Frédéric Gibou¹, Chohong Min², Hector D. Ceniceros³

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.1, pp. 37-48, 2007, DOI:10.3970/fdmp.2007.003.037

Abstract We describe two finite difference schemes for simulating incompressible flows on nonuniform meshes using quadtree/octree data structures. The first one uses a cell-centered Poisson solver that yields first-order accurate solutions, while producing symmetric linear systems. The second uses a node-based Poisson solver that produces second-order accurate solutions and second-order accurate gradients, while producing nonsymmetric linear systems as the basis for a second-order accurate Navier-Stokes solver. The grids considered can be non-graded, i.e. the difference of level between two adjacent cells can be arbitrary. In both cases semi-Lagrangian methods are used to update the intermediate fluid More >

Chih-Ping Wu^1,2, Kuo-Yen Liu²

CMC-Computers, Materials & Continua, Vol.6, No.3, pp. 177-200, 2007, DOI:10.3970/cmc.2007.006.177

Abstract Based on the three-dimensional (3D) piezoelectricity, we present the exact solutions of simply-supported, doubly curved functionally graded (FG) elastic and piezoelectric shells using a state space approach. A set of the dimensionless coordinates and field variables is introduced in the present formulation to prevent from the ill-conditioned problem in the relevant computation. By means of direct elimination, we reduce the twenty-two basic differential equations to a set of eight state variable equations (or state equations) with variable coefficients of the thickness coordinate. By means of the successive approximation method, we artificially divide the shell into… More >

V. Kozulić¹, H. Gotovac¹, B. Gotovac¹

CMC-Computers, Materials & Continua, Vol.6, No.2, pp. 51-70, 2007, DOI:10.3970/cmc.2007.006.051

Abstract In this paper, we present a multi-resolution adaptive algorithm for solving problems described by partial differential equations. The technique is based on the collocation method using Fup basis functions, which belong to a class of Rvachev's infinitely differentiable finite functions. As it is possible to calculate derivation values of Fup basis functions of high degree in a precise yet simple way, so it is possible to efficiently apply strong formulation procedures. The mesh free method developed in this work is named Adaptive Fup Collocation Method (AFCM). The distribution of collocation points within the observed area… More >

L. Dieng¹, A. Abdul-Latif², M. Haboussi, C. Cunat³

CMC-Computers, Materials & Continua, Vol.6, No.1, pp. 21-34, 2007, DOI:10.3970/cmc.2007.006.021

Abstract Being of particular interest in this work, a complicated phenomenon related to cyclic softening of metallic polycrystals is modeled. As in the Waspaloy, this phenomenon can take place when a non-proportional tension-torsion cyclic loading of 90° out-of-phase is followed, after cyclic steady state, by a uniaxial one (tension-compression) with the same maximum equivalent plastic strain. By using the DNLR (Distribution of Non Linear Relaxation) model recently proposed by the authors describing the cyclic plasticity of metals, a new extension is here developed. It is recognized that such an extension can satisfactorily reproduce this softening phenomenon. More >

G. Q. Xie^1,2,3, X. Han², S. Y. Long³

CMC-Computers, Materials & Continua, Vol.6, No.1, pp. 1-12, 2007, DOI:10.3970/cmc.2007.006.001

Abstract A multi-walled carbon nanotube is modeled as a multiple-elastic cylindrical structure. The numerical-analytical method is adopted to analyze the characteristics of harmonic waves propagating along an anisotropic carbon nanotube. Each wall of the carbon nanotube is divided into three-nodal-line layer elements. The deflections of two adjacent tubes are coupled through the van der Waals. The governing equation of element is obtained from Hamilton's principle. A set of system equation of dynamics equilibrium for the entire structure is obtained by the assembling of all the elements. From solution of the eigenvalue equations, the dispersive characteristics, group More >

Le-Chung Shiau¹, Shih-Yao Kuo²

CMC-Computers, Materials & Continua, Vol.5, No.3, pp. 213-222, 2007, DOI:10.3970/cmc.2007.005.213

Abstract A high precision high order triangular plate element is developed for the linear flutter analysis of thermally buckled composite sandwich plates. Due to uneven thermal expansion in the two local material directions, the buckling mode of the plate may be shifted from one pattern to another for certain fiber orientation or plate aspect ratio as the aerodynamic pressure is present. This buckle pattern change alters the frequencies and modes of the plate and that in turn changes the flutter coalescent modes. Numerical results show that temperature has a destabilizing effect on the flutter boundary but More >

M. Timmel¹, M. Kaliske¹, S. Kolling², R. Mueller³

CMC-Computers, Materials & Continua, Vol.5, No.3, pp. 161-172, 2007, DOI:10.3970/cmc.2007.005.161

Abstract A damage approach based on a material model with microstructural evolution is presented. In contrast to phenomenological constitutive laws, the material response is given by mechanisms at the microscale. At first, a micromechanical substructure is chosen, which represents the overall material behaviour. Then the system is described using a micromechanical model. A geometrical modification of the microstructure is allowed to minimize the total energy. Consequently, the global stiffness is reduced. In this context, thermodynamical considerations are based on configurational forces. With the help of the discussed approach, void growth phenomena of materials, which lead to More >

Jin Yeon Cho¹

CMC-Computers, Materials & Continua, Vol.5, No.2, pp. 99-116, 2007, DOI:10.3970/cmc.2007.005.099

Abstract A novel way is proposed to fulfill Kronecker delta condition in moving least squares (MLS) approximation along the essential boundary. In the proposed scheme, the original MLS weight is modified to boundary interpolatable (BI) weight based on the observation that the support of weight function is exactly the same as the support of MLS nodal shape function. The BI weight is zero along the boundary edges except the edges containing the nodal point associated with the concerned weight. In order to construct the BI weight from the original weight, concept of edge distance function is… More >

A. H. Muhr¹

CMC-Computers, Materials & Continua, Vol.5, No.1, pp. 11-30, 2007, DOI:10.3970/cmc.2007.005.011

Abstract The mechanics of laminates of elastomer and shims of high modulus material are reviewed. Such structures are often built to provide engineering components with specified, and quite different, stiffnesses in different modes of deformation. The shims may either be rigid or flexible, flat or curved, but are usually close to inextensible, being made of a high modulus material such as steel. On the other hand, rubber has an exceptionally low shear modulus, about one thousandth of its bulk modulus, so that shear of the rubber layers and flexure of the high modulus layers (if thin)… More >

Ramana M. Pidaparti^1,2, Evan J. Neblett²

CMC-Computers, Materials & Continua, Vol.5, No.1, pp. 1-10, 2007, DOI:10.3970/cmc.2007.005.001

Abstract A neural network (NN) model is developed for the analysis and prediction of the mapping between degradation of chemical elements and electrochemical parameters during the corrosion process. The input parameters to the neural network model are alloy composition, electrochemical parameters, and corrosion time. The output parameters are the degradation of chemical elements in AA 2024-T3 material. The NN is trained with the data obtained from Energy Dispersive X-ray Spectrometry (EDS) on corroded specimens. A very good performance of the neural network is achieved after training and validation with the experimental data. After validating the NN More >