Z.Y. Qian, Z.D. Han¹, S.N. Atluri^{1, 2}

CMES-Computer Modeling in Engineering & Sciences, Vol.91, No.6, pp. 463-484, 2013, DOI:10.3970/cmes.2013.091.463

Abstract To predict the sound field in an acoustic problem, the well-known non-uniqueness problem has to be solved. In a departure from the common approaches used in the prior literature, the weak-form of the Helmholtz differential equation, in conjunction with vector test-functions, is utilized as the basis, in order to directly derive non-hyper-singular boundary integral equations for the velocity potential ∅, as well as its gradients q;. Both ∅-BIE and q-BIE are fully regularized to achieve weak singularities at the boundary [i.e., containing singularities of O(r^-1)]. Collocation-based boundary-element numerical approaches [denoted as BEM-R-∅-BIE, and BEM-R-q-BIE] are implemented to More >

E.J. Sellountos¹, D. Polyzos², S.N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.89, No.6, pp. 513-551, 2012, DOI:10.3970/cmes.2012.089.513

Abstract A new meshless Local Boundary Integral Equation (LBIE) method for solving two-dimensional elastostatic problems is proposed. Randomly distributed points without any connectivity requirement cover the analyzed domain and Local Radial Basis Functions (LRBFs) are employed for the meshless interpolation of displacements. For each point a circular support domain is centered and a local integral representation for displacements is considered. At the local circular boundaries tractions are eliminated with the aid of companion solution, while at the intersections between the local domains and the global boundary displacements and tractions are treated as independent variables avoiding thus More >

Chih-Wen Chang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.2, pp. 65-92, 2012, DOI:10.3970/cmes.2012.088.065

Abstract We utilize a regularized integral equation scheme to resolve the three-dimensional backward advection-dispersion equation (BADE) for identifying the groundwater pollution source identification problems in this research. First, the Fourier series expansion method is employed to estimate the concentration field C(x, y, z, t) at any time t < T. Second, we contemplate a direct regularization by adding an extra term a(x, y, z, 0) to transform a second-kind Fredholm integral equation for C(x, y, z, 0). The termwise separable property of the kernel function permits us to acquire a closed-form regularized solution. In addition, a More >

A. Sellier

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.2, pp. 157-176, 2012, DOI:10.3970/cmes.2012.087.157

Abstract A new approach is proposed to accurately compute at a reasonable cpu time cost the hydrodynamic net force and net torque exerted on a slip and arbitrarily-shaped solid particle experiencing a prescribed slow rigid-body migration in a quiescent Newtonian liquid. The advocated method appeals to a boundary formulation which makes it possible to reduce the task to the treatment of a relevant regularized boundary-integral equation on the particle slipping surface. This integral equation is numerically inverted by implementing a boundary element collocation method. In addition to benchmark tests against analytical and numerical results available in 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… 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. 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… 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 More >

Dan Ma, Xianbiao Mao, Chong Li, Feng Du

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.6, pp. 561-574, 2012, DOI:10.3970/cmes.2012.083.561

Abstract Water resisting key strata (WRKS) is one of the most important structures in green coal mining engineering, which has the functions of water-preserved mining and disaster prevention of water inrush, while elastic WRKS is treated as one of the problems for elastic plates in this paper. The existing literatures on elastic plates have largely restricted to different engineering but minority in coal mining engineering. Based on the mechanical models of clamped circular plate with sub-uniform load and simply supported by a concentrated force for elastic WRKS, using the boundary integral equations which is obtained by More >

Xiaoping Zhang

The International Conference on Computational & Experimental Engineering and Sciences, Vol.18, No.2, pp. 35-36, 2011, DOI:10.3970/icces.2011.018.035

Abstract In this paper, we first discuss the midpoint rule for evaluating hypersingular integrals with the kernel \qopname \relax osin-2(x-s)/2 defined on a circle, and the key point is placed on its pointwise superconvergence phenomenon. We show that this phenomenon occurs when the singular point s is located at the midpoint of each subinterval and obtain the corresponding supercovergence analysis. Then we apply the rule to construct a collocation scheme for solving the relevant hypersingular integral equation, by choosing the midpoints as the collocation points. It's interesting that the inverse of coefficient matrix for the resulting More >