J. Sladek¹, V. Sladek¹, Ch. Zhang², C.L. Tan³

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.1, pp. 57-68, 2006, DOI:10.3970/cmes.2006.016.057

Abstract The Meshless Local Petrov-Galerkin (MLPG) method for linear transient coupled thermoelastic analysis is presented. Orthotropic material properties are considered here. A Heaviside step function as the test functions is applied in the weak-form to derive local integral equations for solving two-dimensional (2-D) problems. In transient coupled thermoelasticity an inertial term appears in the equations of motion. The second governing equation derived from the energy balance in coupled thermoelasticity has a diffusive character. To eliminate the time-dependence in these equations, the Laplace-transform technique is applied to both of them. Local integral equations are written on small sub-domains with a circular shape.… More >

Jin Ma, Yang Liu, Hongbing Lu, Ranga Komanduri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.1, pp. 41-56, 2006, DOI:10.3970/cmes.2006.016.041

Abstract A multiscale simulation technique coupling three scales, namely, the molecular dynamics (MD) at the atomistic scale, the discrete dislocations at the meso scale and the generalized interpolation material point (GIMP) method at the continuum scale is presented. Discrete dislocations are first coupled with GIMP using the principle of superposition (van der Giessen and Needleman (1995)). A detection band seeded in the MD region is used to pass the dislocations to and from the MD simulations (Shilkrot, Miller and Curtin (2004)). A common domain decomposition scheme for each of the three scales was implemented for parallel processing. Simulations of indentation were… More >

K.H. Chen¹, J.T. Chen², J.H. Kao³

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.1, pp. 27-40, 2006, DOI:10.3970/cmes.2006.016.027

Abstract In this paper, we employ the regularized meshless method (RMM) to search for eigenfrequency of two-dimension acoustics with multiply-connected domain. The solution is represented by using the double layer potentials. The source points can be located on the physical boundary not alike method of fundamental solutions (MFS) after using the proposed technique to regularize the singularity and hypersingularity of the kernel functions. The troublesome singularity in the MFS methods is desingularized and the diagonal terms of influence matrices are determined by employing the subtracting and adding-back technique. Spurious eigenvalues are filtered out by using singular value decomposition (SVD) updating term… More >

Y.C. Shiah¹, Y.C. Lin¹, C. L. Tan²

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.1, pp. 15-26, 2006, DOI:10.3970/cmes.2006.016.015

Abstract In this paper, the order of singularity of the integrals appearing in the boundary integral equation for two-dimensional BEM analysis in anisotropic elasticity is reduced using integration by parts. The integral containing the traction fundamental solution is then analytically integrated to give an exact formulation for a general element of n-order interpolation of the variables. This allows the integrals to be very accurately evaluated even for very thin, slender bodies without the need for excessively refined meshes as in conventional BEM analysis. Three example problems involving thin, layered materials are presented to demonstrate the veracity and successful implementation of the… More >

Fabian M. E. Duddeck¹

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.1, pp. 1-14, 2006, DOI:10.3970/cmes.2006.016.001

Abstract In general, the use of Boundary Element Methods (BEM) is restricted to physical cases for which a fundamental solution can be obtained. For simple differential operators (e.g. isotropic elasticity) these special solutions are known in their explicit form. Hence, the realization of the BEM is straight forward. For more complicated problems (e.g. anisotropic materials), we can only construct the fundamental solution numerically. This is normally done before the actual problem is tackled; the values of the fundamental solutions are stored in a table and all values needed later are interpolated from these entries. The drawbacks of this approach lie in… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 179-196, 2006, DOI:10.3970/cmes.2006.015.179

Abstract This paper studies the numerical computations of the second-order singularly perturbed boundary value problems (SPBVPs). In order to depress the singularity we consider a coordinate transformation from the x-domain to the t-domain. The relation between singularity and stiffness is demonstrated, of which the coordinate transformation parameter λ plays a key role to balance these two tendencies. Then we construct a very effective Lie-group shooting method to search the missing initial condition through a weighting factor r ∈ (0,1) in the t-domain formulation. For stabilizing the new method we also introduce two new systems by a translation of the dependent variable.… More >

B. Yang², V. K. Tewary³

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 165-178, 2006, DOI:10.3970/cmes.2006.015.165

Abstract Green's function (GF) modeling of defects may take effect only if the GF as well as its various integrals over a line, a surface and/or a volume can be efficiently evaluated. The GF is needed in modeling a point defect, while integrals are needed in modeling line, surface and volumetric defects. In a matrix of multilayered, generally anisotropic and linearly elastic and piezoelectric materials, the GF has been derived by applying 2D Fourier transforms and the Stroh formalism. Its use involves another two dimensions of integration in the Fourier inverse transform. A semi-analytical scheme has been developed previously for efficient… More >

A. Wacher¹, D. Givoli²

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 147-164, 2006, DOI:10.3970/cmes.2006.015.147

Abstract The recently proposed String Gradient Weighted Moving Finite Element (SGWMFE) method is extended to include remeshing and refining. The method simultaneously determines, at each time step, the solution of the governing partial differential equations and an optimal location of the finite element nodes. It has previously been applied to the nonlinear time-dependent two-dimensional shallow water equations, under the demanding conditions of large Coriolis forces, inducing large mesh and field rotation. Such effects are of major importance in geophysical fluid dynamics applications. Two deficiencies of the original SGWMFE method are (1) possible tangling of the mesh which causes the method's failure,… More >

S. Chantasiriwan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 137-146, 2006, DOI:10.3970/cmes.2006.015.137

Abstract The multiquadric collocation method is the collocation method based on radial basis function known as multiquadrics. It has been successfully used to solve several linear and nonlinear problems. Although fluid flow problems are among problems previously solved by this method, there is still an outstanding issue regarding the influence of the free parameter of multiquadrics (or the shape parameter) on the performance of the method. This paper provides additional results of using the multiquadric collocation method to solve the lid-driven cavity flow problem. The method is used to solve the problem in the stream function-vorticity formulation and the velocity-vorticity formulation.… More >

G. Kakuba¹, R.M.M. Mattheij², M.J.H. Anthonissen³

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 127-136, 2006, DOI:10.3970/cmes.2006.015.127

Abstract This paper presents an efficient way to implement the Boundary Element Method (BEM) to capture high activity regions in a boundary value problem. In boundary regions where accuracy is critical, like in adaptive surface meshes, the method of choice is Local Defect Correction (LDC). We formulate the method and demonstrate its applicability and reliability by means of an example. Numerical results show that LDC and BEM together provide accurate solutions with less computational requirements given that BEM systems usually consist of dense matrices. More >