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CONTENTS
Volume 55, Number 4, August25 2015
 

Abstract
A method based on derivatives of eigen-parameters is presented for damage detection in discrete systems with dampers. The damage is simulated by decrease on the stiffness coefficient and increase of the damping coefficient. In the forward analysis, the derivatives of eigen-parameters are derived for the discrete system. In the inverse analysis, a derivative of eigen-parameters based model updating approach is used to identify damages in frequency domain. Two numerical examples are investigated to illustrate efficiency and accuracy of the proposed method. Studies in this paper indicate that the proposed method is efficient and robust for both single and multiple damages and is insensitive to measurement noise. And satisfactory identified results can be obtained from few numbers of iterations.

Key Words
damage detection; stiffness; damping; derivatives of eigen-parameters; model updating; discrete system

Address
H. Li, J.K. Liu and Z.R. Lu: Department of Applied Mechanics and Engineering, Sun Yat-sen University, Guangzhou, Guangdong, P.R. China

Abstract
In this paper, a simple n-order refined theory based on neutral surface position is developed for bending and frees vibration analyses of functionally graded beams. The present theory is variationally consistent, uses the n-order polynomial term to represent the displacement field, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The governing equations are derived by employing the Hamilton\'s principle and the physical neutral surface concept. The accuracy of the present solutions is verified by comparing the obtained results with available published ones.

Key Words
mechanical properties; vibration; functionally graded; deformation; modeling

Address
Lazreg Hadji: Université Ibn Khaldoun, BP 78 Zaaroura, 14000 Tiaret, Algérie
El Abbes Adda Bedia: Laboratoire des Matériaux & Hydrologie, Université de Sidi Bel Abbes, 22000 Sidi Bel Abbes, Algérie

Abstract
This paper dealt the free vibration analysis of thick truncated conical composite sandwich shells with transversely flexible cores and simply supported boundary conditions based on a new improved and enhanced higher order sandwich shell theory. Geometries were used in the present work for the consideration of different radii curvatures of the face sheets and the core was unique. The coupled governing partial differential equations were derived by the Hamilton\'s principle. The in-plane circumferential and axial stresses of the core were considered in the new enhanced model. The first order shear deformation theory was used for the inner and outer composite face sheets and for the core, a polynomial description of the displacement fields was assumed based on the second Frostig\'s model. The effects of types of boundary conditions, conical angles, length to radius ratio, core to shell thickness ratio and core radius to shell thickness ratio on the free vibration analysis of truncated conical composite sandwich shells were also studied. Numerical results are presented and compared with the latest results found in literature. Also, the results were validated with those derived by ABAQUS FE code.

Key Words
free vibration; truncated conical sandwich shells; improved higher order theory

Address
Keramat Malekzadeh Fard and Mostafa Livani: Department of Structural Analysis and Simulation, Space research institute, MalekAshtar University of Technology, Tehran-Karaj Highway, PO Box. 13445-768, Tehran, Iran

Abstract
This work presents a new nonlocal hyperbolic shear deformation beam theory for the static, buckling and vibration of nanoscale-beams embedded in an elastic medium. The present model is able to capture both the nonlocal parameter and the shear deformation effect without employing shear correction factor. The nonlocal parameter accounts for the small size effects when dealing with nanosize structures such as nanobeams. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the nanoscale-beam are obtained using Hamilton\'s principle. The effect of the surrounding elastic medium on the deflections, critical buckling loads and frequencies of the nanobeam is investigated. Both Winklertype and Pasternak-type foundation models are used to simulate the interaction of the nanobeam with the surrounding elastic medium. Analytical solutions are presented for a simply supported nanoscale-beam, and the obtained results compare well with those predicted by the other nonlocal theories available in literature.

Key Words
nonlocal theory; nanobeam; elastic medium

Address
Khadidja Aissani: Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, Faculté de Technologie, Département de Génie Cvil, Algérie
Mohamed Bachir Bouiadjra: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
Mama Ahouel: Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria
Abdelouahed Tounsi: Algerian National Thematic Agency of Research in Science and Technology (ATRST), Algeria

Abstract
Connections are usually designed either as pinned usually associated with simple construction or rigid normally is associated with continuous construction. However, the actual behaviour falls in between these two extreme cases. The use of partial strength or semi-rigid connections has been encouraged by Euro-code 3 and studies on semi-continuous construction have shown substantial savings in steel weight of the overall construction. Composite connections are proposed in this paper as partial or full strength connections. Standardized connection tables are developed based on checking on all possible failure modes as suggested by \"component method\" for beam-to-column composite connection on major axis. Four experimental tests were carried out to validate the proposed standardised connection table. The test results showed good agreement between experimental and theoretical values with the ratio in the range between 1.06 to 1.50. All tested specimens of the composite connections showed ductile type of failure with the formation of cracks occurred on concrete slab at maximum load. No failure occurred on the Trapezoidal Web Profiled Steel Section as beam and on the British Section as column.

