Open Access
ARTICLE
Yueting Zhou1, Xing Li2, Dehao Yu1
CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.3, pp. 191-222, 2009, DOI:10.3970/cmes.2009.043.191
Abstract The transient response of an orthotropic functionally graded strip with a partially insulated crack under convective heat transfer supply is considered. It is modeled there exists thermal resistant in the heat conduction through the crack region. The mixed boundary value problems of the temperature field and displacement field are reduced to a system of singular integral equations in Laplace domain. The expressions with high order asymptotic terms for the singular integral kernel are considered to improve the accuracy and efficiency. The numerical results present the effect of the material nonhomogeneous parameters, the orthotropic parameters and dimensionless thermal resistant on the… More >
Open Access
ARTICLE
J. Sladek1, V. Sladek1, P. Solek2
CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.3, pp. 223-252, 2009, DOI:10.3970/cmes.2009.043.223
Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for solution of static and elastodynamic problems in 3-D continuously non-homogeneous anisotropic bodies. Functionally graded materials (FGM) are multi-phase materials with the phase volume fractions varying gradually in space, in a pre-determined profile. The Heaviside step function is used as the test functions in the local weak form resulting into the derived local integral equations (LIEs). For transient elastodynamic problems either the Laplace transform or the time difference techniques are applied. Nodal points are randomly distributed in the 3D analyzed domain and each node is surrounded by a spherical… More >
Open Access
ARTICLE
Chein-Shan Liu1, Satya N. Atluri2
CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.3, pp. 253-276, 2009, DOI:10.3970/cmes.2009.043.253
Abstract Since the works of Newton and Lagrange, interpolation had been a mature technique in the numerical mathematics. Among the many interpolation methods, global or piecewise, the polynomial interpolation p(x) = a0 + a1x + ... + anxn expanded by the monomials is the simplest one, which is easy to handle mathematically. For higher accuracy, one always attempts to use a higher-order polynomial as an interpolant. But, Runge gave a counterexample, demonstrating that the polynomial interpolation problem may be ill-posed. Very high-order polynomial interpolation is very hard to realize by numerical computations. In this paper we propose a new polynomial interpolation… More >
Open Access
ARTICLE
Q.W. Ma1,2, J.T. Zhou1
CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.3, pp. 277-304, 2009, DOI:10.3970/cmes.2009.043.277
Abstract Following our previous work, the Meshless Local Petrov-Galerin me -thod based on Rankine source solution (MLPG_R) will be extended in this paper to deal with breaking waves. For this purpose, the governing equation for pressure is improved and a new technique called Mixed Particle Number Density and Auxiliary Function Method (MPAM) is suggested for identifying the free surface particles. Due to complexity of the problem, two dimensional (2D) breaking waves are only concerned here. Various cases are investigated and some numerical results are compared with experimental data available in literature to show the newly developed method is robust. More >
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