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CONTENTS
Volume 25, Number 6, April20 2007
 

Abstract
This paper presents stacking sequence optimization of laminated angle-ply cylindrical panel based on natural frequency. Finite element method (FEM) is used to obtain the vibration characteristic of an anisotropic panel using the first order shear deformation theory(FSDT) and genetic algorithm (GA) is used to obtain the optimal stacking sequence of the layers. Cylindrical panel has finite length and arbitrary boundary conditions. The thicknesses of the layers are assumed constant and their angles are specified as design variables. The effect of the number of plies and boundary conditions in the fitness function is considered. Numerical examples are presented for four, six and eight layered anisotropic cylindrical panels.

Key Words
composite laminate; optimal design; genetic algorithm; panel; vibration.

Address
A. Alibeigloo; Mechanical Engineering Department, Bu-AliSina University, Hamedan, Iran
M. Shakeri and A. Morowat; Mechanical Engineering Department, Amirkabir University of Technology, 424 Hafez Ave, Tehran, Iran

Abstract
This paper discusses the application of piezoelectric sensors used for evaluation of damping ratio of PVC plastics. The development of the mathematical formulation based on the Empirical Mode Decomposition for calculating the damping coefficient and natural frequency of the system is presented. A systematic experimental and analytical investigation was also carried out to demonstrate the integrity of several methods commonly used to evaluate the damping of materials based on a single degree freedom formulation. The influence of the sensors? location was also investigated. Besides the commonly used methods, a newly emerging time-frequency method, namely the Empirical Mode decomposition, is also employed. Mathematical formulations based on the Hilbert-Huang formulation, and a frequency spacing technique were also developed for establishing the natural frequency and damping ratio based on the output voltage of a single piezoelectric sensor. An experimental investigation was also conducted and the results were compared and verified with Finite Element Analysis (FEA), revealing good agreement.

Key Words
plastics; damping; FFT; finite analysis; Hilbert transform; frequency spacing; Empirical Mode Decomposition (EMD).

Address
N. Cheraghi, M.J. Riley and F. Taheri; Dept. of Civil Engineering, Dalhousie Univ., 1360 Barrington Street, Halifax, Nova Scotia B3J 1Z1, Canada

Abstract
In order to study the ductility and the lateral load carrying capacity of the masonry walls strengthened with CFRPs (Carbon Fiber Reinforced Polymer sheets), three pieces of masonry walls subjected to cyclic loads with low frequency and vertical load of constant amplitude have been tested. Two different strengthening methods have been used. The strengthening efficiency is affected by the strengthening method. A simplified calculation approach has been introduced based on the experimental test results, and the theoretical results agree reasonably well with the experimental results. It is found that the critical loads, the critical displacements, the ultimate loads, the ultimate displacements and the ductile coefficients of the masonry walls strengthened with CFRPs improve remarkably (6%~57%). Therefore, the masonry structures strengthened with CFRPs are of better ductility and of better lateral load carrying
capacity than the masonry structures without any strengthening measurements.

Key Words
CFRPs (Carbon Fiber Reinforced Polymer sheet); masonry walls; strengthening method; lateral load carrying capacity.

Address
Chang-Qin Wei; School of Civil Engineering, Yantai University, Yantai 264005, P. R. China
Xin-Gang Zhou; School of Civil Engineering, Yantai University, Yantai 264005, P. R. China
Dept. of Civil Engineering, Tsinghua University, Beijing 100084, P. R. China
Lie-Ping Ye; Dept. of Civil Engineering, Tsinghua University, Beijing 100084, P. R. China

Abstract
The purpose of the present work is to establish a method for predicting the location and depth of a crack in a circular cross section beam by only considering the frequencies of the cracked beam. An accurate knowledge of the material properties is not required. The crack location and size is identified by finding the point of intersection of pulsation ratio contour lines of lower vertical and horizontal modes. This process is presented and numerically validated in the case of a simply supported beam with various crack locations and sizes. If the beam has structural symmetry, the identification of crack location is performed by adding an off-center placed mass to the simply supported beam. In order
to avoid worse diagnostic, it was demonstrated that a robust identification of crack size and location is possible if two tests are undertaken by adding the mass at the left and then right end of the simply supported beam. Finally, the pulsation ratio contour lines method is generalized in order to be extended to the case of rectangular cross section beams or more complex structures.

