W.M.G.. So¹, K.J. Lau¹, S.W. Ng¹

CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.3, pp. 189-200, 2004, DOI:10.3970/cmes.2004.005.189

Abstract A new finite element analysis procedure is implemented for the determination of complex stress intensity factors in interfacial cracks. Only nodal displacements and strain energies of the near-crack-tip elements are involved in this procedure so that element stiffness matrices need not be made available. The method is first tested using a closed form solution for infinite media to obtain a suitable finite element mesh. It is then applied to finite plates and four-point bending specimens containing interfacial cracks. In cases where reference values are available for comparison, good agreement of results can be obtained with relatively coarse element meshes. More >

D. Soares Jr.¹, V. Sladek², J. Sladek², M. Zmindak³, S. Medvecky³

CMC-Computers, Materials & Continua, Vol.27, No.2, pp. 101-127, 2012, DOI:10.32604/cmc.2012.027.101

Abstract This work proposes a modified procedure, based on analytical integrations, to analyse poroelastic models discretized by time-domain Meshless Local Petrov-Galerkin formulations. In this context, Taylor series expansions of the incognita fields are considered, and the related integrals of the meshless formulations are solved analytically, rendering a so called modified methodology. The work is based on the u-p formulation and the incognita fields of the coupled analysis in focus are the solid skeleton displacements and the interstitial fluid pore pressures. Independent spatial discretization is considered for each phase of the model, rendering a more flexible and efficient methodology. The Moving Least… More >

X.S. He¹, Q.X. Liu¹, X.C. Huang², Y.M. Chen^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.108, No.3, pp. 159-169, 2015, DOI:10.3970/cmes.2015.108.159

Abstract This paper presented dynamic response analysis for an MEMS viscometer. The responses are governed by a set of differential equations containing fractional derivatives. The memory-free Yuan-Agrawal’s approach was extended to solve fractional differential equations containing arbitrary fractional order derivative and then a simple yet efficient numerical scheme was constructed. Numerical examples show that the proposed method can provide very accurate results and computational efforts can be significantly saved. Moreover, the numerical scheme was extended to solve problems with a nonlinear spring. The influences of the nonlinear parameters on the dynamic responses were also efficiently analyzed. The dependence of the angular… More >

S. Saha Ray¹

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.3, pp. 231-249, 2015, DOI:10.3970/cmes.2015.105.231

Abstract In the present article, a relatively very new technique viz. Coupled Fractional Reduced Differential Transform, has been executed to attain the approximate numerical solution of the predator-prey dynamical system. The fractional derivatives are defined in the Caputo sense. Utilizing the present method we can solve many linear and nonlinear coupled fractional differential equations. The results thus obtained are compared with those of other available methods. Numerical solutions are presented graphically to show the simplicity and authenticity of the method. More >

Diptiranjan Behera¹, S. Chakraverty²

CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.3, pp. 211-225, 2015, DOI:10.3970/cmes.2015.104.211

Abstract This paper presents the numerical solution of a viscoelastic continuous beam whose damping behaviours are defined in term of fractional derivatives of arbitrary order. Homotopy Perturbation Method (HPM) is used to obtain the dynamic response with respect to unit impulse load. Obtained results are depicted in term of plots. Comparisons are made with the analytic solutions obtained by Zu-feng and Xiao-yan (2007) to show the effectiveness and validation of the present method. More >

A.H. Bhrawy^1,2, E.H. Doha³, S.S. Ezz-Eldien⁴, M.A. Abdelkawy²

CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.3, pp. 185-209, 2015, DOI:10.3970/cmes.2015.104.185

Abstract In this paper, a high accurate numerical approach is investigated for solving the time-fractional linear and nonlinear Korteweg-de Vries (KdV) equations. These equations are the most appropriate and desirable definition for physical modeling. The spectral collocation method and the operational matrix of fractional derivatives are used together with the help of the Gauss-quadrature formula in order to reduce such problem into a problem consists of solving a system of algebraic equations which greatly simplifying the problem. Our approach is based on the shifted Jacobi polynomials and the fractional derivative is described in the sense of Caputo. In addition, the presented… More >

H. S. Shukla¹, Mohammad Tamsir¹, Vineet K. Srivastava², Jai Kumar³

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.1, pp. 1-17, 2014, DOI:10.3970/cmes.2014.103.001

Abstract The objective of this article is to carry out an approximate analytical solution of the time fractional order Cauchy-reaction diffusion equation by using a semi analytical method referred as the fractional-order reduced differential transform method (FRDTM). The fractional derivative is illustrated in the Caputo sense. The FRDTM is very efficient and effective powerful mathematical tool for solving wide range of real world physical problems by providing an exact or a closed approximate solution of any differential equation arising in engineering and allied sciences. Four test numerical examples are provided to validate and illustrate the efficiency of FRDTM. More >

W.M. Abd- Elhameed^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.3, pp. 159-185, 2014, DOI:10.3970/cmes.2014.101.159

Abstract This paper is concerned with developing two new algorithms for direct solutions of linear and nonlinear sixth-order two point boundary value problems. These algorithms are based on the application of the two spectral methods namely, collocation and Petrov-Galerkin methods. The suggested algorithms are completely new and they depend on introducing a novel operational matrix of derivatives which is expressed in terms of the well-known harmonic numbers. The basic idea for the suggested algorithms rely on reducing the linear or nonlinear sixth-order boundary value problem governed by its boundary conditions to a system of linear or nonlinear algebraic equations which can… More >

F. Yang¹, C.L. Fu², X.X. Li¹

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.1, pp. 19-29, 2014, DOI:10.3970/cmes.2014.100.019

Abstract Numerical differentiation is a classical ill-posed problem. The generalized Tikhonov regularization method is proposed to solve this problem. The error estimates are obtained for a priori and a posteriori parameter choice rules, respectively. Numerical examples are presented to illustrate the validity and effectiveness of this method. More >

A.E. Martínez-Castro¹, I.H. Faris¹, R. Gallego¹

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.3, pp. 177-206, 2012, DOI:10.3970/cmes.2012.087.177

Abstract In this paper, the identification of hidden defects inside a three-dimen -sional layer is set as an Identification Inverse Problem. This problem is solved by minimizing a cost functional which is linearized with respect to the volume defects, leading to a procedure that requires only computations at the host domain free of defects. The cost functional is stated as the misfit between experimental and computed displacements and spherical and/or ellipsoidal cavities are the defects to locate. The identification of these cavities is based on the measured displacements at a set of points due to time-harmonic point loads at an array… More >