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CONTENTS
Volume 2, Number 2, June 2009
 

Abstract
Multiscale analysis is a stepwise procedure to obtain macro-scale material laws, directly amenable to structural analysis, based on information from finer scales. An essential ingredient of this mode of analysis is mathematical homogenization of heterogeneous materials at these scales. The purpose of this paper is to demonstrate the potential of multiscale analysis in civil engineering. The materials considered in this work are wood, shotcrete, and asphalt.

Key Words
multiscale engineering; New Austrian Tunneling Method; wood; asphalt

Address
H.A. Mang: Institute for Mechanics of Materials and Structures, Vienna University of Technology, Karlsplatz 13, 1040 Vienna, Austria
E. Aigner: Institute for Mechanics of Materials and Structures, Vienna University of Technology, Karlsplatz 13, 1040 Vienna, Austria
J. Eberhardsteiner: Institute for Mechanics of Materials and Structures, Vienna University of Technology, Karlsplatz 13, 1040 Vienna, Austria
C. Hackspiel: Institute for Mechanics of Materials and Structures, Vienna University of Technology, Karlsplatz 13, 1040 Vienna, Austria
C. Hellmich: Institute for Mechanics of Materials and Structures, Vienna University of Technology, Karlsplatz 13, 1040 Vienna, Austria
K. Hofstetter: Institute for Mechanics of Materials and Structures, Vienna University of Technology, Karlsplatz 13, 1040 Vienna, Austria
R. Lackner: Material-Technology Unit, Institute for Construction and Materials Science, University of Innsbruck
Technikerstrasse 13, 6020 Innsbruck, Austria
B. Pichler: Institute for Mechanics of Materials and Structures, Vienna University of Technology, Karlsplatz 13, 1040 Vienna, Austria
S. Scheiner: Institute for Mechanics of Materials and Structures, Vienna University of Technology, Karlsplatz 13, 1040 Vienna, Austria
R. Sturzenbecher: Institute for Mechanics of Materials and Structures, Vienna University of Technology, Karlsplatz 13, 1040 Vienna, Austria

Abstract
This paper presents a meshfree procedure using a convex generalized meshfree (GMF) approximation for the large deformation analysis of particle-reinforced rubber compounds on microscopic level. The convex GMF approximation possesses the weak-Kronecker-delta property that guarantees the continuity of displacement across the material interface in the rubber compounds. The convex approximation also ensures the positive mass in the discrete system and is less sensitive to the meshfree nodal support size and integration order effects. In this study, the convex approximation is generated in the GMF method by choosing the positive and monotonic increasing basis function. In order to impose the periodic boundary condition in the unit cell method for the microscopic analysis, a singular kernel is introduced on the periodic boundary nodes in the construction of GMF approximation. The periodic boundary condition is solved by the transformation method in both explicit and implicit analyses. To simulate the interface de-bonding phenomena in the rubber compound, the cohesive interface element method is employed in corporation with meshfree method in this study. Several numerical examples are presented to demonstrate the effectiveness of the proposed numerical procedure in the large deformation analysis.

Key Words
meshfree; microscopic; periodic boundary condition; basis function; Kronecker-delta property; unit cell

Address
C. T. Wu: Livermore Software Technology Corporation, Livermore, CA 94550, USA
M. Koishi: CAE Laboratory, The Yokohama Rubber Co, Ltd., Japan

Abstract
Damage detection methods using structural dynamic responses have received much attention in the past decades. For bridge and offshore structures, these methods are usually based on beam models. To ensure the successful application of these methods, it is necessary to examine the sensitivity of modal properties to structural damages. To this end, an analytic solution is presented of the modal properties of simply-supported Euler-Bernoulli beams that contain a general damage with no additional assumptions. The damage can be a reduction in the bending stiffness or a loss of mass within a beam segment. This solution enables us to thoroughly discuss the sensitivities of different modal properties to various damages. It is observed that the lower natural frequencies and mode shapes do not change so much when a section of the beam is damaged, while the mode of rotation angle and curvature modes show abrupt change near the damaged region. Although similar observations have been reported previously, the analytical solution presented herein for clarifying the mechanism involved is considered a contribution to the literature. It is helpful for developing new damage detection methods for structures of the beam type.

Key Words
damage; damage detection; Euler-Bernoulli beam; modal property; sensitivity

Address
Zhihai Xiang: Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, P. R. China
Yao Zhang: Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, P. R. China

Abstract
Machine or structural members subjected to fatigue loading will have a crack initiated during early part of their life. Therefore analysis of members with cracks and other discontinuities is very important. Finite element method has enjoyed widespread use in engineering, but it is not convenient for crack problems as the region very close to crack tip is to be discretized with very fine mesh. However, as the body force method (BFM), requires only the boundary of the discontinuity (crack or hole) to be discretized it is easy versatile technique to analyze such problems. In the present work fundamental solution for concentrated load x + iy acting in the semi-infinite plate at an arbitrary point z0 = x0 + iy0 is considered. These fundamental solutions are in complex form

Key Words
body force method; complex potentials; Melan potentials

Address
B. S. Manjunath: Department of Mechanical Engineering, K. L.E. Society

Abstract
Dynamics of the electric system for the toroidal drive under mechanical disturbance is presented. Using the method of perturbation, free vibrations of the electric system under mechanical disturbance are studied. The forced responses of the electric system to voltage excitation under mechanical disturbance are also presented. We show that as the time grows, the resonance vibration caused by voltage excitation still exists and the vibrations caused by mechanical disturbance are enlarged. The coupled resonance vibration caused by mechanical disturbance and voltage excitation is discussed. The conditions of the occurrence of coupled resonance are studied.

Key Words
toroidal drive; electromechanical integrated; dynamics; free vibration; forced response

Address
Xiuhong Hao: Mechanical engineering institute, Yanshan University, Qinhuangdao 066004, China
Lizhong Xu: Mechanical engineering institute, Yanshan University, Qinhuangdao 066004, China

Abstract
This article describes recent work on mechanics of carbon nanotubes, one of the most fundamental and amazing man-made nanostructures. The noteworthy point is that \"nano\"-scale mechanics of carbon nanotubes can be well described by the continuum elastic theories for \"macro\"-scale thin shells. This provides an efficient means to elucidate mechanical deformation effects of carbon nanotubes on their physical and chemical properties, which is significant to develop new-generation nanomaterials based on nanotubes and their composites. Potential applications of the mechanical deformation of nanotubes in nano-electronics and nano-biology are also commented. In addition, theoretical investigations regarding external pressure buckling is carried out here and we have numerically confirmed that larger N (the number of layers) and a smaller D (the innermost diameter) make \"corrugation modes\" with a larger mode-index k be energetically favored.

Key Words
carbon nanotube; elastic deformation; buckling; high pressure

Address
Motohiro Sato: Department of Socio-Environmental Engineering, Graduate School of Engineering, Hokkaido University, Sapporo, Japan
Hiroyuki Shima: Department of Applied Physics, Graduate School of Engineering, Hokkaido University, Sapporo, Japan


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