Jacek Narski^1,2, Marco Picasso¹

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.1, pp. 49-64, 2007, DOI:10.3970/fdmp.2007.003.049

Abstract An adaptive phase field model for the solidification of binary alloys in three space dimensions is presented. The fluid flow in the liquid due to different liquid/solid densities is taken into account. The unknowns are the phase field, the alloy concentration and the velocity/pressure in the liquid. Continuous, piecewise linear finite elements are used for the space discretization, a semi-implicit scheme is used for time discretization. An adaptive method allows the number of degrees of freedom to be reduced, the mesh tetrahedrons having high aspect ratio whenever needed. Numerical results show that our method is More >

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 >

Mark Sussman¹, Mitsuhiro Ohta²

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.1, pp. 21-36, 2007, DOI:10.3970/fdmp.2007.003.021

Abstract In this paper, we describe new techniques for numerically approximating two-phase flows. Specifically, we present new techniques for treating the viscosity and surface tension terms that appear in the Navier-Stokes equations for incompressible two-phase flow. Our resulting numerical method has the property that results computed using our two-phase algorithm approach the corresponding "one-phase'' algorithm in the limit of zero gas density/viscosity; i.e. the two-phase results approach the one-phase free-boundary results in the limit that the gas is assumed to become a uniform pressure void. By grid convergence checks and comparison with previous experimental data, we More >

J.S. Lowengrub¹, J-J. Xu², A. Voigt³

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.1, pp. 1-20, 2007, DOI:10.3970/fdmp.2007.003.001

Abstract We introduce and investigate numerically a thermodynamically consistent simple model of a drop or vesicle in which the interfacial surface contains multiple constitutive components (e.g. amphiphilic molecules). The model describes the nonlinear coupling among the flow, drop/vesicle morphology and the evolution of the surface phases. We consider a highly simplified version of the Helfrich model for fluid-like vesicle membranes in which we neglect the effects of bending forces and spontaneous curvature but keep the effects of inhomogeneous surface tension forces. Thus, this model may also describe liquid drops. To solve the highly nonlinear, coupled system More >

Haomiao Zhou^1,2, Youhe Zhou^1,3, Xiaojing Zheng¹

CMC-Computers, Materials & Continua, Vol.6, No.3, pp. 201-212, 2007, DOI:10.3970/cmc.2007.006.201

Abstract This paper presents some simulation results of nonlinear dynamic responses for a laminated composite beam embedded by actuators of the giant magnetostrictive material (Terfenol-D) subjected to external magnetic fields, where the giant magnetostrictive materials utilizing the realignment of magnetic moments in response to applied magnetic fields generate nonlinear strains and forces significantly larger than those generated by other smart materials. To utilize the full potential application of the materials in the function and safety designs, e.g., active control of vibrations, the analysis of dynamic responses is requested in the designs as accurately as possible on… 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 >

H. Nguyen-Van¹, N. Mai Duy², T. Tran-Cong ³

CMC-Computers, Materials & Continua, Vol.6, No.3, pp. 159-176, 2007, DOI:10.3970/cmc.2007.006.159

Abstract This paper reports the development of a simple but efficient and accurate four-node quadrilateral element for models of laminated, anisotropic plate behaviour within the framework of the first-order shear deformation theory. The approach incorporates the strain smoothing method for mesh-free conforming nodal integration into the conventional finite element techniques. The membrane-bending part of the element stiffness matrix is calculated by the line integral on the boundaries of the smoothing elements while the shear part is performed using an independent interpolation field in the natural co-ordinate system. Numerical results show that the element offered here is More >

J. Oh¹, N. Katsube², F.W. Brust³

CMC-Computers, Materials & Continua, Vol.6, No.3, pp. 129-158, 2007, DOI:10.3970/cmc.2007.006.129

Abstract In this paper, intergranular cavity growth in regimes, where both surface diffusion and deformation enhanced grain boundary diffusion are important, is studied. In order to continuously simulate the cavity shape evolution and cavity growth rate, a fully-coupled numerical method is proposed. Based on the fully-coupled numerical method, a gradual cavity shape change is predicted and this leads to the adverse effect on the cavity growth rate. As the portion of the cavity volume growth due to jacking and viscoplastic deformation in the total cavity volume growth increases, spherical cavity evolves to V-shaped cavity. The obtained More >

Chein-Shan Liu¹

CMC-Computers, Materials & Continua, Vol.6, No.2, pp. 117-128, 2007, DOI:10.3970/cmc.2007.006.117

Abstract In this paper the Landau-Lifshitz equation is subjected to a circularly polarized field in the plane, as well as both a dc field and an anisotropy field along the vertical easy axis perpendicular to the plane. The representation of Landau-Lifshitz equation in the Minkowski space is a Lie-type system. By performing a computation through the Lie-group solvers we can develop a consistent numerical method, which satisfies the consistency condition exactly, and thus can retain the invariant behavior. Then, we use the consistent numerical method to investigate the magnetization reversal, whose switching criterion is displayed through More >

E.J. Sapountzakis¹, G.C. Tsiatas²

CMC-Computers, Materials & Continua, Vol.6, No.2, pp. 103-116, 2007, DOI:10.3970/cmc.2007.006.103

Abstract In this paper the general flexural-torsional buckling and vibration problems of composite Euler-Bernoulli beams of arbitrarily shaped cross section are solved using a boundary element method. The general character of the proposed method is verified from the formulation of all basic equations with respect to an arbitrary coordinate system, which is not restricted to the principal one. The composite beam consists of materials in contact each of which can surround a finite number of inclusions. It is subjected to a compressive centrally applied load together with arbitrarily transverse and/or torsional distributed or concentrated loading, while… More >