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 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 More >

CHRIS VORSTER, ANNIE JOUBERT

BIOCELL, Vol.34, No.2, pp. 71-80, 2010, DOI:10.32604/biocell.2010.34.071

Abstract In the search for new and improved anticancer therapies, researchers have identified several potentially useful compounds. One of these agents is 2-methoxyestradiol-bis-sulphamate (2ME-BM), a sulphamoylated derivative of 2-methoxyestradiol. The objective of this study was to evaluate 2ME-BM’s in vitro efficacy as antiproliferative agent in the MCF-7 breast adenocarcinoma cell line. Light- and fluorescent microscopy showed decreased cell density, increased apoptotic characteristics and significant ultrastructural aberrations indicative of autophagic cell death after 24 hours of exposure at a concentration of 0.4μM. In addition, mitotic indices revealed that 2ME-BM induces a G₂M block. The latter was confirmed by flow More >

H.B. Chen¹, Masa. Tanaka²

CMES-Computer Modeling in Engineering & Sciences, Vol.69, No.1, pp. 19-42, 2010, DOI:10.3970/cmes.2010.069.019

Abstract Highly accurate calculation of derivative values to the field variable is a key issue in numerical analysis of engineering problems. The boundary integral equations (BIEs) of potential second derivatives are of third order singularities and obviously the direct calculation of these high order singular integrals is rather cumbersome. The idea of the present paper is to use an indirect algorithm which is based on the regularized BIE formulations of the potential second derivatives, following the work of the present first author and his coworkers. The regularized formulations, numerical strategies and example tests are given for 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 More >

Chein-Shan Liu¹

CMC-Computers, Materials & Continua, Vol.15, No.3, pp. 221-240, 2010, DOI:10.3970/cmc.2010.015.221

Abstract We propose a simple numerical scheme for solving the space- and time-fractional derivative Burgers equations: D_t^αu + εuu_x = vu_xx + ηD_x^βu, 0 < α, β ≤ 1, and u_t + D_*^β(D_*^1-βu)²/2 = vu_xx, 0 < β ≤ 1. The time-fractional derivative D_t^αu and space-fractional derivative D_x^βu are defined in the Caputo sense, while D_*^βu is the Riemann-Liouville space-fractional derivative. A fictitious time τ is used to transform the dependent variable u(x,t) into a new one by (1+τ)^γu(x,t) =: v(x,t,τ), where 0 < γ ≤ 1 is a parameter, such that the original equation is written as a new functional-differential type partial differential equation More >

Zai You Yan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.46, No.1, pp. 1-20, 2009, DOI:10.3970/cmes.2009.046.001

Abstract It is well-known that the velocity potential and its first normal derivative on the structure surface can be easily found in the boundary element method for problems of potential flow. Based on an investigation in progress, the gradient of the normal derivative of the velocity potential will be very helpful in the treatment of the so-called hypersingular integral. Through a coordinate transformation, such gradient can be expressed by the combination of the first and the second normal derivatives of the velocity potential. Then one interesting problem is how to find the second normal derivative of More >

Wen Chen¹, Hongguang Sun¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.9, No.4, pp. 215-218, 2009, DOI:10.3970/icces.2009.009.215

Abstract This report is to make a survey on the numerical techniques for fractional derivative equations in mechanical and physical fields, including numerical integration of fractional time derivative and emerging approximation strategies for fractional space derivative equations. The perplexing issues are highlighted, while the encouraging progresses are summarized. We also point out some emerging techniques which will shape the future of the numerical solution of fractional derivative equations. More >

R.M. Reddy¹, B.N. Rao²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.12, No.4, pp. 149-150, 2009, DOI:10.3970/icces.2009.012.149

Abstract Probabilistic fracture mechanics (PFM) blends the theory of fracture mechanics and the probability theory provides a more rational means to describe the actual behavior and reliability of structures. However in PFM, the fracture parameters and their derivatives are often required to predict the probability of fracture initiation and/or instability in cracked structures. The calculation of the derivatives of fracture parameters with respect to load and material parameters, which constitutes size-sensitivity analysis, is not unduly difficult. However, the evaluation of response derivatives with respect to crack size was a challenging task, since it requires shape sensitivity… 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… More >