E.J. Sellountos¹, S.V. Tsinopoulos², D. Polyzos³

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.2, pp. 145-170, 2012, DOI:10.3970/cmes.2012.086.145

Abstract A Local Boundary Integral Equation (LBIE) method for solving two dimensional problems in gradient elastic materials is presented. The analysis is performed in the context of simple gradient elasticity, the simplest possible case of Mindlin's Form II gradient elastic theory. For simplicity, only smooth boundaries are considered. The gradient elastic fundamental solution and the corresponding boundary integral equation for displacements are used for the derivation of the LBIE representation of the problem. Nodal points are spread over the analyzed domain and the moving least squares (MLS) scheme for the approximation of the interior and boundary variables is employed. Since in… More >

S.V. Tsinopoulos¹, D. Polyzos², D.E. Beskos^3,4

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.2, pp. 113-144, 2012, DOI:10.3970/cmes.2012.086.113

Abstract This paper reviews the theory and the numerical implementation of the direct boundary element method (BEM) as applied to static and dynamic problems of strain gradient elastic solids and structures under two- and three- dimensional conditions. A brief review of the linear strain gradient elastic theory of Mindlin and its simplifications, especially the theory with just one constant (internal length) in addition to the two classical elastic moduli, is provided. The importance of this theory in successfully modeling microstructural effects on the structural response under both static and dynamic conditions is clearly described. The boundary element formulation of static and… More >

J.E. Lee¹and S.J. Kim²

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.2, pp. 93-112, 2012, DOI:10.3970/cmes.2012.086.093

Abstract As the option trading nowadays has become popular, it is important to simulate efficiently large amounts of option pricings. The purpose of this paper is to show valuations of large amount of options, using network distribute computing resources. We valuated 108 options simultaneously on the self-made cluster computer system which is very inexpensive, compared to the supercomputer or the GPU adopting system. For the numerical valuations of options, we developed the option pricing software to solve the Black-Scholes partial differential equation by the finite element method. This yielded accurate values of options and the Greeks with reasonable computational times. This… More >

C. Shi¹, C. Wang¹, T. Wei^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.2, pp. 71-92, 2012, DOI:10.3970/cmes.2012.086.071

Abstract In this paper, we consider a typical ill-posed inverse heat source problem, that is, we determine a space-dependent heat source term in a multi-dimensional heat equation from a pair of Cauchy data on a part of boundary. By a simple transformation, the inverse heat source problem is changed into a Cauchy problem of a homogenous heat conduction equation. We use the method of fundamental solutions (MFS) coupled with the Tikhonov regularization technique to solve the ill-conditioned linear system of equations resulted from the MFS discretization. The generalized cross-validation rule for determining the regularization parameter is used. Numerical results for four… More >

Yixian Du^1,2, De Chen^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.1, pp. 53-70, 2012, DOI:10.3970/cmes.2012.086.053

Abstract This study proposes a new topology optimization method for continuum structures, which includes modified heuristic optimality criteria in conjunction with the SIMP scheme to suppress gray-scale elements occurred in topology optimization of continua through smoothed Heaviside function. In the process of numerical implementation, the gray scale elements are suppressed to approach the binary bounds of 0 or 1 by utilizing the proposed approach and the corresponding convergence criterion. Two typical numerical examples are used to demonstrate the effectiveness of the proposed method in suppressing the gray-scale elements with intermediate densities, as well as the efficiency of this method in the… More >

H. Çerdik Yaslan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.1, pp. 29-38, 2012, DOI:10.3970/cmes.2012.086.029

Abstract This paper presents the approximate analytical solutions to the time fractional differential equations of elasticity for 3D quasicrystals with initial conditions. These equations are written in the form of a vector partial differential equation of the second order. The time fractional vector partial differential equations with initial conditions are solved by variational iteration method (VIM). The fractional derivatives are described in the Caputo sense. Numerical example shows that the proposed method is quite effective and convenient for solving kinds of time fractional system of partial differential equations. More >

Subhankar Sen¹, Sanjay Mittal², Gautam Biswas¹

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.1, pp. 1-28, 2012, DOI:10.3970/cmes.2012.086.001

Abstract The steady flow around elliptic cylinders is investigated using a stabilized finite-element method. The Reynolds number, Re, is based on cylinder major axis and free-stream speed. Results are presented for Re ≤ 40 and 0° ≤ α ≤ 90°, where α is angle of attack. Cylinder aspect ratios, AR considered are 0.2 (thin), 0.5, 0.8 (thick) and 1.0. Results for the laminar separation Reynolds number, Re_s available in the literature are only for thin cylinder and exhibit large scatter. Also, very limited information is available for separation angle. The present study attempts to provide this data. In addition, issues concerning… More >

J. Sladek¹, V. Sladek¹, P. Stanak¹, P.H. Wen², S.N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.6, pp. 543-572, 2012, DOI:10.3970/cmes.2012.085.543

Abstract A meshless local Petrov-Galerkin (MLPG) method is applied to solve laminate piezoelectric plates described by the Reissner-Mindlin theory. The piezoelectric layer can be used as a sensor or actuator. A pure mechanical load or electric potential are prescribed on the top of the laminated plate. Both stationary and transient dynamic loads are analyzed here. The bending moment, the shear force and normal force expressions are obtained by integration through the laminated plate for the considered constitutive equations in each lamina. Then, the original three-dimensional (3-D) thick plate problem is reduced to a two-dimensional (2-D) problem. Nodal points are randomly distributed… More >

Tsung-Yu Huang¹, Wen-Hwa Chen^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.6, pp. 521-542, 2012, DOI:10.3970/cmes.2012.085.521

Abstract A rigorous three-dimensional analysis model is established to calculate the restoring force and restoring torque for the self-alignment of the micropart with the binding site in solution using the Surface Evolver Program, which is developed for analyzing the liquid formation due to surface tension and other energies. The motions of the micropart studied include translation, compression, yawing and rolling, respectively. More >

C.-D. Tran¹, N. Mai-Duy^1,1, K. Le-Cao¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.6, pp. 499-520, 2012, DOI:10.3970/cmes.2012.085.499

Abstract A numerical computation of continuum-microscopic model for visco-elastic flows based on the Integrated Radial Basis Function (IRBF) Control Volume and the Stochastic Simulation Techniques (SST) is reported in this paper. The macroscopic flow equations are closed by a stochastic equation for the extra stress at the microscopic level. The former are discretised by a 1D-IRBF-CV method while the latter is integrated with Euler explicit or Predictor-Corrector schemes. Modelling is very efficient as it is based on Cartesian grid, while the integrated RBF approach enhances both the stability of the procedure and the accuracy of the solution. The proposed method is… More >