Chein-Shan Liu¹, Chung-Lun Kuo²

CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.2, pp. 109-132, 2011, DOI:10.3970/cmes.2011.076.109

Abstract The Tikhonov method is a famous technique for regularizing ill-posed systems. In this theory a regularization parameter α needs to be determined. Based-on an invariant-manifold defined in the space of (x,t) and from the Tikhonov minimization functional, we can derive an optimal vector driven system of nonlinear ordinary differential equations (ODEs). In the Optimal Vector Driven Algorithm (OVDA), the optimal regularization parameter αk is presented in the iterative solution of x, which means that a dynamical Tikhonov regularization method is involved in the solution of nonlinear ill-posed problem. The OVDA is an extension of the Landweber-Scherzer iterative algorithm. Numerical examples… More >

Cheng-Yu Ku^1,2,3,Weichung Yeih^1,2, Chein-Shan Liu⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.2, pp. 83-108, 2011, DOI:10.3970/cmes.2011.076.083

Abstract In this paper, a general dynamical method based on the construction of a scalar homotopy function to transform a vector function of Non-Linear Algebraic Equations (NAEs) into a time-dependent scalar function by introducing a fictitious time-like variable is proposed. With the introduction of a transformation matrix, the proposed general dynamical method can be transformed into several dynamical Newton-like methods including the Dynamical Newton Method (DNM), the Dynamical Jacobian-Inverse Free Method (DJIFM), and the Manifold-Based Exponentially Convergent Algorithm (MBECA). From the general dynamical method, we can also derive the conventional Newton method using a certain fictitious time-like function. The formulation presented… More >

Delfim Soares Jr.¹

CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.1, pp. 61-82, 2011, DOI:10.3970/cmes.2011.076.061

Abstract This work proposes an iterative procedure to analyse pore-dynamic models discretized by time-domain Meshless Local Petrov-Galerkin formulations. By considering an iterative procedure based on a successive renew of variables, each phase of the coupled problem in focus can be treated separately, uncoupling the governing equations of the model. Thus, smaller and better conditioned systems of equations are obtained, rendering a more attractive methodology. A relaxation parameter is introduced here in order to improve the efficiency of the iterative procedure and an expression to compute optimal values for the relaxation parameter is discussed. Linear and nonlinear models are focused, highlighting that… More >

Mohammad Mashayekhi¹, Hossein M. Shodja^1,2, Reza Namakian¹

CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.1, pp. 19-60, 2011, DOI:10.3970/cmes.2011.076.019

Abstract A meshless method called reproducing kernel particle method (RKPM) is exploited to cope with elastic-plastic fracture mechanics (EPFM) problems. The idea of arithmetic progression is assumed to place particles within the refinement zone in the vicinity of the crack tip. A comparison between two conventional treatments, visibility and diffraction, to crack discontinuity is conducted. Also, a tracking to find the appropriate diffraction parameter is performed. To assess the suggestions made, two mode I numerical simulations, pure tension and pure bending tests, are executed. Results including J integral, crack mouth opening displacement (CMOD), and plastic zone size and shape are compared… More >

J.L. Morales¹, J.A. Moreno², F. Alhama³

CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.1, pp. 1-18, 2011, DOI:10.3970/cmes.2011.076.001

Abstract Following the rules of the network simulation method, a general purpose network model is designed and numerically solved for linear elastostatic problems formulated by the Navier equations. Coupled and nonlinear terms of the PDE, as well as boundary conditions, are easily implemented in the model by means of general purpose electrical devices named controlled current (or voltage) sources. The complete model is run in the commercial software PSPICE and the numerical results are post-processed by MATLAB to facilitate graphical representation. To demonstrate the reliability and efficiency of the proposed method two applications are presented: a cantilever loaded at one end… More >

N. Ohba^1,2, S. Ogata², T. Tamura², S. Yamakawa¹, R. Asahi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.3&4, pp. 247-266, 2011, DOI:10.3970/cmes.2011.075.247

Abstract Understanding the stress dependence of Li diffusivity in the Li-graphite intercalation compound (Li-GIC) that has been used in the Li-ion rechargeable battery as a negative electrode, is important to search for better conditions to improve the power performance of the battery. In the Li-GIC, the Li ion creates a long-ranged stress field around itself by expanding the inter-layer distance of the graphite. To take into account such a long-ranged stress field in the first-principles simulation of the Li diffusion, we develop the hybrid quantum (QM)-classical (CL) simulation code. In the hybrid code, the QM region selected adaptively around the Li… More >

W. Wei, David CC LAM¹

CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.3&4, pp. 235-246, 2011, DOI:10.3970/cmes.2011.075.235

Abstract Chain rotations in macromolecular solids are constrained by entanglements. The effects of constraints on strain deformation and strain gradient deformation were investigated using molecular dynamic (MD) simulation in this paper. The effects on the chains were examined by embedding the chains inside bent beams. For thick beams, the simulated elastic moduli for styrene butyl rubber (SBR), polyimide (PI) and polyethylene (PE) were in good agreement with elastic moduli reported in the literature. The elastic moduli varied linearly with entanglements and inversely with the molecular weight. For thin beams where strain gradients were non-negligible, the results showed that l₂, the higher… More >

Canan Köroğlu¹, Turgut Öziş²

CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.3&4, pp. 223-234, 2011, DOI:10.3970/cmes.2011.075.223

Abstract He's parameter-expanding method with an adjustment of restoring forces in terms of Chebyshev's series is used to construct approximate frequency-amplitude relations for a conservative nonlinear singular oscillator in which the restoring force is inversely proportional to the dependent variable or in form of rational function of dependant variable. The procedure is used to solve the nonlinear differential equation approximately. The approximate frequency obtained using this procedure is more accurate than those obtained using other approximate methods and the discrepancy between the approximate frequency and the exact one negligible. More >

Zai You Yan¹, Qiang Zhang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.3&4, pp. 205-222, 2011, DOI:10.3970/cmes.2011.075.205

Abstract In a boundary element method, the treatment of all the possible singular integrals is very important for the correctness and accuracy of the solutions. Generally, the directional derivative of a weakly singular integral is computed by an integral in the sense of Cauchy principal value if the directional derivative of the weakly singular integral kernel is strongly singular or in the sense of Hadamard finite part integral if it is hypersingular. In this paper, we try to discover how the strongly singular and hypersingular integrals are generated and propose an idea to avoid the appearance of such kind of strongly… More >

Nizami Gasilov¹, Şahin Emrah Amrahov², Afet Golayoğlu Fatullayev¹, Halil İbrahim Karakaş¹, Ömer Akın³

CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.3&4, pp. 189-204, 2011, DOI:10.3970/cmes.2011.075.189

Abstract In this paper, linear systems with a crisp real coefficient matrix and with a vector of fuzzy triangular numbers on the right-hand side are studied. A new method, which is based on the geometric representations of linear transformations, is proposed to find solutions. The method uses the fact that a vector of fuzzy triangular numbers forms a rectangular prism in n-dimensional space and that the image of a parallelepiped is also a parallelepiped under a linear transformation. The suggested method clarifies why in general case different approaches do not generate solutions as fuzzy numbers. It is geometrically proved that if… More >