Juan Zheng^1,2,3, Shuyao Long^1,2, Yuanbo Xiong^1,2, Guangyao Li¹

CMES-Computer Modeling in Engineering & Sciences, Vol.42, No.1, pp. 19-34, 2009, DOI:10.3970/cmes.2009.042.019

Abstract In this paper, the finite volume meshless local Petrov-Galerkin method (FVMLPG) is applied to carry out a topology optimization design for the continuum structures. In FVMLPG method, the finite volume method is combined with the meshless local Petrov-Galekin method, and both strains as well as displacements are independently interpolated, at randomly distributed points in a local domain, using the moving least squares (MLS) approximation. The nodal values of strains are expressed in terms of the independently interpolated nodal values of displacements, by simple enforcing the strain-displacement relationships directly. Considering the relative density of nodes as design variable, and the minimization… More >

M. Azreg-Aïnou¹

CMES-Computer Modeling in Engineering & Sciences, Vol.42, No.1, pp. 1-18, 2009, DOI:10.3970/cmes.2009.042.001

Abstract Adomian polynomials (AP's) are expressed in terms of new objects called reduced polynomials (RP's). These new objects, which carry two subscripts, are independent of the form of the nonlinear operator. Apart from the well-known two properties of AP's, curiously enough no further properties are discussed in the literature. We derive and discuss in full detail the properties of the RP's and AP's. We focus on the case where the nonlinear operator depends on one variable and construct the most general analytical expressions of the RP's for small values of the difference of their subscripts. It is shown that each RP… More >

Chein-Shan Liu¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.3, pp. 243-262, 2009, DOI:10.3970/cmes.2009.041.243

Abstract The Fictitious Time Integration Method (FTIM) previously developed by Liu and Atluri (2008a) is employed here to solve a system of ill-posed linear algebraic equations, which may result from the discretization of a first-kind linear Fredholm integral equation. We rationalize the mathematical foundation of the FTIM by relating it to the well-known filter theory. For the linear ordinary differential equations which are obtained through the FTIM (and which are equivalently used in FTIM to solve the ill-posed linear algebraic equations), we find that the fictitous time plays the role of a regularization parameter, and its filtering effect is better than… More >

E. J. Sellountos¹, A. Sequeira¹, D. Polyzos²

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.3, pp. 215-242, 2009, DOI:10.3970/cmes.2009.041.215

Abstract A Meshless Local Petrov-Galerkin (MLPG) method based on Local Boundary Integral Equation (LBIE) techniques is employed here for the solution of transient elastic problems with damping. The Radial Basis Functions (RBF) interpolation scheme is exploited for the meshless representation of displacements throughout the computational domain. On the intersections between the local domains and the global boundary, tractions are treated as independent variables via conventional boundary interpolation functions. The MLPG(LBIE)/RBF method is applied to both transient and steady-state Fourier transform elastodynamic domains. In both cases the LBIEs employ the simple elastostatic fundamental solution instead of the complicated time and frequency dependent… More >

C. L. Tan¹, Y.C. Shiah², C.W. Lin²

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.3, pp. 195-214, 2009, DOI:10.3970/cmes.2009.041.195

Abstract The explicit, closed-form expressions of the Green's functions for generally anisotropic elastic solids in three-dimensions that have been derived using Stroh's formalism are employed in a formulation of the boundary element method (BEM). Unlike several other existing schemes, the evaluation of these fundamental solutions does not require further numerical integration in the BEM algorithm; they have surprisingly not been implemented previously. Three numerical examples are presented to demonstrate the veracity of the implementation and the general applicability of the BEM for the 3D elastic stress analysis of generally anisotropic solids. The results are compared with known solutions in the literature… More >

Y.-M. Guo¹

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.3, pp. 177-194, 2009, DOI:10.3970/cmes.2009.041.177

Abstract In this paper, for analyses of the rigid-plastic metal forming problems, a hybrid PCM/FEM is developed. By introducing a boundary layer of finite element in boundary domain of workpiece, unsatisfactory issue of the positivity conditions of boundary points can be avoided, and the complicated boundary conditions can be easily imposed with the boundary layer of finite element. A plane strain upsetting process is analyzed by using the hybrid PCM/FEM. More >

Peter Lucas¹, Alexander H. van Zuijlen¹, Hester Bijl¹

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.2, pp. 147-176, 2009, DOI:10.3970/cmes.2009.041.147

Abstract Mesh adaptation is a fairly established tool to obtain numerically accurate solutions for flow problems. Computational efficiency is, however, not always guaranteed for the adaptation strategies found in literature. Typically excessive mesh growth diminishes the potential efficiency gain. This paper, therefore, extends the strategy proposed by [Aftosmis and Berger (2002)] to compute the refinement threshold. The extended strategy computes the refinement threshold based on a user desired number of grid cells and adaptations, thereby ensuring high computational efficiency. Because our main interest is flow around wind turbines, the adaptation strategy has been optimized for flow around wind turbine airfoils. The… More >

E. Majchrzak¹, B. Mochnacki², A. L. Greer³, J. S. Suchy⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.2, pp. 131-146, 2009, DOI:10.3970/cmes.2009.041.131

Abstract Multi-layered thin metal film subjected to a short-pulse laser heating is considered. Mathematical description of the process discussed bases on the equation in which there appear the relaxation time and the thermalization time (dual-phase-lag-model). In this study we develop a three level implicit finite difference scheme for numerical modelling of heat transfer in non-homogeneous metal film. At the interfaces an ideal contact between successive layers is assumed. At the stage of computations a solution of only one three-diagonal linear system corresponds to transition from time t to t + Δt. The mathematical model, numerical algorithm and examples of computations are… More >

Elsa Báez, Alfredo Nicolás¹

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.2, pp. 107-130, 2009, DOI:10.3970/cmes.2009.041.107

Abstract The unsteady Navier-Stokes equations in primitive variables that govern viscous incompressible fluid flow are numerically solved by a simple projection method which involves an operator splitting technique of three steps in the time discretization process. The numerical scheme does not involve any iteration, is independent of the spatial dimension, and its costly part relies on the solution of elliptic problems for which very efficient solvers exist regardless of the spatial discretization. The scheme is tested with the well known two-dimensional lid-driven cavity problem at moderate and high Reynolds numbers Re in the range 400 ≤ Re ≤ 15000. For moderate… More >

I-L. Chang¹, M.-S. Yeh¹

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.2, pp. 95-106, 2009, DOI:10.3970/cmes.2009.041.095

Abstract One-dimensional copper nanospring with elliptic cross section was studied using molecular statics method based on minimum energy consideration. Various geometric sizes (wire semi-axis length, radius, pitch) and crystal orientations of nanosprings were systematically modeled to investigate the size dependence of elastic properties for both normal and binormal nanosprings. It was observed that as the wire semi-axis increases, and the radius and pitch decrease, the nanospring stiffness would increase irrespective to the crystal orientations. Moreover, it was noticed that the normal nanosprings always behave stiffer than the binormal ones for the same radius, pitch and cross-sectional geometry in our study. More >