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CONTENTS
Volume 27, Number 3, October20 2007
 

Abstract
This paper presents a fuzzy finite element model for the analysis of structures in the presence of multiple uncertainties. A new methodology to evaluate the cumulative effect of multiple uncertainties on structural response is developed in the present work. This is done by modifying Muhanna?s approach for handling single uncertainty. Uncertainty in load and material properties is defined by triangular membership functions with equal spread about the crisp value. Structural response is obtained in terms of fuzzy interval displacements and rotations. The results are further post-processed to obtain interval values of bending moment, shear force and axial forces. Membership functions are constructed to depict the uncertainty in structural response. Sensitivity analysis is performed to evaluate the relative sensitivity of displacements and forces to uncertainty in structural parameters. The present work demonstrates the effectiveness of fuzzy finite element model in establishing sharp bounds to the uncertain structural response in the presence of multiple uncertainties.

Key Words
fuzzy finite element model; multiple uncertainties; structural response; sensitivity.

Address
M. V. Rama Rao: Dept. of Civil Engineering, Vasavi College of Engineering, Hyderabad-500 031, India
R. Ramesh Reddy: Dept. of Civil Engineering, Osmania University College of Engineering, Hyderabad-7, India

Abstract
Based on the composite finite element simulation and a series of hydrostatic pressure and burst tests, autofrettage effects on strength and deformation of fiber reinforced pressure vessel with metallic liners have been studied in the paper (autofrettage: during the course of one pressure taking effect, the increasing internal stress in metallic liner can surpass the yielding point and the plastic deformation will happen, which result in that when there is no internal pressure, there are press stress in liner while tensile stress in fiber lamination). By making use of a composite finite element Ansys code and a series of experiments, the autofrettage pressure is determined in order to make the aluminium liner be totally in elastic state, under given hydrostatic test pressure. The stress intensity factors of the longitudinal crack in aluminum liner end under internal pressure and thermal loads have been computed and analyzed before and after the autofrettage processing. Through numerical calculation and experiment investigations, it is found that a correct choice for autofrettage pressure can improve the gas-tightness and fatigue strength of FRP vessel.

Key Words
fiber reinforced pressure vesses; autofrettage process; thermal load; stress intensity factor.

Address
X. Wang and X. Chen: Dept. of Engineering Mechanics, School of Naval Architecture and Civil Engineering, Shanghai Jiaotong University, Shanghai 200240, P. R. China

Abstract
Theoretical foundation for the buckling load determination in reinforced concrete columns is described and analytical solutions for buckling loads of the Euler-type straight reinforced concrete columns given. The buckling analysis of the limited set of restrained reinforced concrete columns is also included, and some conclusions regarding effects of material non-linearity and restrain stiffnesses on the buckling loads and the buckling lengths are presented. It is shown that the material non-inearity has a substantial effect on the buckling load of the restrained reinforced concrete columns. By contrast, the steel/concrete area ratio and the layout of reinforcing bars are less important. The influence on the effective buckling length is small.

Key Words
reinforced concrete; restrained column; stability; buckling load.

Address
Nana Krauberger: Vegrad, d.d., Staritrg 35, 3320 Velenje, Slovenia
Miran Saje,Igor Planinc and Sebastjan Bratina: University of Ljubljana, Faculty of Civil and Geodetic Engineering, Jamova 2, SI-1115 Ljubljana, Slovenia

Abstract
The purpose of this paper is to study shear locking-free analysis of thick plates using Mindlin?s theory and to determine the effects of the thickness/span ratio, the aspect ratio and the boundary conditions on the linear responses of thick plates subjected to uniformly distributed loads. Finite element formulation of the equations of the thick plate theory is derived by using higher order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates clamped or simply supported along all four edges. In the analysis, 8- and 17-noded quadrilateral finite elements are used. Graphs and tables are presented that should help engineers in the design of thick plates. It is concluded that 17-noded finite element converges to exact results much faster than 8-noded finite element, and that it is better to use 17-noded finite element for shear-locking free analysis of plates. It is also concluded, in general, that the maximum displacement and bending moment increase with increasing aspect ratio, and that the results obtained in this study are better than the results given in the literature.

