CMC-Vol. 8, No. 2, 2008

Open Access

ARTICLE

A Time-Marching Algorithm for Solving Non-Linear Obstacle Problems with the Aid of an NCP-Function
Chein-Shan Liu¹
CMC-Computers, Materials & Continua, Vol.8, No.2, pp. 53-66, 2008, DOI:10.3970/cmc.2008.008.053
Abstract Proposed is a time-marching algorithm to solve a nonlinear system of complementarity equations: P_i(x_j) ≥ 0, Q_i(x_j) ≥ 0 , P_i(x_j)Q_i(x_j) = 0, i, j = 1,...,n, resulting from a discretization of nonlinear obstacle problem. We transform the above nonlinear complementarity problem (NCP) into a nonlinear algebraic equations (NAEs) system: F_i(x_j) = 0 with the aid of the Fischer-Burmeister NCP-function. Such NAEs are semi-smooth, highly nonlinear and usually implicit, being hard to handle by the Newton-like method. Instead of, a first-order system of ODEs is derived through a fictitious time equation. The time-stepping equations are obtained by applying a numerical… More >

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ARTICLE

Application of Component Mode Synthesis to Protein Structure for Dynamic Analysis
Jae In Kim¹, Kilho Eom², Moon Kyu Kwak³, Sungsoo Na⁴
CMC-Computers, Materials & Continua, Vol.8, No.2, pp. 67-74, 2008, DOI:10.3970/cmc.2008.008.067
Abstract This paper concerns the application of component mode synthesis for biomolecule modeling to understand protein dynamics. As for protein dynamics, eigenvalue problem should be formulated to obtain eigenvalue, eigenvector and thermal fluctuation. To describe the thermal fluctuation of protein, normal mode analysis is introduced and normal modes identify the dynamic behavior of protein very well. Component mode synthesis considers the given complex structure as an assembly of smaller components. The selection of a component may be arbitrary. When the component mode synthesis is applied to formulate the eigenvalue problem of protein structure, we selected a protein which may be composed… More >

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ARTICLE

Peridynamic Simulation of Electromigration
Walter Gerstle¹, Stewart Silling², David Read³, Vinod Tewary⁴, Richard Lehoucq⁵
CMC-Computers, Materials & Continua, Vol.8, No.2, pp. 75-92, 2008, DOI:10.3970/cmc.2008.008.075
Abstract A theoretical framework, based upon the peridynamic model, is presented for analytical and computational simulation of electromigration. The framework allows four coupled physical processes to be modeled simultaneously: mechanical deformation, heat transfer, electrical potential distribution, and vacancy diffusion. The dynamics of void and crack formation, and hillock and whisker growth can potentially be modeled. The framework can potentially be applied at several modeling scales: atomistic, crystallite, multiple crystallite, and macro. The conceptual simplicity of the model promises to permit many phenomena observed in microchips, including electromigration, thermo-mechanical crack formation, and fatigue crack formation, to be analyzed in a systematic and… More >

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REVIEW

A Review on the Three-Dimensional Analytical Approaches of Multilayered and Functionally Graded Piezoelectric Plates and Shells
Chih-Ping Wu^1,2, Kuan-Hao Chiu², Yung-Ming Wang²
CMC-Computers, Materials & Continua, Vol.8, No.2, pp. 93-132, 2008, DOI:10.3970/cmc.2008.008.093
Abstract The article is to present an overview of various three-dimensional (3D) analytical approaches for the analysis of multilayered and functionally graded (FG) piezoelectric plates and shells. The reported 3D approaches in the literature are classified as four different approaches, namely, Pagano's classical approach, the state space approach, the series expansion approach and the asymptotic approach. Both the mixed formulation and displacement-based formulation for the 3D analysis of multilayered piezoelectric plates are derived. The analytical process, based on the 3D formulations, for the aforementioned approaches is briefly interpreted. The present formulations of multilayered piezoelectric plates can also be used for the… More >

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