P. Areias^1,2,3, T. Rabczuk⁴, D. Dias-da-Costa^5,6

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.6, pp. 475-506, 2012, DOI:10.3970/cmes.2012.088.475

Abstract Surprisingly good displacement results are obtained by using the Petrov-Galerkin method with assumed and enhanced metric components in the test functions and enhanced metric components in the trial functions. Cartesian trial functions are required to ensure completeness and assumed/enhanced metric components are introduced to ensure high coarse-mesh accuracy. In the trial functions, the original incompatible-mode in-plane Q6 element by Wilson et al. can be used without violating the patch test. As a beneficial side-effect, Newton-Raphson convergence behavior for non-linear problems is improved. Transverse-shear and in-plane patch tests are satisfied while distorted-mesh performance is better than with symmetric formulations due to… More >

A.S Vinod Kumar, Ranjan Ganguli²

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.6, pp. 443-474, 2012, DOI:10.3970/cmes.2012.088.443

Abstract The governing differential equation of a rotating beam becomes the stiff-string equation if we assume uniform tension. We find the tension in the stiff string which yields the same frequency as a rotating cantilever beam with a prescribed rotating speed and identical uniform mass and stiffness. This tension varies for different modes and are found by solving a transcendental equation using bisection method. We also find the location along the rotating beam where equivalent constant tension for the stiff string acts for a given mode. Both Euler-Bernoulli and Timoshenko beams are considered for numerical results. The results provide physical insight… More >

Zhiqiang Yang¹, Junzhi Cui², Yufeng Nie¹, Qiang Ma²

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.5, pp. 419-442, 2012, DOI:10.3970/cmes.2012.088.419

Abstract In this paper, a new second-order two-scale (SOTS) method is developed to predict heat transfer performances of periodic porous materials with interior surface radiation. Firstly, the second-order two-scale formulation for computing temperature field of the problem is given by means of construction way. Then, the error estimation of the second-order two-scale approximate solution is derived on some regularity hypothesis. Finally, the corresponding finite element algorithms are proposed and some numerical results are presented. They show that the SOTS method in this paper is feasible and valid for predicting the heat transfer performances of periodic porous materials. More >

S. Brischetto¹

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.5, pp. 367-418, 2012, DOI:10.3970/cmes.2012.088.367

Abstract The paper analyzes the hygrothermal loading effects in the bending of multilayered composite plates. Refined two-dimensional models are used to evaluate these effects, they are implemented in the framework of the Carrera's Unified Formulation (CUF) which also allows classical models to be obtained. Hygroscopic and thermal effects are evaluated by means of hygroscopic and thermal load applications, respectively. Such loads can be determined via a priori linear or constant moisture content and temperature profiles through the thickness of the plate, or by calculating them via the solution of the Fick moisture diffusion law and the Fourier heat conduction equation, respectively.… More >

Lior Banai

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.5, pp. 351-366, 2012, DOI:10.3970/cmes.2012.088.351

Abstract The explosive Engineering field is a costly one in which not every organization can effort the time and money it takes to performed field tests on its explosives. The purpose of this article is to present a program that was developed in the Israeli Navy for performance estimations and safety issues of warheads and explosives. With a relative small developing time one can create a tool that gives preliminary results in a few minutes without the need to design and order a field tests or run finite elements analyses. By implementing a few known models, in this tool, the user… More >

Changsheng Wang¹, Ping Hu^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.5, pp. 325-350, 2012, DOI:10.3970/cmes.2012.088.325

Abstract Based on the Reissner-Mindlin plate theory, two 3-node triangular flat shell elements QCS31 and QCS32 are proposed by using Timoshenko's beam function within the framework of quasi-conforming technique. The exact displacement function of the Timoshenko's beam is used as the displacement on the element boundary in the bending part and the interpolated inner field function is also derived by the function. In the shear part the re-constitution technique is adopted. The drilling degrees of freedom are added in the membrane part to improve membrane behavior. The proposed elements can be used for the analysis of both moderately thick and thin… More >

Bin Gu^1,2,3, L. C. Zhang², Weifeng Yuan¹, Youjun Ning¹

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.4, pp. 309-324, 2012, DOI:10.3970/cmes.2012.088.309

Abstract Bridging the atomic and continuous analyses is an important aspect in multi-scale mechanics. This paper develops a computational method to integrate the atomic potential of a material with the finite element method. The novelty of this method is that strain energy is calculated from the atomic potential without the assumption in the Cauchy-Born rule that deformation in a virtual atomic cell is homogeneous. In this new method, the virtual atomic cell deformation is interpolated according to the continuum displacements associated with the shape functions. The applications of the method to single crystal Si and Ge bars under uniaxial tension and… More >

Ridha Djebali^1,2, Bernard Pateyron², Mohamed El Ganaoui³

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.4, pp. 293-308, 2012, DOI:10.3970/cmes.2012.088.293

Abstract We present in this study a numerical investigation of unsteady two-dimensional natural convection of an electrically conducting fluid in a square cavity under an externally imposed magnetic field. A temperature gradient is applied between the two opposing side walls parallel to y-direction, while the floor and ceiling parallel to x-direction are adiabatic. The flow is characterized by the Rayleigh number Ra raged in 103-106, the Prandtl number Pr ranged in 0.01-10, the Hartman number Ha determined by the strength of the imposed magnetic field ranged in 0-100 and its tilting angle from x-axis ranging from 0 to 90 . The… More >

Chih-Wen Chang^1,2, Chein-Shan Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.4, pp. 269-292, 2012, DOI:10.3970/cmes.2012.088.269

Abstract In this article, we utilize an optimal vector driven algorithm (OVDA) to cope with the nonlinear heat conduction problems (HCPs). From this set of nonlinear ordinary differential equations, we propose a purely iterative scheme and the spatial-discretization of finite difference method for revealing the solution vector x, without having to invert the Jacobian matrix D. Furthermore, we introduce three new ideas of bifurcation, attracting set and optimal combination, which are restrained by two parameters g and a. Several numerical instances of nonlinear systems under noise are examined, finding that the OVDA has a fast convergence rate, great computation accuracy and… More >

Srinivasan Natesan¹, S. Gowrisankar²

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.4, pp. 245-268, 2012, DOI:10.3970/cmes.2012.088.245

Abstract In this article, we propose a parameter-uniform computational technique to solve singularly perturbed parabolic initial-boundary-value problems exhibiting parabolic layers. The domain is discretized with a uniform mesh on the time direction and a nonuniform mesh obtained via equidistribution of a monitor function for the spatial variable. The numerical scheme consists of the implicit-Euler scheme for the time derivative and the classical central difference scheme for the spatial derivative. Truncation error, and stability analysis are carried out. Error estimates are derived, and numerical examples are presented. More >