Hua Li¹, Shantanu S. Mulay¹, Simon See²

CMES-Computer Modeling in Engineering & Sciences, Vol.48, No.1, pp. 43-82, 2009, DOI:10.3970/cmes.2009.048.043

Abstract Differential Quadrature (DQ) is one of the efficient derivative approximation techniques but it requires a regular domain with all the points distributed only along straight lines. This severely restricts the DQ while solving the irregular domain problems discretized by the random field nodes. This limitation of the DQ method is overcome in a proposed novel strong-form meshless method, called the random differential quadrature (RDQ) method. The RDQ method extends the applicability of the DQ technique over the irregular or regular domains discretized using the random field nodes by approximating a function value with the fixed reproducing kernel particle method (fixed… More >

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 + ... + a_nxⁿ 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 >

Chein-Shan Liu¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.3, pp. 243-262, 2009, DOI:10.3970/cmes.2009.041.243

Abstract The Fictitious Time Integration Method (FTIM) previously developed by Liu and Atluri (2008a) is employed here to solve a system of ill-posed linear algebraic equations, which may result from the discretization of a first-kind linear Fredholm integral equation. We rationalize the mathematical foundation of the FTIM by relating it to the well-known filter theory. For the linear ordinary differential equations which are obtained through the FTIM (and which are equivalently used in FTIM to solve the ill-posed linear algebraic equations), we find that the fictitous time plays the role of a regularization parameter, and its filtering effect is better than… More >

P. Huang^1,2, X. Zhang^1,3, S. Ma¹, H.K. Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.2, pp. 119-148, 2008, DOI:10.3970/cmes.2008.038.119

Abstract The material point method (MPM) is an extension of particle-in-cell method to solid mechanics. A parallel MPM code is developed using FORTRAN 95 and OpenMP in this study, which is designed primarily for solving impact dynamic problems. Two parallel methods, the array expansion method and the domain decomposition method, are presented to avoid data races in the nodal update stage. In the array expansion method, two-dimensional auxiliary arrays are created for nodal variables. After updating grid nodes in all threads, the auxiliary arrays are assembled to establish the global nodal array. In the domain decomposition method, the background grid is… More >

RaviS Nanjundiah¹

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.1&2, pp. 1-24, 2008, DOI:10.3970/cmes.2008.027.001

Abstract In this paper, application of high performance computing to climate modelling with specific reference to global General Circulation Models (GCM) is discussed. Methods of parallelization of global atmospheric models based on their numerical schemes is presented. It is seen that there is an interesting co-evolution of computer architecture and the type of numerical schemes used in general circulation models. A detailed survey of the Indian HPC scenario for meteorological computing is presented. Innovative and pioneering aspects of Indian efforts are highlighted. More >

Xiang Jiawei¹, Chen Xuefeng², Yang Lianfa³, He Zhengjia⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.1, pp. 1-12, 2008, DOI:10.3970/cmes.2008.023.001

Abstract A class of flat shell elements is constructed by using the scaling functions of two-dimensional tensor product B-spline wavelet on the interval (BSWI). Unlike the process of direct wavelets adding in the wavelet Galerkin method, the element displacement field represented by the coefficients of wavelets expansions was transformed from wavelet space into physical space via the constructed two-dimensional transformation matrix. Then, the BSWI flat shell element is constructed by the assembly of BSWI plane elastomechanics and Mindlin plate elements. Because of the good character of BSWI scaling functions, the BSWI flat shell element combine the accuracy of B-spline functions approximation… More >

S.Y. Wang^1,2, K.M. Lim^2,3, B.C. Khoo^2,3, M.Y. Wang⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.1, pp. 1-40, 2007, DOI:10.3970/cmes.2007.021.001

Abstract The level set method is a numerical technique for simulating moving interfaces. In this paper, an unconditionally BIBO (Bounded-Input-Bounded-Output) time-stable consistent meshfree level set method is proposed and applied as a more effective approach to simultaneous shape and topology optimization. In the present level set method, the meshfree infinitely smooth inverse multiquadric Radial Basis Functions (RBFs) are employed to discretize the implicit level set function. A high level of smoothness of the level set function and accuracy of the solution to the Hamilton-Jacobi partial differential equation (PDE) can be achieved. The resulting dynamic system of coupled Ordinary Differential Equations (ODEs)… More >

Shuji Takashima¹, Michihiko Nakagaki², Noriyuki Miyazaki¹

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.3, pp. 193-202, 2007, DOI:10.3970/cmes.2007.020.193

Abstract Composite materials have complicated microstructures. These microstructures affect the macroscopic deformation of composite materials. In the present study, we focus on the effect of particle size in a particle-dispersed composite material on the mechanical strength of the material. For this purpose, we derived a macroscopic elastic-plastic constitutive equation using a modified version of the Eshelby's equivalent inclusion method combined with the gradient plasticity. We incorporated this macroscopic elastic-plastic constitutive equation into a finite element program and performed a homogenized finite element analysis of a particle-dispersed composite material in which both the macroscopic and microscopic behaviors of the composite material were… More >

Daoming Shen¹, Hua Si^1,*, Jinhong Xia¹, Shunqun Li²

FDMP-Fluid Dynamics & Materials Processing, Vol.15, No.1, pp. 63-76, 2019, DOI:10.32604/fdmp.2019.04799

Abstract The correct determination of thermal parameters, such as thermal conductivity and specific heat of soil during freezing, is the most important and basic problem for the construction of an appropriate freezing method. In this study, a calculation model of three stages of soil temperature was established. At the unfrozen and frozen stages, the specific temperatures of dry soil, water, and ice are known. According to the principle of superposition, a calculation model of unfrozen and frozen soils can be established. Informed by a laboratory experiment, the latent heat of the adjacent zone was calculated for the freezing stage based on… More >

Qiuren Ou^1,2,*, Peijun Ji², Jun Xiao¹, Ling Wu²

FDMP-Fluid Dynamics & Materials Processing, Vol.15, No.1, pp. 27-37, 2019, DOI:10.32604/fdmp.2019.04787

Abstract The properties of resin transfer molding (RTM) cyanate ester and its T800 grade carbon fiber composites were studied with the rheometer, differential scanning calorimetry (DSC), FT-IR, dynamic mechanical analyzer (DMA), thermal gravimetric analysis (TGA), mechanical property testing, and scanning electron microscopy (SEM). The results showed that the temperature of cyanate ester suitable for RTM process was 70℃. Curing process of the resin was 130℃/2 h+160℃/2 h+200℃/2 h+220℃/4 h. Glass transition temperature and heat decomposition temperature of the cured resin are 289℃ and 415℃, respectively. Mechanical properties of T800/RTM cyanate composites are 13.5% higher than that of T700/RTM cyanate composites and… More >