M.M. Kaminski

CMES-Computer Modeling in Engineering & Sciences, Vol.80, No.2, pp. 113-140, 2011, DOI:10.3970/cmes.2011.080.113

Abstract The main aim of this work is to demonstrate a solution to the transient problems for the statistically homogeneous media with random physical parameters. This is done with the use of the stochastic perturbation technique based on the general order Taylor series expansions and the additionally modified implementation of the Finite Element Method. Now, both the Direct Differentiation Method as well as the Response Function Method are employed to form and solve up to the nth order state equations. Computational implementation of both approaches is illustrated using two examples - by determination of the probabilistic moments of the temperature histories… More >

Gongsheng Li¹, De Yao², Hengyi Jiang³, Xianzheng Jia¹

CMES-Computer Modeling in Engineering & Sciences, Vol.74, No.2, pp. 83-108, 2011, DOI:10.3970/cmes.2011.074.083

Abstract This paper deals with an inverse problem of determining a time-depen -dent reaction coefficient arising from a disturbed soil-column infiltrating experiment based on measured breakthrough data. A purpose of doing such experiment is to simulate and study transport behaviors of contaminants when they vertically penetrating through the soils. Data compatibility of the inverse problem is discussed showing a sufficient condition to the solution's monotonicity and positivity with the help of an adjoint problem. Furthermore, an optimal perturbation regularization algorithm is applied to solve the inverse problem, and two typical numerical examples are presented to support the inversion algorithm. Finally, transport… More >

Jinling Long^1,2, Bingang Xu^1,3, Xiaoming Tao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.72, No.4, pp. 273-298, 2011, DOI:10.3970/cmes.2011.072.273

Abstract Moving slender threadline structures are widely used in various engineering fields. The dynamics of these systems is sometimes time dependent but in most cases follows a periodic pattern, and slender yarn motion in textile engineering is a typical problem of this category. In the present paper, we propose a nonlinear approach to model the dynamic behavior of slender threadline structures with a real example in the analysis of slender yarn motion in spinning. Moving boundary conditions of yarn are derived and a consequence of the perturbation analysis for the dimensionless governing equations provides the zero order approximate equation of motion… More >

B. Ren^1,2, J. Qian¹, X. Zeng¹, A. K. Jha³, S. Xiao⁴, S. Li^1,5

CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.3, pp. 253-278, 2011, DOI:10.3970/cmes.2011.071.253

Abstract Ductile failure is a complex multi-scale phenomenon evolved from the micro-voids to macro-crack. There are three main failure mechanisms behinds a ductile failure: adiabatic shear band (ASB), spall fracture, and crack. Since this type of thermo-mechanical phenomena involves large deformation and large scale plastic yielding, a meshfree method has intrinsic advantages in solving this kind of problems over the conventional finite element method. In this paper, the numerical methodologies including multi-physics approach for ASB, parametric visibility condition for crack propagation, and multi-scale approach to determine spall strength in simulating ductile failure have been reviewed. A thermo-mechanical coupling algorithm is proposed… More >

G.S. Li¹, D. Yao², Y.Z. Wang³, H.Y. Jiang²

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.1, pp. 53-72, 2009, DOI:10.3970/cmes.2009.051.053

Abstract In this paper, an undisturbed soil-column infiltrating experiment is investigated, and a mathematical model describing multi-components solutes transport behaviors in the column is put forward by combing hydro-chemical analysis with advection dispersion mechanisms, which is a group of advection-dispersion-reaction partial differential equations. Since the model involving six reaction coefficients which can not be obtained directly, an optimal perturbation regularization algorithm of determining these parameters is performed, and numerical simulations under different conditions are carried out. Furthermore, the inversion algorithm is applied to solve the real inverse problem by utilizing the measured breakthrough data. The reconstruction data basically coincide with the… More >

Huamin Zhou¹, Hua Zhang, Dequn Li²

CMES-Computer Modeling in Engineering & Sciences, Vol.46, No.3, pp. 209-220, 2009, DOI:10.3970/cmes.2009.046.209

Abstract Gas-assisted injection molding is an innovative process to manufacture hollow polymeric products, in which gas penetration is the primary and key problem. An analytical solution of the gas penetration interface is presented, based on perturbation method. First, the governing equations and boundary conditions are transformed to be dimensionless, where Capillary number Ca is introduced. Then matching asymptotic expansion method is applied to solve these equations, by using Ca and as perturbation parameters to get the inner and outer solutions, respectively. By matching these two solutions, the analytical model of gas penetration is obtained. More >

Wei Gao¹, Chongmin Song¹, Francis Tin-Loi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.46, No.2, pp. 151-190, 2009, DOI:10.3970/cmes.2009.046.151

Abstract Static response and reliability of structures with a mixture of random and interval parameters under uncertain loads are investigated in this paper. Structural stiffness matrix is a random interval matrix when some structural parameters are modeled as random variables and others are considered as intervals. The structural displacement and stress responses are also random interval variables. From the static finite element governing equations, the random interval structural responses are obtained using the random interval perturbation method based on the first- and second-order perturbations. The expressions for mean value and standard deviation of random interval structural displacement and stress responses are… More >

Sen Yung Lee¹, Shin Yi Lu², Yen Tse Liu², Hui Chen Huang²

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.3, pp. 293-312, 2008, DOI:10.3970/cmes.2008.033.293

Abstract A new analytic solution method is developed to find the exact static deflection of a Timoshenko beam with nonlinear elastic boundary conditions for the first time. The associated mathematic system is shifted and decomposed into six linear differential equations and at most four algebra equations. After finding the roots of the algebra equations, the exact solution of the nonlinear beam system can be reconstructed. It is shown that the proposed method is valid for the problem with strong nonlinearity. Examples, limiting studies and numerical analysis are given to illustrate the analysis. The exact solutions are compared with the perturbation solutions.… More >

Mustafa Uludoğan¹, D. Paula Guarin¹, Zully E. Gomez¹, Tahir Cagin¹, William A. Goddard III²

CMES-Computer Modeling in Engineering & Sciences, Vol.24, No.2&3, pp. 215-238, 2008, DOI:10.3970/cmes.2008.024.215

Abstract Aiming at a presentation of the utility of the state of art of first-principles methods (PBE flavor of Density Functional Theory, DFT) in the area of materials science and engineering, we present our studies of the equation of state and ferroelectric-paraelectricphase transition in several ferroelectric systems, including BaTiO₃, PbTiO₃, SrTiO₃, AgNbO₃, Pb_xBa_1-xTiO₃ and Sr_xBa_1-xTiO₃. We also report the Born effective charges, optical dielectric constant, and phonon dispersion relation properties from Density Functional Perturbation Theory. Computed results are compared with other theoretical results (which were mostly on BaTiO₃, PbTiO₃, cubic SrTiO₃ using various approaches, as well as experiments. The studies on… More >

Ya Yan Lu¹, Jianxin Zhu²

CMES-Computer Modeling in Engineering & Sciences, Vol.22, No.3, pp. 235-248, 2007, DOI:10.3970/cmes.2007.022.235

Abstract The perfectly matched layer (PML) is a widely used technique for truncating unbounded domains in numerical simulations of wave propagation problems. In this paper, the PML technique is used with a standard one-way model to solve a benchmark problem for underwater acoustics modeling. Accurate solutions are obtained with a PML layer with a thickness of only a quarter of the wavelength. The effect of a PML is analyzed in a perturbation analysis for waveguides. More >