Key Words
Thick plate; Mindlin?s theory; finite element method; 8-noded finite element; 17-noded finite element; thickness/span ratio; aspect ratio; boundary conditions.

Address
Y. I. Ozdemir, S. Bekiroglu and Y. Ayvaz: Dept. of Civil Engineering, Karadeniz Technical University, 61080 Trabzon, Turkey

Abstract
In this study, the nonlinear vibrations of stepped beams having different boundary conditions were investigated. The equations of motions were obtained using Hamilton?s principle and made non dimensional. The stretching effect induced non-linear terms to the equations. Forcing and damping terms were also included in the equations. The dimensionless equations were solved for six different set of boundary conditions. A perturbation method was applied to the equations of motions. The first terms of the perturbation series lead to the linear problem. Natural frequencies for the linear problem were calculated exactly for different boundary conditions. Second order non-linear terms of the perturbation series behave as corrections to the linear problem. Amplitude and phase modulation equations were obtained. Non-linear free and forced vibrations were investigated in detail. The effects of the position and magnitude of the step, as well as effects of different boundary conditions on the vibrations, were determined.

Key Words
stepped beam; nonlinear vibration; perturbation method.

Address
E. Ozkaya: Dept. of Mechanical Engineering, Celal Bayar University, 45140, Muradiye, Manisa, Turkey
A. Tekin: Celal Bayar University, 45100, Soma, Manisa, Turkey

Abstract
Assessment of structural behaviour of corrosion affected structures is an important issue, which would help in making certain decisions pertaining to the inspection, repair, strengthening, replacement and demolition of such structures. The paper presents formulations to predict the loss of weight and the loss of cross-sectional area of the reinforcing bar undergoing corrosion based on the earlier study carried out by the present authors (Bhargava et al. 2006). These formulations have further been used to analytically evaluate the ultimate bending moment and ultimate shear force capacity of the corroded concrete beams. Results of the present study indicate that, a considerably good agreement has been observed between the experimental and the analytically predicted values for the weight loss and reduction in radius of the corroded reinforcing bars. A considerably good agreement has also been observed between the experimental and the analytically predicted values of ultimate bending moment and ultimate shear force capacity for the corroded concrete beams.

Key Words
corrosion; concrete; ultimate bending moment; ultimate shear force.

Address
Kapilesh Bhargava: Architecture & Civil Engineering Division, Bhabha Atomic Research Center, Trombay, Mumbai 400 085, India
A. K. Ghosh: Health Safety and Environment Group, Bhabha Atomic Research Center, Trombay, Mumbai 400 085, India
Yasuhiro Mori: Graduate School of Environmental Studies, Nagoya University, Nagoya 464-8603, Japan
S. Ramanujam: Engineering Services Group, Bhabha Atomic Research Center, Trombay, Mumbai 400 085, India

Abstract
The vibration and stability analysis is investigated for composite cylindrical shells that composed of ceramic, FGM, and metal layers subjected to various loads. Material properties of FG layer are varied continuously in thickness direction according to a simple power distribution in terms of the ceramic and metal volume fractions. The modified Donnell type stability and compatibility equations are obtained. Applying Galerkin?s method analytic solutions are obtained for the critical parameters. The detailed parametric studies are carried out to study the influences of thickness variations of the FG layer, radius-to-thickness ratio, lengths-to-radius ratio, material composition and material profile index on the critical parameters of three-layered cylindrical shells. Comparing results with those in the literature validates the present analysis.

Key Words
FG layer; vibration and stability; composite cylindrical shell; buckling loads; frequency parameter.

Address
A.H. Sofiyev: Dept. of Civil Engineering of Suleyman Demirel University, Isparta, Turkey


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