Hokyung Shim¹, Vinh Thuy Tran Ho^1,,Semyung Wang^1,2, Daniel A. Tortorelli³

CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.2, pp. 175-202, 2008, DOI:10.3970/cmes.2008.037.175

Abstract This paper presents a topological shape optimization technique for electromagnetic problems using a level set method and radial basis functions. The proposed technique is a level set (LS) based optimization dealing with geometrical shape derivatives and topological design. The shape derivative is computed by an adjoint variable method to avoid numerous sensitivity evaluations. A level set model embedded into the scalar function of higher dimensions is propagated to represent the design boundary of a domain. The level set function interpolated into a fixed initial domain is evolved by using the Hamilton-Jacobi equation. The moving free boundaries (dynamic interfaces) represented in… More >

Y.C. Shiah¹, C. L. Tan², C.Y. Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.1, pp. 1-22, 2012, DOI:10.3970/cmes.2012.087.001

Abstract The fundamental solution, or Green's function, for 3D anisotropic elastostatics as derived by Ting and Lee (1997) [Q.J. Mech. Appl. Math.; 50: 407-426] is one that is fully explicit and algebraic in form. It has, however, only been utilized in boundary element method (BEM) formulations quite recently even though it is relatively straightforward and direct to implement. This Green's function and its derivatives are necessary items in this numerical analysis technique. By virtue of the periodic nature of the angles when it is expressed in the spherical coordinate system, the present authors have very recently represented the Green's function as… 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 >

Yiming Chen, Mingxu Yi, Chen Chen, Chunxiao Yu

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.6, pp. 639-654, 2012, DOI:10.3970/cmes.2012.083.639

Abstract In this paper, Bernstein polynomials method is proposed for the numerical solution of a class of space-time fractional convection-diffusion equation with variable coefficients. This method combines the definition of fractional derivatives with some properties of Bernstein polynomials and are dispersed the coefficients efficaciously. The main characteristic behind this method is that the original problem is translated into a Sylvester equation. Only a small number of Bernstein polynomials are needed to obtain a satisfactory result. Numerical examples show that the method is effective. More >

C.T.M. Anflor¹, R.J. Marczak²

CMES-Computer Modeling in Engineering & Sciences, Vol.78, No.3&4, pp. 151-168, 2011, DOI:10.3970/cmes.2011.078.151

Abstract This paper aims to demonstrate the final result of an optimization process when a smooth technique is introduced between intermediary iterations of a topological optimization. In a topological optimization process is usual irregular boundary results as the final shape. This boundary irregularity occurs when the way of the material is removed is not very suitable. Avoiding an optimization post-processing procedure some techniques of smooth are implemented in the original optimization code. In order to attain a regular boundary a smoothness technique is employed, which is, Bezier curves. An algorithm was also developed to detect during the optimization process which curve… More >

Y.C. Shiah¹, C. L. Tan²

CMES-Computer Modeling in Engineering & Sciences, Vol.78, No.2, pp. 95-108, 2011, DOI:10.3970/cmes.2011.078.095

Abstract By differentiating the Green function of Ting and Lee (1997) for 3D general anisotropic elastotatics in a spherical coordinate system as an intermediate step, and then using the chain rule, derivatives of up to the second order of this fundamental solution are obtained in exact, explicit, algebraic forms. No tensors of order higher than two are present in these derivatives, thereby allowing these quantities to be numerically evaluated quite expeditiously. These derivatives are required for the computation of the internal point displacements and stresses via Somigliana's identity in BEM analysis. Some examples are presented to demonstrate their successful implementation to… More >

E.A. de Souza Neto¹, S. Amstutz², S.M. Giusti³, A.A. Novotny³

CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.1, pp. 23-56, 2010, DOI:10.3970/cmes.2010.062.023

Abstract A recently proposed algorithm for micro-structural optimization, based on the concept of topological derivative and a level-set domain representation, is applied to the synthesis of elastic and heat conducting bi-material micro-structures. The macroscopic properties are estimated by means of a family of multi-scale constitutive theories where the macroscopic strain and stress tensors (temperature gradient and heat flux vector in the heat conducting case) are defined as volume averages of their microscopic counterparts over a Representative Volume Element (RVE). Several finite element-based examples of micro-structural optimization are presented. Three multi-scale models, providing an upper and a lower bound for the macroscopic… More >

Chein-Shan Liu¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.3, pp. 253-276, 2009, DOI:10.3970/cmes.2009.043.253

Abstract Since the works of Newton and Lagrange, interpolation had been a mature technique in the numerical mathematics. Among the many interpolation methods, global or piecewise, the polynomial interpolation p(x) = a₀ + a₁x + ... + a_nxⁿ expanded by the monomials is the simplest one, which is easy to handle mathematically. For higher accuracy, one always attempts to use a higher-order polynomial as an interpolant. But, Runge gave a counterexample, demonstrating that the polynomial interpolation problem may be ill-posed. Very high-order polynomial interpolation is very hard to realize by numerical computations. In this paper we propose a new polynomial interpolation… More >

A.I. Abreu¹, W.J. Mansur¹, D. Soares Jr^1,2, J.A.M. Carrer³

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.3, pp. 123-132, 2008, DOI:10.3970/cmes.2008.030.123

Abstract This paper is concerned with the numerical computation of space derivatives of a time-domain (TD-) Boundary Element Method (BEM) formulation for the analysis of scalar wave propagation problems. In the present formulation, the Convolution Quadrature Method (CQM) is adopted, i.e., the basic integral equation of the TD-BEM is numerically substituted by a quadrature formula, whose weights are computed using the Laplace transform of the fundamental solution and a linear multi-step method. In order to numerically compute space derivatives, the present work properly transforms the quadrature weights of the CQM-BEM, adopting the so-called Complex-Variable-Differentiation Method (CVDM). Numerical examples are presented at… More >

K. Hashiguchi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.1, pp. 55-62, 2007, DOI:10.3970/cmes.2007.017.055

Abstract Constitutive equation describing the mechanical properties of material has to be formulated in an identical form independent of coordinate systems by which it is described even if there exist any mutual configuration and/or mutual rotation between the material and coordinate systems. This mechanical requirement is attained by describing rate variables as corotational rate tensors with objectivity in constitutive equations in rate form. Besides, in order to use the material-time derivative of yield condition as a consistency condition it has to be replaced to the corotational derivative. In this note a general corotational rate for tensors in arbitrary order having the… More >