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CONTENTS
Volume 2, Number 3, September 2009
 

Abstract
This paper presents a new nonlocal stress variational principle approach for the transverse free vibration of an Euler-Bernoulli cantilever nanobeam with an initial axial tension at its free end. The effects of a nanoscale at molecular level unavailable in classical mechanics are investigated and discussed. A sixth-order partial differential governing equation for transverse free vibration is derived via variational principle with nonlocal elastic stress field theory. Analytical solutions for natural frequencies and transverse vibration modes are determined by applying a numerical analysis. Examples conclude that nonlocal stress effect tends to significantly increase stiffness and natural frequencies of a nanobeam. The relationship between natural frequency and nanoscale is also presented and its significance on stiffness enhancement with respect to the classical elasticity theory is discussed in detail. The effect of an initial axial tension, which also tends to enhance the nanobeam stiffness, is also concluded. The model and approach show potential extension to studies in carbon nanotube and the new result is useful for future comparison.

Key Words
cantilever nanobeam; free vibration; initial tension; nonlocal elasticity; nonlocal stress.

Address
C.W. Lim: Department of Building and Construction, City University of Hong Kong,Tat Chee Avenue, Kowloon, Hong Kong SAR, P.R. China
C. Li: Department of Building and Construction, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong SAR, P.R. China. Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China
J. L. Yu: Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China

Abstract
This study illustrates the differences between the elasto-plastic cap model and Lade\'s model with Cosserat rotation through the analyses of two large-scale geosynthetic-reinforced soil (GRS) retaining wall tests that were brought to failure using a monotonically increasing surcharge pressure. The finite element analyses with Lade\'s model were able to reasonably simulate the large-scale plane strain laboratory tests. On average, the finite element analyses gave reasonably good agreement with the experimental results in terms of global performances and shear band occurrences. In contrast, the cap model was not able to simulate the development of shear banding in the tests. In both test simulations the cap model predicted failure loads that were substantially less than the measured ones.

Key Words
geosynthetic-reinforced soil; GRS; geogrids; geotextile; Lade

Address
Mustafa Alsaleh: Virtual Product Development Division, Caterpillar Inc., 14009 Old Galena Rd., Mossville, IL 61552, U.S.A.
Akadet Kitsabunnarat: HNTB, 11414 W. Park Place, Milwaukee, WI 53224, U.S.A.
Sam Helwany: Department of Civil Engineering and Mechanics, University of Wisconsin at Milwaukee, 3200 North Cramer St., EMS W230 Milwaukee, WI 53201, U.S.A.

Abstract
This paper is intended to investigate interaction response of a train running over a suspension bridge undergoing support settlements. The suspension bridge is modeled as a single-span suspended beam with hinged ends and the train as successive moving oscillators with identical properties. To conduct this dynamic problem with non-homogeneous boundary conditions, this study first divides the total response of the suspended beam into two parts: the static and dynamic responses. Then, the coupled equations of motion for the suspended beam carrying multiple moving oscillators are transformed into a set of nonlinearly coupled generalized equations by Galerkin

Key Words
high speed train; support settlement; resonance; suspension bridge.

Address
J. D. Yau: Department of Architecture, Tamkang University, Taipei 10620, Taiwan

Abstract
The Enriched Free Mesh Method (EFMM) is a patch-wise procedure in which both a displacement field on an element and a stress/strain field on a cluster of elements connected to a node can be defined. On the other hand, the Superconvergent Patch Recovery (SPR) is known to be an efficient post-processing procedure of the finite element method to estimate the error norm at a node. In this paper, we discuss the relationship between solutions of the EFMM and those of the SPR through several convergence studies. In addition, in order to solve the demerit of the smoothing effect on the fracture mechanics fields, we implement a singular stress field to a local patch in the EFMM, and its effectiveness is investigated.

Key Words
patch-wise mixed formulation; adaptive finite element method; enriched free mesh method; free mesh method; superconvergent patch recovery.

Address
Hitoshi Matsubara: Department of Civil Engineering and Architecture, University of the Ryukyus, 1, Senbaru,
Nishihara-cho, Okinawa 903-0213, Japan
Genki Yagawa: Center for Computational Mechanics Research, Toyo University, 2-36-5, Hakusan, Bunkyo-ku, Tokyo 112-0001, Japan

Abstract
In this work, we discuss a reproducing kernel collocation method (RKCM) for solving 2nd order PDE based on strong formulation, where the reproducing kernel shape functions with compact support are used as approximation functions. The method based on strong form collocation avoids the domain integration, and leads to well-conditioned discrete system of equations. We investigate the convergence and the computational complexity for this proposed method. An important result obtained from the analysis is that the degree of basis in the reproducing kernel approximation has to be greater than one for the method to converge. Some numerical experiments are provided to validate the error analysis. The complexity of RKCM is also analyzed, and the complexity comparison with the weak formulation using reproducing kernel approximation is presented.

Key Words
reproducing kernel approximation; convergence; complexity; strong form collocation method.

Address
Hsin-Yun Hu: Department of Mathematics, Tunghai University, Taichung 407, Taiwan R.O.C.
Chiu-Kai Lai: Department of Mathematics, Tunghai University, Taichung 407, Taiwan R.O.C.
Jiun-Shyan Chen: Department of Civil and Environmental Engineering, University of California, Los Angeles, CA 90095, U.S.A.

Abstract
Recent development in composites containing phase-transforming particles, such as vanadium dioxide or barium titanate, reveals the overall stiffness and viscoelastic damping of the composites may be unbounded (Lakes et al. 2001, Jaglinski et al. 2007). Negative stiffness is induced from phase transformation predicted by the Landau phase transformation theory. Although this unbounded phenomenon is theoretically supported with the composite homogenization theory, detailed stress analyses of the composites are still lacking. In this work, we analyze the stress distribution of the Hashin-Shtrikman (HS) composite and its two-dimensional variant, namely a circular inclusion in a square plate, under the assumption that the Young

Key Words
elasticity; composite; negative stiffness; interfacial stress; Eshelby

Address
Yun-Che Wang: Engineering Materials Program, Department of Civil Engineering, Center for Micro/Nano Science and
Technology, National Cheng Kung University, 1 University Avenue, Tainan, Taiwan 70101
Chi-Ching Ko: Engineering Materials Program, Department of Civil Engineering, Center for Micro/Nano Science and
Technology, National Cheng Kung University, 1 University Avenue, Tainan, Taiwan 70101


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