Ch. Zhang²

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.3, pp. 381-398, 2002, DOI:10.3970/cmes.2002.003.381

Abstract A 2-D time-domain boundary integral equation method (BIEM) for transient dynamic analysis of cracked orthotropic solids is presented in this paper. A finite crack in an unbounded orthotropic solid subjected to an impact loading is considered. Hypersingular time-domain traction boundary integral equations (BIEs) are applied in the analysis. A time-stepping scheme is developed for solving the hypersingular time-domain traction BIEs. The scheme uses a convolution quadrature formula for temporal and a Galerkin method for spatial discretizations. Numerical examples are given to show that the presented time-domain BIEM is highly efficient and accurate. More >

G. Cocchetti², G. Maier², X. P. Shen³

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.3, pp. 279-298, 2002, DOI:10.3970/cmes.2002.003.279

Abstract Interface models mean here relationships between displacement jumps and tractions across a locus of displacement discontinuities. Frictional contact and quasi-brittle fracture interpreted by cohesive crack models are typical mechanical situations concerned by the present unifying approach. Plastic-softening multidissipative interface models are studied in piecewise linear formats, i.e. assuming linearity for yield functions, plastic potentials and relationships between static and kinematic internal variables. The properties and the pros and cons of such simplified models in a variety of formulations (fully non-holonomic in rates, holonomic and in finite steps), all mathematically described as linear complementarity problems, are comparatively investigated in view of… More >

J.H. Lv¹, Y. Miao^1,2, H.P. Zhu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.91, No.2, pp. 101-117, 2013, DOI:10.3970/cmes.2013.091.101

Abstract The accurate and efficient evaluation of nearly singular integrals is one of the major concerned problems in the implementation of the boundary element method (BEM). Among the various commonly used nonlinear transformation methods, the distance transformation technique seems to be a promising method to deal with various orders of nearly singular integrals both in potential and elasticity problems. In this paper, some drawbacks of the conventional distance transformation, such as the sensitivity to the position of projection point, are investigated by numerical tests. A general distance transformation technique is developed to circumvent these drawbacks, which is aimed to remove or… More >

Xinhua Liu^1,2, Yongzhi Liu¹, Hao Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.91, No.1, pp. 65-80, 2013, DOI:10.3970/cmes.2013.091.065

Abstract In order to study the rheological characteristics of magnetorheological fluids, a simulation approach through integration of Monte Carlo method and GPU accelerated technology was proposed and the three-dimensional micro-structure of magnetic particles in different strength magnetic fields were simulated. The Monte Carlo method to magnetic particles of magnetorheological fluids and its key steps such as particle modeling, magnetic energy equations calculating and system state updating were elaborated. Moreover, GPU accelerated technology was applied to the simulation of magnetorheological fluids to reduce computational time and a flowchart for the proposed approach was designed. Finally, a physics experiment was carried out and… More >

Y.C. Shiah¹, C. L. Tan², C.Y. Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.1, pp. 1-22, 2012, DOI:10.3970/cmes.2012.087.001

Abstract The fundamental solution, or Green's function, for 3D anisotropic elastostatics as derived by Ting and Lee (1997) [Q.J. Mech. Appl. Math.; 50: 407-426] is one that is fully explicit and algebraic in form. It has, however, only been utilized in boundary element method (BEM) formulations quite recently even though it is relatively straightforward and direct to implement. This Green's function and its derivatives are necessary items in this numerical analysis technique. By virtue of the periodic nature of the angles when it is expressed in the spherical coordinate system, the present authors have very recently represented the Green's function as… More >

J. Sladek¹, V. Sladek¹, P. Stanak¹, P.H. Wen², S.N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.6, pp. 543-572, 2012, DOI:10.3970/cmes.2012.085.543

Abstract A meshless local Petrov-Galerkin (MLPG) method is applied to solve laminate piezoelectric plates described by the Reissner-Mindlin theory. The piezoelectric layer can be used as a sensor or actuator. A pure mechanical load or electric potential are prescribed on the top of the laminated plate. Both stationary and transient dynamic loads are analyzed here. The bending moment, the shear force and normal force expressions are obtained by integration through the laminated plate for the considered constitutive equations in each lamina. Then, the original three-dimensional (3-D) thick plate problem is reduced to a two-dimensional (2-D) problem. Nodal points are randomly distributed… More >

C.-D. Tran¹, N. Mai-Duy^1,1, K. Le-Cao¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.6, pp. 499-520, 2012, DOI:10.3970/cmes.2012.085.499

Abstract A numerical computation of continuum-microscopic model for visco-elastic flows based on the Integrated Radial Basis Function (IRBF) Control Volume and the Stochastic Simulation Techniques (SST) is reported in this paper. The macroscopic flow equations are closed by a stochastic equation for the extra stress at the microscopic level. The former are discretised by a 1D-IRBF-CV method while the latter is integrated with Euler explicit or Predictor-Corrector schemes. Modelling is very efficient as it is based on Cartesian grid, while the integrated RBF approach enhances both the stability of the procedure and the accuracy of the solution. The proposed method is… More >

Roman Chapko¹, B. Tomas Johansson²

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.2, pp. 105-128, 2012, DOI:10.3970/cmes.2012.085.105

Abstract We consider a Cauchy problem for the Laplace equation in a 3-dimen -sional semi-infinite domain that contains a bounded inclusion. The canonical situation is the upper half-space in I\tmspace -.1667em R3 containing a bounded smooth domain. The function value of the solution is specified throughout the plane bounding the upper half-space, and the normal derivative is given only on a finite portion of this plane. The aim is to reconstruct the solution on the surface of the bounded inclusion. This is a generalisation of the situation in Chapko and Johansson (2008) to three-dimensions and with Cauchy data only partially given.… More >

Ahmad Shirzadi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.1, pp. 45-64, 2012, DOI:10.3970/cmes.2012.085.045

Abstract This paper presents a meshless method based on the meshless local integral equation (LIE) method for solving the two-dimensional diffusion and diffusion-convection equations subject to a non-local condition. Suitable finite difference scheme is used to eliminate the time dependence of the problem. A weak formulation on local subdomains with employing the fundamental solution of the Laplace equation as test function transforms the resultant elliptic type equations into local integral equations. Then, the Moving Least Squares (MLS) approximation is employed for discretizing spatial variables. Two illustrative examples with exact solutions being used as benchmark solutions are presented to show the efficiency… More >

N. Thai-Quang¹, K. Le-Cao¹, N. Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.6, pp. 528-558, 2012, DOI:10.3970/cmes.2012.084.528

Abstract This study is concerned with the development of integrated radial-basis-function (IRBF) method for the simulation of two-dimensional steady-state incompressible viscous flows governed by the pressure-velocity formulation on Cartesian grids. Instead of using low-order polynomial interpolants, a high-order compact local IRBF scheme is employed to represent the convection and diffusion terms. Furthermore, an effective boundary treatment for the pressure variable, where Neumann boundary conditions are transformed into Dirichlet ones, is proposed. This transformation is based on global 1D-IRBF approximators using values of the pressure at interior nodes along a grid line and first-order derivative values of the pressure at the two… More >