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 >

S.Yu. Reutskiy¹

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.2, pp. 115-142, 2009, DOI:10.3970/cmes.2009.051.115

Abstract In this paper a new numerical technique for problems of free vibrations of arbitrary shaped non-homogeneous membranes:∇²w + k²q(x)w = 0, x∈ Ω⊂R², B[w] = 0, x∈∂Ω is presented. Homogeneous membranes of a complex form are considered as a particular case. The method is based on mathematically modeling of physical response of a system to excitation over a range of frequencies. The response amplitudes are then used to determine the resonant frequencies. Applying the method, one gets a sequence of boundary value problems (BVPs) depending on the spectral parameter k. The eigenvalues are sought as positions of More >

Sarang Seyrafian¹, Behrouz Gatmiri², Asadollah Noorzad³

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.2, pp. 115-126, 2006, DOI:10.3970/cmes.2006.015.115

Abstract An analytical solution is presented for the response of a non-homogeneous saturated poroelastic half-space under the action of a time-harmonic vertical point load on its surface. The shear modulus is assumed to increase continuously with depth and also the media is considered to obey Biot's poroelastic theory. The system of governing partial differential equations, based on the mentioned assumptions, is converted to ordinary differential equations' system by means of Hankel integral transforms. Then the system of equations is solved by use of generalized power series(Frobenius method) and the expressions for displacements in the interior of More >

V. Sladek¹, J. Sladek¹, M. Tanaka²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.1, pp. 69-84, 2005, DOI:10.3970/cmes.2005.007.069

Abstract An efficient numerical method is proposed for 2-d potential problems in anisotropic media with continuously variable material coefficients. The method is based on the local integral equations (utilizing a fundamental solution) and meshfree approximation of field variable. A lot of numerical experiments are carried out in order to study the numerical stability, accuracy, convergence and efficiency of several approaches utilizing various interpolations. More >

J.T. Katsikadelis¹, M.S. Nerantzaki¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.3, pp. 1-9, 2000, DOI:10.3970/cmes.2000.001.303

Abstract A boundary-only method is presented for the solution of the vibration problem of non-homogeneous membranes. Both free and forced vibrations are considered. The presented method is based on the Analog Equation Method (AEM). According to this method the second order partial differential equation with variable coefficients of hyperbolic type, which governs the dynamic response of the membrane, is substituted by a Poisson's equation describing a quasi-static problem for the homogeneous membrane subjected to a fictitious time dependent load. The fictitious load is established using BEM. Several numerical examples are presented which illustrate the efficiency and More >