Ping Hu¹, Yang Xia¹, Limin Tang²

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.2, pp. 103-136, 2011, DOI:10.3970/cmes.2011.073.103

Abstract In this paper, an assumed displacement quasi-conforming finite element method with truncated polynomial expansions of in-domain displacements and derived expansions of strains is introduced. Based on the method a four-node quadrilateral flat shell element with complete quadratic polynomials for membrane and bending displacement fields is developed. Numerical tests are carried out for validation of the present element. The results show that the present element preserves all the advantages of the quasi-conforming i.e., explicit stiffness matrix, convenient post processing and free from membrane locking and shear locking. The tests also prove that the present element gives More >

Malcolm R. Davidson¹, Dalton J.E. Harvie¹

FDMP-Fluid Dynamics & Materials Processing, Vol.7, No.3, pp. 317-328, 2011, DOI:10.3970/fdmp.2011.007.317

Abstract A volume-of-fluid numerical method, adapted by the authors [Harvie, Cooper-White and Davidson (2008)] to simulate the flow of viscoelastic fluids, is used to predict deformation of a viscoelastic droplet carried by an immiscible Newtonian liquid through an axisymmetric microfluidic contraction-expansion. Values of the capillary number and elasticity number are chosen based on corresponding values for a rectangular contraction for which a reentrant cavity at the rear of the drop and subsequent encapsulation behaviour was observed experimentally by Harvie, Cooper-White and Davidson (2008). A reentrant cavity, similar to the observed one, is predicted; however, encapsulation is More >

Liu ZG^1,2, YL Cai^1,2, K Li^2,3

Phyton-International Journal of Experimental Botany, Vol.79, pp. 81-86, 2010, DOI:10.32604/phyton.2010.79.081

Abstract Induced responses to herbivory are physical, nutritional, and allelochemical traits that change in plants following disturbances, and reduce the performance and/or preference of leaf tissues on herbivores. This study gave evidence to the induced defense theory through the simulated herbivory in Schima superba, one of common dominant trees in subtropical evergreen, broadleaf forests in southern China. Results showed that leaves damaged at the beginning of leaf expansion would develop into having a larger area, higher toughness and higher tannin concentrations, but a lower water content compared with control leaves. As a result, they experienced lower herbivory More >

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 >