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• Open Access

ARTICLE

### A Novel Localized Meshless Method for Solving Transient Heat Conduction Problems in Complicated Domains

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2407-2424, 2023, DOI:10.32604/cmes.2023.024884

Abstract This paper first attempts to solve the transient heat conduction problem by combining the recently proposed local knot method (LKM) with the dual reciprocity method (DRM). Firstly, the temporal derivative is discretized by a finite difference scheme, and thus the governing equation of transient heat transfer is transformed into a non-homogeneous modified Helmholtz equation. Secondly, the solution of the non-homogeneous modified Helmholtz equation is decomposed into a particular solution and a homogeneous solution. And then, the DRM and LKM are used to solve the particular solution of the non-homogeneous equation and the homogeneous solution of the modified Helmholtz equation, respectively.… More >

• Open Access

ARTICLE

### Complete Solid Buckling Analysis With Boundary Face Method

CMES-Computer Modeling in Engineering & Sciences, Vol.98, No.5, pp. 487-508, 2014, DOI:10.3970/cmes.2014.098.487

Abstract In this paper, we will propose a new concept, namely the Complete Solid Buckling Analysis, in which the deformation assumptions for rods, beams and plates are all discarded, and the entire structure, including all its local smallsized features, is modeled as a three-dimensional (3D) solid according to its real shape and dimensions. Firstly, we derive a new control equation, in which physical variables in three directions are considered. Then, an equivalent Boundary Integral Equation (BIE) is derived from the control equation. In the numerical implementation, the Boundary Face Method is employed, by which analyses can be performed directly on the… More >

• Open Access

ARTICLE

### A Novel Method for Solving One-, Two- and Three-Dimensional Problems with Nonlinear Equation of the Poisson Type

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.4, pp. 355-386, 2012, DOI:10.3970/cmes.2012.087.355

Abstract The paper presents a new meshless numerical technique for solving nonlinear Poisson-type equation 2u = f (x) + F(u,x) for x ∈ Rd, d =1,2,3. We assume that the nonlinear term can be represented as a linear combination of basis functions F(u,x) = ∑mMqmφm. We use the basis functions φm of three types: the the monomials, the trigonometric functions and the multiquadric radial basis functions. For basis functions φm of each kind there exist particular solutions of the equation 2ϕm = φm in an analytic form. This permits to write the approximate solution in the form uM = ufMore >

• Open Access

ARTICLE

### A Meshless Hybrid Boundary Node Method for Kirchhoff Plate Bending Problems

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 generalized tractions on the boundary… More >

• Open Access

ARTICLE

### Dual Hybrid Boundary Node Method for Solving Transient Dynamic Fracture Problems

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 functions (RBF). The inner nodes… More >

• Open Access

ARTICLE

### A Dual Hybrid Boundary Node Method for 2D Elastodynamics Problems

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 (DRM), while the general solution… More >

• Open Access

ARTICLE

### Quasilinear Hybrid Boundary Node Method for Solving Nonlinear Problems

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 DRM is introduced into HBNM… More >

• Open Access

ARTICLE

### Dynamic Analysis of Piezoelectric Structures by the Dual Reciprocity Boundary Element Method

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 method (DRM). The boundary quantities… More >

• Open Access

ARTICLE

### Meshless BEM for Three-dimensional Stokes Flows

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 work for applications to the… More >

• Open Access

ARTICLE

### An Efficient Mesh-Free Method for Nonlinear Reaction-Diffusion Equations

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.1, pp. 87-96, 2001, DOI:10.3970/cmes.2001.002.087

Abstract The purpose of this paper is to develop a highly efficient mesh-free method for solving nonlinear diffusion-reaction equations in Rd, d=2, 3. Using various time difference schemes, a given time-dependent problem can be reduced to solving a series of inhomogeneous Helmholtz-type equations. The solution of these problems can then be further reduced to evaluating particular solutions and the solution of related homogeneous equations. Recently, radial basis functions have been successfully implemented to evaluate particular solutions for Possion-type equations. A more general approach has been developed in extending this capability to obtain particular solutions for Helmholtz-type equations by using polyharmonic spline… More >

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