Key Words
computational mechanics; finite element method (FEM); functionally graded; numerical methods; parametric analysis

Address
A. Saggaff: Civil Engineering Department, Faculty of Engineering, Sriwijaya University, Indonesia
M.M. Tahir, A. Sulaiman, S.P. Ngian and J. Mirza: UTM Construction Research Centre, Institute for Smart Infrastructure and Innovative Construction (IISIC),
Faculty of Civil Engineering, Universiti Teknologi Malaysia (UTM), 81310, Johor Bahru, Johor, Malaysia

Abstract
A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of hyperboloidal shells free at the top edge and clamped at the bottom edge like a hyperboloidal cooling tower by the Ritz method based upon the circular cylindrical coordinate system instead of related 3- D shell coordinates which are normal and tangent to the shell midsurface. The Legendre polynomials are used as admissible displacements. Convergence to four-digit exactitude is demonstrated. Natural frequencies from the present 3-D analysis are also compared with those of straight beams with circular cross section, complete (not truncated) conical shells, and circular cylindrical shells as special cases of hyperboloidal shells from the classical beam theory, 2-D thin shell theory, and other 3-D methods.

Key Words
cooling tower; hyperbolic shell; free vibration; Legendre polynomials

Address
Jae-Hoon Kang: Department of Architectural Engineering, Chung-Ang University, Seoul, 156-756 South Korea

Abstract
Flexural stiffness of bridge spans has become even more important parameter since Eurocode 1 introduced for railway bridges the serviceability limit state of resonance. For simply supported bridge spans it relies, in general, on accurate assessment of span moment of inertia that governs span flexural stiffness. The paper presents three methods of estimation of the equivalent moment of inertia for such spans: experimental, analytical and numerical. Test loading of the twin truss bridge spans and test results are presented. Recorded displacements and the method of least squares are used to find an \"experimental\" moment of inertia. Then it is computed according to the analytical method that accounts for joint action of truss girders and composite deck as well as limited span shear stiffness provided by diagonal bracing. Finally a 3D model of finite element method is created to assess the moment of inertia. Discussion of results is given. The comparative analysis proves efficiency of the analytical method.

Key Words
moment of inertia; truss bridge; steel-concrete composite deck; joint action; shear stiffness

Address
Wojciech Siekierski: Institute of Civil Engineering, Poznań University of Technology, ul. Piotrowo 5, 61-138 Poznań, Poland

Abstract
new family of structure-dependent integration methods is developed to enhance with desired numerical damping. This family method preserves the most important advantage of the structure-dependent integration method, which can integrate unconditional stability and explicit formulation together, and thus it is very computationally efficient. In addition, its numerical damping can be continuously controlled with a parameter. Consequently, it is best suited to solving an inertia-type problem, where the unimportant high frequency responses can be suppressed or even eliminated by the favorable numerical damping while the low frequency modes can be very accurately integrated.

Key Words
unconditional stability; explicit formulation; numerical damping; accuracy; structuredependent integration method

Address
Shuenn-Yih Chang, Tsui-Huang Wu and Ngoc-Cuong Tran: Department of Civil Engineering, National Taipei University of Technology, NTUT Box 2653, Taipei 106, Taiwan, Republic of China

Abstract
A multi-contact tooth meshing model for helical gear pairs considering bearing and shaft deformations is proposed. First, to easily incorporate into the system model, the complicated Harris\'s bearing force-displacement relationship is simplified applying a linear least square curve fit. Then, effects of shaft and bearing flexibilities on the helical gear meshing behavior are implemented through transformation matrices which contain the helical gear orientation and spatial displacement under loads. Finally, true contact lines between conjugated teeth are approximated applying a modified meshing equation that includes the influence of tooth flank displacement on the tooth contact induced by shaft and bearing displacements. Based on the model, the bearing\'s force-displacement relation is examined, and the effects of shaft deformation and external load on the multi-contact tooth mesh load distribution are also analyzed. The advantage of this work is, unlike previous works to search true contact lines through time-consuming iterative strategy, to determine true contact lines between conjugated teeth directly with presentation of deformations of bearings and shafts.

