Qiao Wang¹, Yu Miao^1,2, Junjie Zheng¹

CMES-Computer Modeling in Engineering & Sciences, Vol.70, No.2, pp. 123-152, 2010, DOI:10.3970/cmes.2010.070.123

Abstract In this paper, a fast formulation of the hybrid boundary node method (Hybrid BNM) for solving 3D elasticity is presented. Coupling modified variational principle with the Moving Least Squares (MLS) approximation, the Hybrid BNM only requires discrete nodes constructed on the surface of a domain. The preconditioned GMERS is employed to solve the resulting system of equations. At each iteration step of the GMERS, the matrix-vector multiplication is accelerated by the fast multipole method (FMM). The fundamental solution of three-dimensional elasticity problem is expanded in terms of series. An oct-tree data structure is adopted to More >

Xue-Qian Fang¹, Jin-Xi Liu¹, Ming-Zhang Chen¹, Li-Yong Fu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.2, pp. 101-116, 2010, DOI:10.3970/cmes.2010.066.101

Abstract In the authors' previous work (Zhang et al., 2010), the dynamic stress resulting from two cavities in exponential functional graded materials subjected to non-homogeneous shear waves has been studied. In this paper, the wave function expansion method is further developed to the case of two cylindrical inclusions embedded in functional graded materials, and the incident angle is also considered. The multiple scattering and refraction of non-homogeneous shear waves around the two inclusions are described accurately. The dynamic stress concentration factors around the two inclusions are presented analytically and numerically. The multiple effects of geometrical and More >

Han Taw Chen¹, Shao Lun Sun¹, Hui Chen Huang¹, Sen Yung Lee^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.2, pp. 107-126, 2010, DOI:10.3970/cmes.2010.059.107

Abstract A new solution method is proposed to develop the analytic closed form solution for the one dimensional heat conduction with one mixed type boundary condition and general time dependent heat convection coefficient for the first time. The solution method is the combination of an extension of the shifting function method developed by Lee and his colleagues and a series expansion. It is shown that the solution is simple and accurate. The convergence of the present analysis is very fast. One can find that when the dimensionless Fourier number is greater than 0.2, the error for More >

Chan T.L.^1,2, Xie M.L.^1,3, Cheung C.S.¹

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.3, pp. 191-212, 2009, DOI:10.3970/cmes.2009.051.191

Abstract An efficient Petrov-Galerkin Chebyshev spectral method coupled with the Taylor-series expansion method of moments (TEMOM) was developed to simulate the effect of coherent structures on particle coagulation in the exhaust pipe. The Petrov-Galerkin Chebyshev spectral method was presented in detail focusing on the analyticity of solenoidal vector field used for the approximation of the flow. It satisfies the pole condition exactly at the origin, and can be used to expand the vector functions efficiently by using the solenoidal condition. This developed TEMOM method has no prior requirement for the particle size distribution (PSD). It is… More >

Chein-Shan Liu¹, Weichung Yeih², Satya N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.3, pp. 281-312, 2009, DOI:10.3970/cmes.2009.044.281

Abstract Here we develop a general purpose pre/post conditionerT, to solve an ill-posed system of linear equations,Ax=b. The conditionerTis obtained in the course of the solution of the Laplace equation, through a boundary-collocation Trefftz method, leading to:Ty=x, whereyis the vector of coefficients in the Trefftz expansion, andxis the boundary data at the discrete points on a unit circle. We show that the quality of the conditionerTis greatly enhanced by using multiple characteristic lengths (Multiple Length Scales) in the Trefftz expansion. We further show thatTcan be multiplicatively decomposed into a dilationTDand a rotationTR. For an odd-orderedA, we More >

Jin Li¹, Ji-ming Wu², De-hao Yu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.42, No.2, pp. 151-176, 2009, DOI:10.3970/cmes.2009.042.151

Abstract The trapezoidal rule for the computation of Hadamard finite-part integrals in boundary element methods is discussed, and the asymptotic expansion of error function is obtained. A series to approach the singular point is constructed and the convergence rate is proved. Based on the asymptotic expansion of the error functional, algorithm with theoretical analysis of the generalized extrapolation are given. Some examples show that the numerical results coincide with the theoretic analysis very well. More >

Xianwu Ling¹, S.N. Atluri

CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.2, pp. 91-100, 2006, DOI:10.3970/cmes.2006.014.091

Abstract In this paper, a lattice-based cell model is proposed for single wall carbon nanotubes (SWNTs). The finite temperature effect is accounted for via the local harmonic approach. The equilibrium SWNT configurations are obtained by minimizing the Helmholtz free energy with respect to seven primary coordinate variables that are subjected to a chirality constraint. The calculated specific heats agree well with the experimental data, and at low temperature depend on the tube radii with small tubes having much lower values. Our calculated coefficients of thermal expansion (CTEs) are universally positive for all the radial, axial and More >

Chih-Ping Wu¹, Yun-Siang Syu

CMC-Computers, Materials & Continua, Vol.4, No.2, pp. 87-108, 2006, DOI:10.3970/cmc.2006.004.087

Abstract Based on the three-dimensional (3D) piezoelectricity, we presented asymptotic solutions for multilayered piezoelectric hollow cylinders using the method of perturbation. The material properties in the general formulation are firstly regarded to be heterogeneous through the thickness, and then specified as the layerwise step functions in the cases of multilayered cylinders. The transverse normal load and normal electric displacement are respectively applied on the lateral surfaces of the cylinders. The boundary conditions of cylinders are considered to be simply supported at the two edges. In the formulation the twenty-two basic equations of piezoelectricity are reduced to More >

Chih-Ping Wu, Jyh-Yeuan Lo, Jyh-Ka Chao¹

CMC-Computers, Materials & Continua, Vol.2, No.2, pp. 119-138, 2005, DOI:10.3970/cmc.2005.002.119

Abstract An asymptotic theory of doubly curved laminated piezoelectric shells is developed on the basis of three-dimensional (3D) linear piezoelectricity. The twenty-two basic equations of 3D piezoelectricity are firstly reduced to eight differential equations in terms of eight primary variables of elastic and electric fields. By means of nondimensionalization, asymptotic expansion and successive integration, we can obtain recurrent sets of governing equations for various order problems. The two-dimensional equations in the classical laminated piezoelectric shell theory (CST) are derived as a first-order approximation to the 3D piezoelectricity. Higher-order corrections as well as the first-order solution can More >

Jiayong Tian^1,2, Ulrich Gabbert², Harald Berger², Xianyue Su¹

CMC-Computers, Materials & Continua, Vol.1, No.4, pp. 327-336, 2004, DOI:10.3970/cmc.2004.001.327

Abstract In this paper, we investigate Lamb wave interaction with delamination in an infinite carbon fiber reinforced plastics (CFRP) laminate by a hybrid method. The infinite CFRP laminate is divided into an exterior zone and an interior zone. In the exterior zone, the wave fields are expressed by wave mode expansion. In the interior zone, the wave fields are modeled by the finite element method (FEM). Considering the continuity condition at the boundary between the exterior and interior zones, the global wave fields can be calculated. Lastly, numerical examples show how a delamination in the laminate More >