S. D. Akbarov^1,2, C. Ipek³

CMES-Computer Modeling in Engineering & Sciences, Vol.70, No.2, pp. 93-122, 2010, DOI:10.3970/cmes.2010.070.093

Abstract This paper studies the influence of the imperfectness of the interface conditions on the dispersion of the axisymmetric longitudinal waves in the pre-strained compound cylinder. The investigations are made within the framework of the piecewise homogeneous body model by utilizing the 3D linearized theory of elastic waves in elastic bodies with initial stresses. It is assumed that the layers of the compound cylinder are made from high elastic compressible materials and their elasticity relations are given through the harmonic potential. The shear spring type imperfectness of the interface conditions is considered and the degree of this imperfectness is estimated by… More >

Chih-Wen Chang¹, Chein-Shan Liu²

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.3, pp. 261-276, 2009, DOI:10.3970/cmes.2009.051.261

Abstract The backward advection-dispersion equation (ADE) for identifying the groundwater pollution source identification problems (GPSIPs) is numerically solved by employing a fictitious time integration method (FTIM). The backward ADE is renowned as ill-posed because the solution does not continuously count on the data. We transform the original parabolic equation into another parabolic type evolution equation by introducing a fictitious time coordinate, and adding a viscous damping coefficient to enhance the stability of numerical integration of the discretized equations by employing a group preserving scheme. When several numerical examples are amenable, we find that the FTIM is applicable to retrieve all past… More >

A. Wacher¹, D. Givoli²

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 147-164, 2006, DOI:10.3970/cmes.2006.015.147

Abstract The recently proposed String Gradient Weighted Moving Finite Element (SGWMFE) method is extended to include remeshing and refining. The method simultaneously determines, at each time step, the solution of the governing partial differential equations and an optimal location of the finite element nodes. It has previously been applied to the nonlinear time-dependent two-dimensional shallow water equations, under the demanding conditions of large Coriolis forces, inducing large mesh and field rotation. Such effects are of major importance in geophysical fluid dynamics applications. Two deficiencies of the original SGWMFE method are (1) possible tangling of the mesh which causes the method's failure,… More >

Abhijit Sarkar¹, M. V. Kunte², Venkata R. Sonti²

CMES-Computer Modeling in Engineering & Sciences, Vol.81, No.3&4, pp. 249-268, 2011, DOI:10.3970/cmes.2011.081.249

Abstract In this article, we show with some formalism that infinite flexible structural acoustic waveguides have a general form for the dispersion equation. The dispersion equation of all such waveguides should conform to a generic form. This allows us to bring out the common features of structural acoustic waveguides. We take three examples to demonstrate this fact, namely, the rectangular, the circular cylindrical and the elliptical geometries. Where necessary, the equations are simplified for applicability to a particular frequency-regime before demonstrating the conformance to the generic form of the dispersion relation. It is then shown that the coupled wavenumber solutions of… 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 >

C. Du¹, H. Bai², J. Qu³, X. Su^1,4

CMES-Computer Modeling in Engineering & Sciences, Vol.61, No.3, pp. 223-248, 2010, DOI:10.3970/cmes.2010.061.223

Abstract Second, or higher, order harmonics have great potential in fatigue life prediction. In this study, the dispersion properties of waves propagating in the nonlinear random media are investigated. An one dimensional nonlinear model based on the nonlinear Hikata stress-strain relation is used. We applied perturbation method, the Liouville transformation and the smoothing approximation method to solve the one dimensional nonlinear stochastic wave equation. We show easily that the dispersion equations for all higher order terms will be the same with the corresponding linear random medium by perturbation method. The linear stochastic equation with two random coefficients is greatly simplified to… More >

A. Papacharalampopoulos², G. F. Karlis², A. Charalambopoulos³, D. Polyzos⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.1, pp. 45-74, 2010, DOI:10.3970/cmes.2010.058.045

Abstract A Boundary Element Method (BEM) for solving two (2D) and three dimensional (3D) dynamic problems in materials with microstructural effects is presented. The analysis is performed in the frequency domain and in the context of Mindlin's Form II gradient elastic theory. The fundamental solution of the differential equation of motion is explicitly derived for both 2D and 3D problems. The integral representation of the problem, consisting of two boundary integral equations, one for displacements and the other for its normal derivative is exploited for the proposed BEM formulation. The global boundary of the analyzed domain is discretized into quadratic line… More >

Surkay D. Akbarov^1,2,3, Mugan S. Guliev⁴, Ramazan Tekercioglu⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.1, pp. 1-32, 2010, DOI:10.3970/cmes.2010.055.001

Abstract Dispersion relations of axisymmetric longitudinal wave propagation in a finite pre-strained compound (bi-material) cylinder made from high elastic incompressible materials are investigated within the scope of a piecewise homogeneous body model utilizing three-dimensional linearized theory wave propagation in the initially stressed body. The materials of the inner and outer cylinders are assumed to be neo-Hookean. The numerical results regarding the influence of the initial strains in the inner and outer cylinders on the wave dispersion are presented and discussed. These results are obtained for the case where the material of the inner solid cylinder is stiffer than that of the… More >

Surkay D. Akbarov^1,2,3, Mugan S. Guliev⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.39, No.2, pp. 155-178, 2009, DOI:10.3970/cmes.2009.039.155

Abstract The axisymmetric longitudinal wave propagation in a finite pre-strained compound (composite) cylinder is investigated within the scope of a piecewise homogeneous body model utilizing three-dimensional linearized theory wave propagation in an initially stressed body. The materials of the inner and outer cylinder are assumed to be compressible. The elasticity relations for those are given through the harmonic potential. The algorithm for constructing of the computer programmes and obtaining numerical results is discussed. The numerical results regarding the influences of the initial strains in the inner and outer cylinders on the wave dispersion are presented and analysed. These results are obtained… More >

Shueei-Muh Lin^1,3, Sen-Yung Lee², Cheng-Chuan Tsai², Chien-Wi Chen²,Wen-Rong Wang³, Jenn-Fa Lee³

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.1, pp. 33-54, 2008, DOI:10.3970/cmes.2008.034.033

Abstract The conventional theories for circulation of arteries are emphasized on fluid behavior or some simplified models for experimental utility. In this study, a new mathematical theory is proposed to describe the wave propagation through the elastic tube filled with viscous and incompressible fluid. The radial, longitudinal and flexural vibrations of a tube wall are introduced simultaneously. Meanwhile, the linearlized momentum and continuity equations of tube flow field are expressed in the integral form. Based on these considerations, three wave modes are obtained simultaneously. These wave modes are the flexural, Young and Lamb modes, respectively. The characteristics of these modes are… More >