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CONTENTS
Volume 1, Number 3, September 2008
 

Abstract
When carbon-filled rubber specimens are subjected to cyclic loading, they do not return to their initial state after loading and subsequent unloading, but exhibit a residual strain or permanent deformation. We propose a specific form of the pseudo-elastic energy function to represent cyclic loading for incompressible, isotropic materials with stress softening and residual strain. The essence of the pseudo-elasticity theory is that material behaviour in the primary loading path is described by a common elastic strain energy function, and in unloading, reloading or secondary unloading paths by a different strain energy function. The switch between strain energy functions is controlled by the incorporation of a damage variable into the strain energy function. An extra term is added to describe the permanent deformation. The finite element implementation of the proposed model is presented in this paper. All parameters in the proposed model and elastic law can be easily estimated based on experimental data. The numerical analyses show that the results are in good agreement with experimental data.

Key Words
Mullins effect; pseudo-elastic model; finite element method; permenant deformation.

Address
Z. Q. Guo and L. J. Sluys; Faculty of Civil Engineering and Geosciences, Delft University of Technology, Stevinweg 1, 2628 CN Delft, the Netherlands

Abstract
This paper presents the derivation of the generalized governing equations in theory of elasticity, their weak forms and the some applications in the numerical analysis of structural mechanics. Unlike the differential equations in classical elasticity theory, the generalized equations of the equilibrium and compatibility equations presented here take the form of integral equations, and the generalized equilibrium equations contain the classical differential equations and the boundary conditions in a single equation. By using appropriate test functions, the weak forms of these generalized governing equations can be established. It can be shown that various variational principles in structural analysis are merely the special cases of these weak forms of generalized governing equations in elasticity. The present weak forms of elasticity equations extend greatly the choices of the trial functions for approximate solutions in the numerical analysis of various engineering problems. Therefore, the weak forms of generalized governing equations in elasticity provide a powerful modeling tool in the computational structural mechanics.

Key Words
generalized governing equations; weak form; variational principles; finite element method; computational mechanics.

Address
G. Shi; Department of Mechanics, Tianjin University, Tianjin, 300072, China
L. Tang; Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116024, China

Abstract
A Galerkin meshfree method is presented for analyzing shear deformable cylindrical panels. Based upon the analogy between the cylindrical panel and the curved beam a pure bending mode for cylindrical panel is rationally constructed. The meshfree approximation employed herein is characterized by an enhanced moving least square or reproducing kernel basis function that can exactly represent the pure bending mode and thus meets the requirement of Kirchhoff mode reproducing condition. The variational form is discretized using the efficient stabilized conforming nodal integration with a smoothed nodal gradient based curvature. The resulting meshfree formulation satisfies the integration constraint for bending exactness. Moreover, it is shown here that the smoothed gradient preserves several desired properties which are valid for the standard gradient obtained by direct differentiation, such as partition of nullity and reproduction of a constant strain field. The efficacy of the proposed approach is demonstrated by two benchmark cylindrical panel examples.

Key Words
cylindrical panel; meshfree method; stabilized conforming nodal integration; smoothed nodal gradient.

Address
Dongdong Wang; Department of Civil Engineering, Xiamen University, Xiamen, Fujian, 361005, China
Youcai Wu; Karagozian & Case, 2550 N Hollywood Way, Suite 500, Burbank, CA 91505, USA

Abstract
The result of damage detection from on-site measurements is commonly polluted by unavoidable measurement noises. It is widely recognized that this side influence could be reduced to some extent if the sensor placement was properly designed. Although many methods have been proposed to find the optimal number and location of mono-type sensors, the optimal layout of multi-type sensors need further investigation, because a network of heterogeneous sensors is commonly used in engineering. In this paper, a new criterion of the optimal placement for different types of sensors is proposed. A corresponding heuristic is developed to search for good results. In addition, Monte Carlo simulation is suggested to design a robust damage detection system which contains certain redundancies. The validity of these methods is illustrated by two bridge examples.

Key Words
damage detection; sensor placement; bridge.

Address
Y. Q. Li; Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China
M. S. Zhou; CCCC Highway and Bridge Consultants Co., Ltd, China
Z. H. Xiang and Z. Z. Cen; Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China

Abstract
A combined stochastic diffusion and mean-field model is developed for a systematic study of the grain growth in a pure single-phase polycrystalline material. A corresponding Fokker-Planck continuity equation is formulated, and the interplay/competition of stochastic and curvature-driven mechanisms is investigated. Finite difference results show that the stochastic diffusion coefficient has a strong effect on the growth of small grains in the early stage in both two-dimensional columnar and three-dimensional grain systems, and the corresponding growth exponents are ~ 0.33 and ~ 0.25, respectively. With the increase in grain size, the deterministic curvature-driven mechanism becomes dominant and the growth exponent is close to 0.5. The transition ranges between these two mechanisms are about 2-26 and 2-15 nm with boundary energy of 0.01-1 J m? in two- and three-dimensional systems, respectively. The grain size distribution of a three-dimensional system changes dramatically with increasing time, while it changes a little in a two-dimensional system. The grain size distribution from the combined model is consistent with experimental data available.

Key Words
grain growth; stochastic diffusion; curvature-driven process; mean-field model; the finite difference method.

Address
Y. G. Zheng and H. W. Zhang;State Key Laboratory of Structural Analysis for Industrial Equipment, Dept. of Engineering Mechanics, Dalian Univ. of Technology, Dalian, 116024, China
Z. Chen; Department of Civil and Environmental Engineering, Univ. of Missouri, Columbia, Missouri 65211-2200, USA

Abstract
The aerostatic instability of cable-supported bridges is studied, with emphasis placed on modeling of the geometric nonlinear effects of various components of cable-supported bridges. Two-node catenary cable elements, which are more rational than truss elements, are adopted for simulating cables with large or small sags. Aerostatic loads are expressed in terms of the mean drag, lift and pitching moment coefficients. The geometric nonlinear analysis is performed with the dead loads and wind loads applied in two stages. The critical wind velocity for aerostatic instability is obtained as the condition when the pitching angle of the bridge deck becomes unbounded. Unlike those existing in the literature, each intermediate step of the incremental-iterative procedure is clearly given and interpreted. As such, the solutions obtained for the bridges are believed to be more rational than existing ones. Comparisons and discussions are given for the examples studied.

Key Words
catenary cable; critical wind load; geometric nonlinear analysis; aerostatic instability; cable-supported bridge.

Address
Y. B. Yang; Dept. of Building and Construction, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong
Jiunn-Yin Tsay; Dept. of Civil Engineering, National Taiwan University, Taipei, 10617, Taiwan


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