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CONTENTS
Volume 3, Number 3, September 2010
 

Abstract
A multiscale method is presented for analysis of thin slab structures in which the microstructures can not be reduced to two-dimensional plane stress models and thus three dimensional treatment of microstructures is necessary. This method is based on the classical asymptotic expansion multiscale approach but with consideration of the special geometric characteristics of the slab structures. This is achieved via a special form of multiscale asymptotic expansion of displacement field. The expanded three dimensional displacement field only exhibits in-plane periodicity and the thickness dimension is in the global scale. Consequently by employing the multiscale asymptotic expansion approach the global macroscopic structural problem and the local microscopic unit cell problem are rationally set up. It is noted that the unit cell is subjected to the in-plane periodic boundary conditions as well as the traction free conditions on the out of plane surfaces of the unit cell. The variational formulation and finite element implementation of the unit cell problem are discussed in details. Thereafter the in-plane material response is systematically characterized via homogenization analysis of the proposed special unit cell problem for different microstructures and the reasoning of the present method is justified. Moreover the present multiscale analysis procedure is illustrated through a plane stress beam example.

Key Words
slab structure; multiscale method; asymptotic expansion; unit cell, homogenization.

Address
Dongdong Wang and Lingming Fang: Dept. of Civil Engineering, Xiamen University, Xiamen, Fujian, 361005, China

Abstract
This paper investigates the heat equation for domains subjected to an internal source with a sharp spatial gradient. The solution is first approximated using linear finite elements, and sufficiently small time-step sizes to yield stable simulations. The main area of interest is then in the ability to approximate the solution using Generalized Finite Elements, and again explore the time-step limitations required for stable simulations. Both high order elements, as well as elements with special enrichments are used to generate solutions. When compared to linear finite elements, the high order elements deliver better accuracy at a given level of mesh refinement, but do not offer an increase in critical time-step size. When special enrichment functions are used, the solution can be approximated accurately on very coarse meshes, while yielding solutions which are both accurate and computationally efficient. The major conclusion of interest is that the significantly larger element size yields larger allowable time-step sizes while still maintaining stability of the time-stepping algorithm.

Key Words
generalized FEM; extended FEM; partition of unity methods; multi-scale methods; explicit time-stepping; critical time-step sizes.

Address
P. O\'Hara and C.A. Duarte: Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Newmark Laboratory, 205 North Mathews Avenue, Urbana, Illinois 61801, USA
T. Eason: Air Force Research Laboratory, Air Vehicles Directorate, WPAFB, Ohio, USA

Abstract
A novel resonance based proximity DC current sensor is proposed. The sensor consists of a piezo sensed and actuated cantilever beam with a permanent magnet mounted at its free end. When the sensor is placed in proximity to a wire carrying DC current, resonant frequency of the beam changes with change in current. This change in resonant frequency is used to determine the current through the wire. The structure is simulated in micro and meso scale using COMSOL Multi physics software and the sensor is found to be linear with good sensitivity.

Key Words
cantilever beam; resonant sensor; current sensor; proximity sensor; magnetic force.

Address
B.V.M.P Santhosh Kumar, K. Suresh, U. Varun Kumar, G. Uma and M. Umapathy: Dept. of Instrumentation and Control Engineering, National Institute of Technology, Tiruchirappalli . 620 015, India

Abstract
A nonlocal finite element model is developed for solving elasto-static frictional contact problems of nanostructures and nanoscale devices. A two dimensional Eringen-type nonlocal elasticity model is adopted. The material is characterized by a stress-strain constitutive relation of a convolution integral form whose kernel is capable to take into account both the diffusion process of nonlocal elasticity and the scale ratio effects. The incremental convex programming procedure is exploited as a solver. Two examples of different nature are presented, the first one presents the behavior of a nanoscale contacting system and the second example discusses the nano-indentation problem.

Key Words
nonlocal finite element; nano-structured materials; nano-indentation; contact mechanics.

Address
F.F. Mahmoud and E.I. Meletis: Dept. of Material Science and Engineering, UT Arlington, Texas, USA

Abstract
The complex variable reproducing kernel particle method (CVRKPM) and the FEM are coupled in this paper to analyze the two-dimensional potential problems. The coupled method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, resulting in improved computational efficiency. A hybrid approximation function is applied to combine the CVRKPM with the FEM. Formulations of the coupled method are presented in detail. Three numerical examples of the two-dimensional potential problems are presented to demonstrate the effectiveness of the new method.

Key Words
potential; complex variable reproducing kernel particle method; finite element method; coupled CVRKP-FE method; hybrid approximation function.

Address
Li Chen: Dept. of Building and Construction, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong SAR
Department of Engineering Mechanics, Chang


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