Key Words
helical gear; multi-contact; load analysis

Address
Chengwu Li, Yulin He and Xianxiong Ning: State Key Lab for Mechanical Transmission, Chongqing University, No. 174 Shazhengjie, Shapingba, Chongqing, P.R. China

Abstract
The aluminum 7075-T6 is known as an alloy widely used in aircraft structural applications, which does not exhibit strain rate sensitivity during dynamic compressive tests. Despite mechanical importance of the material, there is not enough attention to determine appropriate sample dimensions such as a sample diameter relative to the device bar diameter and sample length to diameter (L/D) ratio for dynamic tests and how these two parameters can change mechanical behaviors of the sample under dynamic loading condition. In this study, various samples which have different diameters of 31.8, 25.4, 15.9, and 9.5 mm and sample L/D ratios of 2.0, 1.5, 1.0, 0.5, and 0.25 were tested using Split Hopkinson Pressure Bar (SHPB), as this testing device is proper to characterize mechanical behaviors of solid materials at high strain rates. The mechanical behavior of this alloy was examined under ~200–5,500 s-1 dynamic strain rate. Aluminum samples of 2.0, 1.5 and 1.0 of L/D ratios were well fitted into the stress-strain curve, Madison and Green\'s diagram, regardless of the sample diameters. Also, the 0.5 and 0.25 L/D ratio samples having the diameter of 31.8 and 25.4 mm followed the stress-strain curve. As results, larger samples (31.8 and 25.4 mm) in diameters followed the stress-strain curve regardless of the L/D ratios, whereas the 0.5 and 0.25 L/D ratios of small diameter sample (15.9 and 9.5 mm) did not follow the stress-strain diagram but significantly deviate from the diagram. Our results indicate that the L/D ratio is important determinant in stress-strain responses under the SHPB test when the sample diameter is small relative to the test bar diameter (31.8 mm), but when sample diameter is close to the bar diameter, L/D ratio does not significantly affect the stress-strain responses. This suggests that the areal mismatch (non-contact area of the testing bar) between the sample and the bar can misrepresent mechanical behaviors of the aluminum 7075-T6 at the dynamic loading condition.

Key Words
aluminum 7075-T6; Split Hopkinson Pressure Bar; stress/strain response; strain rate insensitivity; length to diameter ratio; sample diameter to the bar diameter

Address
Eunhye Kim: Department of Mining Engineering, Colorado School of Mines, Golden, CO, USA
Hossein Changani: Department of Mining Engineering, University of Utah, Salt Lake City, UT, USA

Abstract
In the present study, separate and combined effects of rotary inertia, shear deformation and material non-homogeneity (MNH) on the values of natural frequencies of the simply supported beam are examined. MNH is characterized considering the parabolic variations of the Young\'s modulus and density along the thickness direction of the beam, while the value of Poisson\'s ratio is assumed to remain constant. At first, the equation of the motion including the effects of the rotary inertia, shear deformation and MNH is provided. Then the solutions including frequencies of the first three modes for various combinations of the parameters of the MNH, depth to length ratios, and shear corrections factors are reported. To show the accuracy of the present results, two comparisons are carried out and good agreements are found.

Key Words
rotary inertia; shear deformation; material non-homogeneity; natural frequency; beam

Address
Mehmet Avcar: Department of Civil Engineering, Faculty of Engineering, Suleyman Demirel University, Cunur, Isparta, Turkey

Abstract
This paper introduces Romberg-Richardson\'s method as one of the numerical integration tools for computation of stress intensity factor in a pre-cracked specimen subjected to a complex stress field across the crack faces. Also, the computation of stress intensity factor for various stress fields using existing three methods: average stress over interval method, piecewise linear stress method, piecewise quadratic method are modified by using Richardson extrapolation method. The direct integration method is used as reference for constant and linear stress distribution across the crack faces while Gauss-Chebyshev method is used as reference for nonlinear distribution of stress across the crack faces in order to obtain the stress intensity factor. It is found that modified methods (average stress over intervals-Richardson method, piecewise linear stress-Richardson method, piecewise quadratic-Richardson method) yield more accurate results after a few numbers of iterations than those obtained using these methods in their original form. Romberg-Richardson\'s method is proven to be more efficient and accurate than Gauss-Chebyshev method for complex stress field.

Key Words
pre-cracked specimen; stress intensity factor; weight function; mode-I loading; numerical integration

Address
Gaurav Dubey: Department of Mechanical Engineering, Institute of Technology, Guru Ghasidas Vishwavidyalaya,
Bilaspur, Chhattisgarh 495009, India
Shailendra Kumar: Department of Civil Engineering, Institute of Technology, Guru Ghasidas Vishwavidyalaya, Bilaspur, Chhattisgarh 495009, India


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