CMES-Vol. 16, No. 1, 2006

Open Access

ARTICLE

An Alternative Approach to Boundary Element Methods via the Fourier Transform
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… More >

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ARTICLE

Boundary Element Stress Analysis of Thin Layered Anisotropic Bodies
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 More >

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Regularized Meshless Method for Solving Acoustic Eigenproblem with Multiply-Connected Domain
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 More >

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Multiscale Simulation of Nanoindentation Using the Generalized Interpolation Material Point (GIMP) Method, Dislocation Dynamics (DD) and Molecular Dynamics (MD)
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 More >

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Meshless Local Petrov-Galerkin Method for Linear Coupled Thermoelastic Analysis
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 More >

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