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CONTENTS
Volume 38, Number 3, May10 2011
 

Abstract
A new method of formulation of a class of elements that are immune to mesh distortion effects is proposed here. The simple three-noded bar element with an offset of the internal node from the element center is employed here to demonstrate the method and the principles on which it is founded upon. Using the function space approach, the modified formulation is shown here to be superior to the conventional isoparametric version of the element since it satisfies the completeness requirement as the metric formulation, and yet it is in agreement with the best-fit paradigm in both the metric and the parametric domains. Furthermore, the element error is limited to only those that are permissible by the classical projection theorem of strains and stresses. Unlike its conventional counterpart, the modified element is thus not prone to any errors from mesh distortion. The element formulation is symmetric and thus satisfies the requirement of the conservative nature of problems associated with all self-adjoint differential operators. The present paper indicates that a proper mapping set for distortion immune elements constitutes geometric and displacement interpolations through parametric and metric shape functions respectively, with the metric components in the displacement/strain replaced by the equivalent geometric interpolation in parametric co-ordinates.

Key Words
metric and parametric; unsymmetric and symmetric formulations; element distortion; best-fit paradigm; variational correctness; orthogonal projection; function spaces; modified shape functions.

Address
Somenath Mukherjee: Central Mechanical Engineering Research Institute, CSIR, Durgapur 713209, India
S. Manju: National Aerospace Laboratories, CSIR, Bangalore 560017, India

Abstract
A new conception of fundamental tasks in dynamics of the bridge-track-train systems (BTT), with the aim to evaluate moving load\'s models adequacy, has been developed. The 2D physical models of BTT systems, corresponding to the fundamental tasks, have been worked out taking into account one-way constraints between the moving unsprung masses and the track. A method for deriving the implicit equations of motion, governing vibrations of BTT systems\' models, as well as algorithms for numerical integration of these equations, leading to the solutions of high accuracy and relatively short times of simulations, have been also developed. The derived equations and formulated algorithms constitute the basis for numerical simulation of vibrations of the considered systems.

Key Words
bridge-track-train system; fundamental tasks; bridge beam; moving elements streams; one-way contact; implicit equations of motion; numerical integration.

Address
M. Podworna: Institute of Civil Engineering, Wroclaw University of Technology, Wroclaw, Poland

Abstract
The paper constitutes the second part of the author\'s study. The first part (Podworna 2010) formulates four fundamental tasks in dynamics of the bridge-track-train systems. The following cyclic moving loads are considered: a concentrated forces stream (model P), an unsprung masses stream (model M), a single-mass viscoelastic oscillators stream (model Mo) and a double-mass viscoelastic oscillators stream (model MMo). Three problems precluding to the numerical simulations have been developed, i.e., prediction of the forced resonances, the parameters of integration of equations of motion, the output results. A computer programme was written in Pascal and numerical research in the scope of the fundamental tasks was worked out. The investigations were focused on adequacy evaluation of the moving load models, P, M, Mo, MMo, in predicting dynamic processes in railway bridges.

Key Words
bridge-track-train system; fundamental tasks; bridge beam; moving elements streams; oneway contact; numerical simulations.

Address
M. Podworna: Institute of Civil Engineering, Wroclaw University of Technology, Wroclaw, Poland

Abstract
The Combined Deterministic Stochastic Subspace based System Identification Technique (CDSSSIT) is a powerful input-output system identification technique which is known to be always convergent and numerically stable. The technique determines a Kalman state sequence from the projection of the output-input data. The state space matrices are determied subsequently from this Kalman state sequence using least squares. The objective of this paper is to examine the efficiency of the CDSSSIT in identifying the modal parameters (frequencies and mode shapes) of a stiff structure. The results show that the CDSSSIT predicts the modal parameters of stiff buildings quite accurately but is very sensitive to the location of sensors.

Key Words
system identification; optimal sensor placement; structural health monitoring; subspace based system identification.

