V.G.Yakhno¹

CMC-Computers, Materials & Continua, Vol.21, No.1, pp. 1-16, 2011, DOI:10.3970/cmc.2011.021.001

Abstract Homogeneous non-dispersive anisotropic materials, characterized by a positive constant permeability and a symmetric positive definite conductivity tensor, are considered in the paper. In these anisotropic materials, the electric and magnetic dyadic Green's functions are defined as electric and magnetic fields arising from impulsive current dipoles and satisfying the time-dependent Maxwell's equations in quasi-static approximation. A new method of deriving these dyadic Green's functions is suggested in the paper. This method consists of several steps: equations for electric and magnetic dyadic Green's functions are written in terms of the Fourier modes; explicit formulae for the Fourier More >

K. Williams¹, T. Cagin^1,2

The International Conference on Computational & Experimental Engineering and Sciences, Vol.15, No.4, pp. 153-160, 2010, DOI:10.3970/icces.2010.015.153

Abstract Designing magnetic shape memory materials with practicable engineering applications requires a thorough understanding of their electronic, magnetic, and mechanical properties. Experimental and computational studies on such materials provide differing perspectives on the same problems, with theoretical approaches offering fundamental insight into complex experimental phenomena. Many recent computational approaches have focused on first-principles calculations, all of which have been successful in reproducing ground-state structures and properties such as lattice parameters, magnetic moments, electronic density of states, and phonon dispersion curves. With all of these successes, however, such methods fail to include the effects of finite temperatures,… More >

J.S. Ren^*

Molecular & Cellular Biomechanics, Vol.7, No.4, pp. 213-224, 2010, DOI:10.3970/mcb.2010.007.213

Abstract Dynamic analysis of an axially stretched arterial wall with collagen fibers distributed in two preferred directions under a suddenly applied constant internal pressure along with the possibility of the formation and rupture of aneurysm are examined within the framework of nonlinear dynamics. A two layer tube model with the fiber-reinforced composite-based incompressible anisotropic hyper-elastic material is employed to model the mechanical behavior of the arterial wall. The maximum amplitudes and the phase diagrams are given by numerical computation of the differential relation. It is shown that the arterial wall undergoes nonlinear periodic oscillation and no More >

Y.C. Shiah¹, C. L. Tan², R.F. Lee¹

CMES-Computer Modeling in Engineering & Sciences, Vol.69, No.2, pp. 167-198, 2010, DOI:10.3970/cmes.2010.069.167

Abstract In this paper, fully explicit, algebraic expressions are derived for the first and second derivatives of the Green's function for the displacements in a three dimensional anisotropic, linear elastic body. These quantities are required in the direct formulation of the boundary element method (BEM) for determining the stresses at internal points in the body. To the authors' knowledge, similar quantities have never previously been presented in the literature because of their mathematical complexity. Although the BEM is a boundary solution numerical technique, solutions for the displacements and stresses at internal points are sometimes required for More >

F. S. Lobato¹, V. Steffen Jr², A. J. Silva Neto³

CMES-Computer Modeling in Engineering & Sciences, Vol.69, No.1, pp. 1-18, 2010, DOI:10.3970/cmes.2010.069.001

Abstract Differential Evolution Algorithm (DE) has shown to be a powerful evolutionary algorithm for global optimization in a variety of real world problems. DE differs from other evolutionary algorithms in the mutation and recombination phases. Unlike some other meta-heuristic techniques such as genetic algorithms and evolutionary strategies, where perturbation occurs in accordance with a random quantity, DE uses weighted differences between solution vectors to perturb the population. Although the efficiency of DE algorithm has been proven in the literature, studies indicate that the efficiency of the DE methods is sensitive to its control parameters (perturbation rate More >

Ali Kemal Baltacıoğlu¹, Ömer Civalek^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.68, No.1, pp. 1-24, 2010, DOI:10.3970/cmes.2010.068.001

Abstract Geometrically nonlinear static analysis of an anisotropic thick plate resting on nonlinear two-parameter elastic foundations has been studied. The plate formulation is based on first-order shear deformation theory (FSDT). The governing equation of bending for rectangular orthotropic thick plate is derived by using von Karman equation. The nonlinear static deflections of orthotropic plates on elastic foundation are investigated using the discrete singular convolution method. The effects of foundation, material and geometric parameters of orthotropic plates on nonlinear deflections are investigated. More >

K.P. Baxevanakis¹, A.E. Giannakopoulos²

CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.2, pp. 181-198, 2010, DOI:10.3970/cmes.2010.060.181

Abstract The present work gives a systematic and rigorous implementation of (edge type) circular Volterra dislocation loops in ordinary axisymmetric finite elements using the thermal analogue and the integral representation of dislocations through stresses. The accuracy of the proposed method is studied in problems where analytical solutions exist. The full fields are given for loop dislocations in isotropic and anisotropic crystals and the Peach-Koehler forces are calculated for loops approaching free surfaces and bimaterial interfaces. The results are expected to be very important in the analysis of plastic yield strength, giving quantitative results regarding the influence More >

Y.C. Chen¹, Chyanbin Hwu²

CMES-Computer Modeling in Engineering & Sciences, Vol.57, No.1, pp. 31-50, 2010, DOI:10.3970/cmes.2010.057.031

Abstract The Green's function for anisotropic bimaterials has been investigated around three decades ago. Since the mathematical formulation of piezoelectric elasticity can be organized into the same form as that of anisotropic elasticity by just expanding the dimension of the corresponding matrix to include the piezoelectric effects, the extension of the Green's function to piezoelectric bimaterials can be obtained immediately through the associated anisotropic bimaterials. In this paper, the Green's function for the bimaterials bonded together with one anisotropic material and one piezoelectric material is derived by applying Stroh's complex variable formalism with the aid of… More >

Dalin Tang¹, Chun Yang^1,2, Tal Geva^3,4, Glenn Gaudette⁴, and Pedro J. del Nido⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.2, pp. 113-130, 2010, DOI:10.3970/cmes.2010.056.113

Abstract Right and left ventricle (RV/LV) combination models with three different patch materials (Dacron scaffold, treated pericardium, and contracting myocardium), two-layer construction, fiber orientation, and active anisotropic material properties were introduced to evaluate the effects of patch materials on RV function. A material-stiffening approach was used to model active heart contraction. Cardiac magnetic resonance (CMR) imaging was performed to acquire patient-specific ventricular geometries and cardiac motion from a patient with severe RV dilatation due to pulmonary regurgitation needing RV remodeling and pulmonary valve replacement operation. Computational models were constructed and solved to obtain RV stroke volume,… More >

Liviu Marin¹

CMC-Computers, Materials & Continua, Vol.17, No.3, pp. 233-274, 2010, DOI:10.3970/cmc.2010.017.233

Abstract We investigate two algorithms involving the relaxation of either the given boundary temperatures (Dirichlet data) or the prescribed normal heat fluxes (Neumann data) on the over-specified boundary in the case of the iterative algorithm of Kozlov91 applied to Cauchy problems for two-dimensional steady-state anisotropic heat conduction (the Laplace-Beltrami equation). The two mixed, well-posed and direct problems corresponding to every iteration of the numerical procedure are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method. For each direct problem considered, the optimal value of the regularization parameter is chosen according More >