Chien-Ching Ma^1,2, Wen-Cha Wu²

CMC-Computers, Materials & Continua, Vol.11, No.2, pp. 79-108, 2009, DOI:10.3970/cmc.2009.011.079

Abstract The two-dimensional problem of a planar transversely isotropic piezoelectric layered half-plane subjected to generalized line forces and edge dislocations in the layer is analyzed by using the Fourier-transform method and the series expansion technique. The full-field solutions for displacements, stresses, electrical displacements and electric fields are expressed in explicit closed forms. The complete solutions consist only of the simplest solutions for an infinite piezoelectric medium with applied loadings. It is shown in this study that the physical meaning of this solution is the image method. The explicit solutions include Green's function for originally applied loadings… More >

Xuefei He¹, Kian-Meng Lim^1,2,3, Siak-Piang Lim^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.1, pp. 21-48, 2008, DOI:10.3970/cmes.2008.035.021

Abstract The boundary element method (BEM) is known to have the advantage of reducing the dimension of problem by discretizing only the boundary of the domain. But it becomes less attractive for solving Poisson-type equations, due to the need to evaluate the domain integral which is computationally expensive. In this paper, we present the extension of a recently developed fast algorithm for Laplace equation, based on fast Fourier transform on multipoles (FFTM), to solve large scale 3D Poisson-type equations. We combined the Laplace solver with two fast methods for handling the domain integral based on fast More >

B. Yang², V. K. Tewary³

CMC-Computers, Materials & Continua, Vol.8, No.1, pp. 23-32, 2008, DOI:10.3970/cmc.2008.008.023

Abstract A three-dimensional Green's function for a material system consisting of anisotropic and linearly elastic planar multilayers with interfacial membrane and flexural rigidities has been derived. The Stroh formalism and two-dimensional Fourier transforms are applied to derive the general solution for each homogeneous layer. The Green's function for the multilayers is then solved by imposing the surface boundary condition, the interfacial displacement continuity condition, and the interfacial traction discontinuity condition. The last condition is given by the membrane and bending equilibrium equations of the interphases modeled as Kirchhoff plates. Numerical results that demonstrate the validity and 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… 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… More >

Chun-Ying Wu^1,3, Xue-Yan Liu², A. Scarpas², Xiu-Run Ge³

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.2, pp. 149-158, 2006, DOI:10.3970/cmes.2006.012.149

Abstract For the spectral analysis of the three-dimensional multi-layered pavement, 3D layer spectral element method is presented to solve the problems of bounded layer system subjected to a transient load pulse. In spectral element, each layer is treated as one spectral element. The wave propagation inside each layer element is achieved by the superposition of the incident wave and the reflection wave. Fast Fourier transformation is used to transform FWD datum from time domain to frequency domain. The accuracy and efficiency of 3D layer spectral element approach were verified by analyzing the Falling weight deflectometer(FWD) testing More >

M. M. Rahman¹, A. K. Ariffin¹, N. Jamaludin¹, C. H. C. Haron¹

Structural Durability & Health Monitoring, Vol.1, No.2, pp. 121-130, 2005, DOI:10.3970/sdhm.2005.001.121

Abstract The focus of this paper is to design a new two-stroke linear generator engine. This paper describes the finite element based vibration fatigue analysis techniques that can be used to predict fatigue life using total life approach. Fatigue damage in traditionally determined from time signals of loading, usually in the form of stress and strain. However, there are scenarios when a spectral form of loading is more appropriate. In this case the loading is defined in terms of its magnitude at different frequencies in the form of a power spectral density (PSD) plot. A power… More >

Julieta António^1,2, António Tadeu², Luís Godinho², Nuno Simões²

CMC-Computers, Materials & Continua, Vol.2, No.1, pp. 1-12, 2005, DOI:10.3970/cmc.2005.002.001

Abstract The evaluation of heat propagation in the time domain generated by transient heat sources placed in the presence of three-dimensional media requires the use of computationally demanding numerical schemes. The implementation of numerical 3D solutions may benefit from the existence of benchmark solutions to test the accuracy of approximate schemes.
With this purpose inmind, this article presents analyticalnumerical solutions to evaluate the heat-field elicited by monopole heat sources in the presence of three different inclusions, namely, a cylindrical circular solid inclusion, a cylindrical circular cavity with null fluxes and a cavity with null temperatures prescribed along… More >

W. J. Mansur¹, A. I. Abreu¹, J. A. M. Carrer¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.1, pp. 31-42, 2004, DOI:10.3970/cmes.2004.006.031

Abstract This work is concerned with the computation of the contribution of initial conditions in two-dimensional (2D) frequency-domain analysis of transient scalar wave propagation problems with the corresponding Boundary Element Method (BEM) formulation. The paper describes how pseudo-forces, represented by generalized functions, can replace the initial conditions, related to the potential and its time derivative. The generation of such pseudo-forces is the subject of a detailed discussion. The formulation presented here carries out Discrete Fourier Transform (Direct: DFT, and Inverse: IDFT) via FFT (Fast Fourier Transform) algorithms. At the end of the paper four examples are More >

T. Tsangaris¹, Y.–S. Smyrlis^{1, 2}, A. Karageorghis^{1, 2}

CMC-Computers, Materials & Continua, Vol.1, No.3, pp. 245-258, 2004, DOI:10.3970/cmc.2004.001.245

Abstract The Method of Fundamental Solutions (MFS) is a boundary-type method for the solution of certain elliptic boundary value problems. In this work, we develop an efficient matrix decomposition MFS algorithm for the solution of biharmonic problems in annular domains. The circulant structure of the matrices involved in the MFS discretization is exploited by using Fast Fourier Transforms. The algorithm is tested numerically on several examples. More >