Address
Pelin Gundes Bakir: Department of Civil Engineering, Istanbul Technical University, Adnan Saygun Cad., Selin apt. No:15-9, D:13, Ulus, Besiktas, Istanbul, Turkey

Abstract
This paper shows the solution for an orthotropic disk under the plane strain condition obtained with complex stress functions. These stress functions were induced by Lekhnitskii and expanded by one of the authors. Regarding diametrical compression test, the finite element method poses difficulties in representing the concentrated force because the specimens must be divided into finite elements during calculation. On the other hand, the method shown in this study can exactly represent this force. Some numerical results are shown and compared with those obtained under the plane stress condition for both stress and displacement. This comparison shows that the differences between the tensile stresses occurred under the plane strain condition and also that the differences under a plane stress condition increase as the orthotropy ratio increases for some cases.

Key Words
orthotropy; diametrical compression; tensile stress; displacement; plane strain condition.

Address
Takashi Tsutsumi: Department of Civil Engineering, Kagoshima National College of Technology, Kirishima, Kagoshima, 899-5193, Japan
Hiroshi Iwashita: Kyushu Railway Company, Fukuoka, 812-8566, Japan
Kagenobu Miyahara: Department of Civil Engineering, Kagoshima National College of Technology, Kirishima, Kagoshima, 899-5193, Japan


Abstract
Input excitation and output response of structure are needed in conventional modal analysis methods. However, input excitation is often difficult to be obtained in the dynamic load test of bridge structures. Therefore, what attracts engineers\' attention is how to get dynamic parameters from the output response. In this paper, a structural experimental modal analysis method is introduced, which can be used to conveniently obtain dynamic parameters of the structure from the free decay response. With known damping coefficients, this analysis method can be used to identify the natural frequencies and the mode shapes of MDOF structures. Based on the modal analysis theory, the mathematical relationship of damping ratio and frequency is obtained. By using this mathematical relationship to improve the previous method, an improved experimental modal analysis method is proposed in this paper. This improved method can overcome the deficiencies of the previous method, which can not identify damping ratios and requires damping coefficients in advance. Additionally, this improved method can also identify the natural frequencies, mode shapes and damping ratios of the bridge only from the free decay response, and ensure the stability of identification process by using modern mathematical means. Finally, the feasibility and effectiveness of this method are demonstrated by a numerical example of a simply supported reinforced concrete beam.

Key Words
dynamic load test; dynamic parameters; free decay response; modal analysis method; modal damping ratio.

Address
Guo-jin Tan, Yong-chun Cheng, Han-bing Liu and Long-lin Wang: College of Transportation, Jilin University, Changchun, China

Abstract
Earlier studies on hollow-circular rubber bearings, all of which are conducted for steelreinforced bearings, indicate that the hole presence not only decreases the compression modulus of the bearing but also increases the maximum shear strain developing in the bearing due to compression, both of which are basic design parameters also for fiber-reinforced rubber bearings. This paper presents analytical solutions to the compression problem of hollow-circular fiber-reinforced rubber bearings. The problem is handled using the most-recent formulation of the \"pressure method\". The analytical solutions are, then, used to investigate the effects of reinforcement flexibility and hole presence on bearing\'s compression modulus and maximum shear strain in the bearing in view of four key parameters: (i) reinforcement extensibility, (ii) hole size, (iii) bearing\'s shape factor and (iv) rubber compressibility. It is shown that the compression stiffness of a hollow-circular fiber-reinforced bearing may decrease considerably as reinforcement flexibility and/or hole size increases particularly if the shape factor of the bearing is high and rubber compressibility is not negligible. Numerical studies also show that the existence of even a very small hole can increase the maximum shear strain in the bearing significantly, which has to be considered in the design of such annular bearings.

Key Words
rubber; elastomeric bearing; hollow-circular bearing; fiber-reinforced bearing; reinforcement flexibility; radius ratio; bulk compressibility; shape factor; compression modulus; seismic isolation.

Address
Seval Pinarbasi and Fuad Okay: Department of Civil Engineering, Kocaeli University, Umuttepe Campus, 41380, Kocaeli, Turkey


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