Key Words
vibration; crack; identification.

Address
Laboratoire de Tribologie et Dynamique des Systemes UMR-CNRS 5513, Ecole Centrale de Lyon,36 avenue Guy de Collongue, 69134 Ecully Cedex, France

Abstract
A formula to approximate the fundamental period of a fixed-free mass-spring varying mass and varying stiffness is formulated. The formula is derived mainly by taking parts from the general form of the characteristic polynomial, and adjusting the initial approximation coefficient derived from the exact solution of a uniform case. The formula is tested for a large randomly generated structures, and the results show that the approximated fundamental periods the error range of 4% with 90% of confidence. Also, the error is shown to be normally distributed zero mean, and the width of the distribution (as measured by the standard deviation) tends the total number of discretized elements in the system increases. Other possible extensions are discussed, including an extension to a continuous cantilever structure with distributed stiffness. The suggested formula provides an efficient way to estimate the fundamental period structures and other systems that can be modeled as mass-spring systems.

Key Words
earthquake engineering; eigenvalue; eigensystem; fundamental period.

Address
Juwhan Kim; School of Civil & Environmental Engineering, College of Engineering, Yonsei University, Seoul 120-749, Korea
Kevin R. Collins; 5 Greystone Court Ledyard, CT 06339, USA
Yun Mook Lim; School of Civil & Environmental Engineering, College of Engineering, Yonsei University, Seoul 120-749, Korea

Abstract
The metis element method (Hung 1978) has been applied to analyse free edge interlaminar stresses and delamination in composite laminates, which are subjected to extension and bending. The paper recalls Lekhnitskii?s solution for generalized plane strain state of composite laminate and Wang?s singular solution for determination of stress singularity order and of eigen coefficients Cm for delamination problem. Then the formulae of metis displacement finite element in two-dimensional problem are established. Computation of the stress intensity factors and the energy release rates are presented in details. The energy release rate, G, is computed by Irwin?s virtual crack technique using metis elements. Finally, results of interlaminar stresses, the three stress intensity factors and the energy release rates for delamination crack in composite laminates under extension and bending are illustrated and compared with
the literature to demonstrate the efficiency of the present method.

Key Words
finite element method; interlaminar stresses; composite laminate; delamination; extension; bending.

Address
Tien Duong Nguyen; Hanoi University of Technology, Vietnam, No 1, Dai Co Viet St., Hanoi, Vietnam
Dang Hung Nguyen; LTAS . Fracture Mechanics, University of Liege, Belgium Institut de Mecanique et Genie Civil, Bat. B52/3, Chemin des Chevreuils 1, B-4000 Liege, Belgium

Abstract
The response histories and distribution of dynamic interlaminar stresses in composite laminated plates under free vibration and thermal load is studied based on a thermoelastodynamic differential equations. The stacking sequence of the laminated plates may be arbitrary. The temperature change is considered as a linear function of coordinates in planes of each layer. The dynamic mode of
displacements is considered as triangle series. The in-plane stresses are calculated by using geometric equations and generalized Hooke?s law. The interlaminar stresses are evaluated by integrating the 3-D equations of equilibrium, and utilizing given boundary conditions and continuity conditions of stresses between layers. The response histories and distribution of interlaminar stress under thermal load are presented for various vibration modes and stacking sequence. The theoretical analyses and results are of certain significance in practical engineering application.

Key Words
composite laminated plates; dynamic interlaminar stresses; thermal environment.

Address
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University,
Shanghai 200240, P.R. China

Abstract
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Key Words
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Address
Oktay Demirda; Pamukkale University, Engineering Faculty, Civil Engineering Department, 20070 K n kl , Denizli, Turkey
Hikmet Huseyin Catal; Dokuz Eylul University, Engineering Faculty, Civil Engineering Department, 35160 Buca, zmir, Turkey


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