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CONTENTS
Volume 1, Number 2, June 2008
 

Abstract
In this paper, both experimental measurement and theoretical analysis are used to investigate the out-of-plane resonant characteristics of a cantilevered piezoceramic plate in air and three different kinds of fluid. The experimental method, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), is the major technique used in this study to measure the resonant characteristics of the cantilivered piezoceramic plate. Both resonant frequencies and full-field mode shapes are obtained from this experimental technique. Numerical computations based on the finite element analysis are presented for comparison with the experimental results. Good quality of mode shapes for the cantilevered piezoceramic plate in air is obtained from the AF-ESPI technique. However, the quality decreases as the viscosity of fluids increases. From the results provided from experimental measurements and numerical computations, it is indicated that the resonant frequencies of the cantilevered piezoceramic plate in fluid decrease with the increase of the viscosity of fluids. Good agreements between the experimental measured data and the numerical calculated results are found for both resonant frequencies and mode shapes of the cantilevered piezoceramic plate in fluid

Key Words
piezoceramic plate; fluid; electronic speckle pattern interferometry; resonant frequencies; mode shape

Address
Yu-Chih Lin; Department of Biomedical Engineering, Yuanpei University, Hsinchu, Taiwan 300, Republic of China
Chien-Ching Ma; Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 106, Republic of China

Abstract
In this paper, we model grain boundary evolution based on a multiple level set method. Grain boundary migration under a curvature-induced driving force is considered and the level set method is employed to deal with the resulting topological changes of grain structures. The complexity of using a level set method for modeling grain structure evolution is due to its N-phase nature and the associated geometry compatibility constraint. We employ a multiple level set method with a predictor-multicorrectors approach to reduce the gaps in the triple junctions down to the grid resolution level. A ghost cell approach for imposing periodic boundary conditions is introduced without solving a constrained problem with a Lagrange multiplier method or a penalty method. Numerical results for both uniform and random grain structures evolution are presented and the results are compared with the solutions based on a front tracking approach (Chen and Kotta et al. 2004b).

Key Words
level set method; multiple level set; grain boundary migration; microstructure evolution.

Address
Xinwei Zhang, Jiun-Shyan Chen and Stanley Osher; University of California, Los Angeles (UCLA), Los Angeles, CA 90095, USA

Abstract
Owing to the growing size of the eigenvalue problem and the growing number of eigenvalues desired, solution methods of iterative nature are becoming more popular than ever, which however suffer from low efficiency and lack of proper convergence criteria. In this paper, three efficient iterative eigenvalue algorithms are considered, i.e., subspace iteration method, iterative Ritz vector method and iterative Lanczos method based on the cell sparse fast solver and loop-unrolling. They are examined under the mode error criterion, i.e., the ratio of the out-of-balance nodal forces and the maximum elastic nodal point forces. Averagely speaking, the iterative Ritz vector method is the most efficient one among the three. Based on the mode error convergence criteria, the eigenvalue solvers are shown to be more stable than those based on eigenvalues only. Compared with ANSYS

Key Words
aggressive shifting; generalized eigenvalue problem; finite element analysis

Address
P. Chen, S. L. Sun, Q. C. Zhao, Y. C. Gong, Y. Q. Chen and M. W. Yuan; LTCS, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing, 100871, China

Abstract
The statistical two-order and two-scale method is developed for predicting the mechanics parameters, such as stiffness and strength of core-shell particle-filled polymer composites. The representation and simulation on meso-configuration of random particle-filled polymers are stated. And the major statistical two-order and two-scale analysis formulation is briefly given. The two-order and two-scale expressions for the strains and stresses of conventionally strength experimental components, including the tensional or compressive column, the twist bar and the bending beam, are developed by means of their classical solutions with orthogonal-anisotropic coefficients. Then a new effective mesh generation algorithm is presented. The mechanics parameters of core-shell particle-filled polymer composites, including the expected stiffness parameters, minimum stiffness parameters, and the expected elasticity limit strength and the minimum elasticity limit strength, are defined by means of the stiffness coefficients and elasticity strength criterions for core, shell and matrix. Finally, the numerical results for predicting both stiffness and elasticity limit strength parameters are compared with the experimental data.

