stokes flow problems by the velocity-vorticity formulation, where the DRM is based on the compactly supported, positive definite radial basis functions (CS-PD-RBF). In the velocity-vorticity formulation, both of the diffusion type vorticity equations and the Poisson type velocity equations are solved by DRM-MFS. Here a typical internal cubic cavity flow and an external flow past a sphere are presented. The results are acceptable. Furthermore, this paper provides a preliminary More >