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CONTENTS
Volume 14, Number 4, October 2002
 

Abstract
This paper presents several applications of an improved estimator of the constitutive relation error (CRE) for plasticity problems. The cumulative aspect of the CRE estimator with respect to time is analyzed and we propose a first analysis of the local effectivity indexes of the CRE estimator in plasticity.

Key Words
finite element method; plasticity; error estimation; local qualities.

Address
L.M.T. Cachan, ENS Cachan/CNRS/Univ. Paris 6, 61 avenue du President Wilson, 94235 Cachan CEDEX, France

Abstract
This paper presents a domain decomposition method for buckling analysis of rectangular Kirchhoff plates subjected to uniaxial inplane load and with mixed edge support conditions. A plate is decomposed into two rectangular subdomains along the change of the discontinuous support conditions. The automated Ritz method is employed to derive the governing eigenvalue equation for the plate system. Compatibility conditions are imposed for transverse displacement and slope along the interface of the two subdomains by modifying the Ritz trial functions. The resulting Ritz function ensures that the transverse displacement and slope are continuous along the entire interface of the two subdomains. The validity and accuracy of the proposed method are verified with convergence and comparison studies. Buckling results are presented for several selected rectangular plates with various combination of mixed edge support conditions.

Key Words
buckling of plates; domain decomposition; Kirchhoff plate; mixed edge support conditions;

Address
Centre for Construction Technology and Research, University of Western Sydney,
Penrith South DC, 1797, Australia

Abstract
This paper explores the possibility of using a combination of the empirical mode
decomposition (EMD) and the Hilbert transform (HT), termed the Hilbert-Huang transform (HHT) method, to identify the modal damping ratios of the structure with closely spaced modal frequencies. The principle of the HHT method and the procedure of using the HHT method for modal damping ratio identification are briefly introduced first. The dynamic response of a two-degrees-of-freedom (2DOF)
system under an impact load is then computed for a wide range of dynamic properties from well-separated modal frequencies to very closely spaced modal frequencies. The natural frequencies and modal damping ratios identified by the HHT method are compared with the theoretical values and those identified using the fast Fourier transform (FFT) method. The results show that the HHT method is
superior to the FFT method in the identification of modal damping ratios of the structure with closely spaced modes of vibration. Finally, a 36-storey shear building with a 4-storey light appendage, having closely spaced modal frequencies and subjected to an ambient ground motion, is analyzed. The modal damping ratios identified by the HHT method in conjunction with the random decrement technique (RDT) are much better than those obtained by the FFT method. The HHT method performing in the frequency-time domain seems to be a promising tool for system identification of civil engineering structures.

Key Words
system identification; closely spaced modal frequencies; modal damping ratio; the HHT

Address
Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Abstract
The paper proposes analytical forms able to represent with very good approximation the constitutive law experimentally deducible by means of uniaxial cyclic compressive tests on material having softening post-peak behaviour in compression and negligible tensile strength. The envelope, unloading and reloading curves characterizing the proposed model adequately approach structural responses corresponding to different levels of nonlinearity and ductility, requiring a not very high number of parameters to be calibrated experimentally. The reliability of the model is shown by comparing the results that it is able to provide with the ones analytically deduced from two reference models (one for
concrete, another for masonry) available in the literature, and with experimental results obtained by the authors in the framework of a research in progress.

Key Words
concrete model; masonry model; uniaxial compression; cyclic loading; constitutive law.

Address
Dipartimento di Ingegneria Strutturale e Geotecnica, Universit? di Palermo,
viale delle Scienze 90128-Palermo, Italy

Abstract
The paper involves the study on the elastic and elasto-plastic stress wave propagation in the 1-D and 2-D solid media. The Smooth Particle Hydrodynamics equations governing the elastic and elasto-plastic large deformation dynamic response of solid structures are presented. The proposed additional stress points are introduced in the formulation to mitigate the tensile instability inherent in the SPH approach. Both incremental rate approach and leap-frog algorithm for time integration are introduced and the new solution algorithm is developed and implemented. Two examples on stress wave propagation in aluminium bar and 2-D elasto-plastic steel plate are included. Results from the proposed SPH approach
are compared with available analytical values and finite element solutions. The comparison illustrates that the stress wave propagation problems can be effectively solved by the proposed SPH method. The study shows that the SPH simulation is a reliable and robust tool and can be used with confidence to treat
transient dynamics such as linear and non-linear transient stress wave propagation problems.

Key Words
dynamic response; elastic and elasto-plastic materials; large deformation; Smooth Particle

Address
Computational Mechanics Division, Institute of High Performance Computing, 1 Science Park Road, #01-01 The Capricorn, Singapore Science Park II, Singapore, 117528, Singapore
Department of Civil Engineering, The National University of Singapore, 10 Kent Ridge Crescent Singapore, 119260, Singapore

Abstract
A static linear programming formulation for minimum weight design of frames that is based on a matrix displacement method is presented in this paper. According to elementary theory of plasticity, minimum weight design of frames can be carried out by using only the equilibrium equations, because the system is statically determinate when at an incipient collapse state. In the present formulation, a statically determinate released frame is defined by introducing hinges into the real frame and the bending moments in yield constraints are expressed in terms of unit hinge rotations and the external loads respectively, by utilizing the matrix displacement method. Conventional Simplex algorithm with some modifications is
utilized for the solution of linear programming problem. As the formulation is based on matrix displacement method, it may be easily adopted to the weight optimization of frames with displacement and deformation limitations. Four illustrative examples are also given for comparing the results to those obtained in previous studies.

Key Words
minimum weight design; optimal plastic design; linear programming.

Address
Faculty of Civil Engineering, Technical University of Istanbul, 80626, Maslak, Istanbul, Turkey

Abstract
A state-space method is proposed to analyze the aerodynamically coupled flutter problems of long-span bridges based on the modal coordinates of structure. The theory about complex modes is applied in this paper. The general governing equation of the system is converted into a complex standard characteristic equation in a state space format, which contains only two variables. The proposed method is a single-parameter searching method about reduced velocity, and it need not choose the participating modes beforehand and has no requirement for the form of structure damping matrix. The information about variations of system characteristics with reduced velocity and wind velocity can be provided. The
method is able to find automatically the lowest critical flutter velocity and give relative amplitudes, phases and energy ratios of the participating modes in the flutter motion. Moreover, the flutter analysis of Jiangyin Yangtse suspension bridge with 1385 m main span is performed. The proposed method has proved reliable in its methodology and efficient in its use.

Key Words
long-span bridges; coupled flutter; state space method; multimode; complex mode;Jiangyin suspension bridge.

Address
State Key Lab for Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China


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