Key Words
polymer matrix composites; finite element modeling (FEM); core-shell particle; elastic limit strength

Address
Fei Han and Yan Yu; Dept. of Applied Mathematics, Northwestern Polytechnical University, Xi\'an, 710072 China
Junzhi Cui; Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080 China

Abstract
In this study, we investigate the discontinuous-derivative treatment at the gas-liquid interface in underwater explosion (UNDEX) problems by using the Moving Least Squares-Smoothed Particle Hydrodynamics (MLS-SPH) method, which is known as one of the particle methods suitable for problems where large deformation and inhomogeneity occur in the whole domain. Because the numerical oscillation of pressure arises from derivative discontinuity in the UNDEX analysis using the standard SPH method, the MLS shape function with Discontinuous-derivative Basis Function (DBF) that is able to represent the derivative discontinuity of field function is utilized in the MLS-SPH formulation in order to suppress the nonphysical pressure oscillation. The effectiveness of the MLS-SPH with DBF is demonstrated in comparison with the standard SPH and conventional MLS-SPH though a shock tube problem and benchmark standard problems of UNDEX of a trinitrotoluene (TNT) charge.

Key Words
gas-liquid interface; discontinuous derivative; underwater explosion; smoothed particle hydrodynamics; moving least squares.

Address
Gaku Hashimoto; RIKEN, 2-1 Hirosawa, Woko-shi, Saitama 351-0198, Japan
Hirohisa Noguchi; Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama-shi, Kanagawa 223-8522, Japan

Abstract
This paper develops a 3D homogenization based continuumdamage mechanics (HCDM) model for fiber reinforced composites undergoing micromechanical damage under monotonic and cyclic loading. Micromechanical damage in a representative volume element (RVE) of the material occurs by fiber-matrix interfacial debonding, which is incorporated in the model through a hysteretic bilinear cohesive zone model. The proposed model expresses a damage evolution surface in the strain space in the principal damage coordinate system or PDCS. PDCS enables the model to account for the effect of non-proportional load history. The loading/unloading criterion during cyclic loading is based on the scalar product of the strain increment and the normal to the damage surface in strain space. The material constitutive law involves a fourth order orthotropic tensor with stiffness characterized as a macroscopic internal variable. Three dimensional damage in composites is accounted for through functional forms of the fourth order damage tensor in terms of components of macroscopic strain and elastic stiffness tensors. The HCDM model parameters are calibrated from homogenization of micromechanical solutions of the RVE for a few representative strain histories. The proposed model is validated by comparing results of the HCDM model with pure micromechanical analysis results followed by homogenization. Finally, the potential of HCDM model as a design tool is demonstrated through macro-micro analysis of monotonic and cyclic damage progression in composite structures.

Key Words
continuum damage mechanics; fatigue damage; homogenization; interfacial debonding; cohesive zone element; principal damage coordinate system

Address
Jayesh R. Jain and Somnath Ghosh; Computational Mechanics Research Laboratory, Dept. of Mechanical Engineering, The Ohio State University, Columbus, OH 43210, USA

Abstract
In this paper, thermodynamical properties of crystalline silicon under strain are calculated using classical molecular dynamics (MD) simulations based on the Tersoff interatomic potential. The Helmholtz free energy of the silicon crystal under strain is calculated by using the ensemble method developed by Frenkel and Ladd (1984). To account for quantum corrections under strain in the classical MD simulations, we propose an approach where the quantum corrections to the internal energy and the Helmholtz free energy are obtained by using the corresponding energy deviation between the classical and quantum harmonic oscillators. We calculate the variation of thermodynamic properties with temperature and strain and compare them with results obtained by using the quasi-harmonic model in the reciprocal space.

Key Words
modeling of materials; silicon; finite temperature; thermodynamical properties; strain effects; Molecular Dynamics; Tersoff potential.

Address
H. Zhao and N. R. Aluru; Dept. of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA


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