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CONTENTS
Volume 66, Number 1, April10 2018
 

Abstract
Column is usually floating on the stone base directly with or without positioning tenon in traditional Chinese timber structure. Vertical load originated by the heavy upper structure would induce large friction force and compression force between interfaces of column foot and stone base. This study focused on the mechanical behaviors of column foot joint with consideration of the influence of vertical load. Mechanism of column rocking and stress state of column foot has been explored by theoretical analysis. A nonlinear finite element model of column foot joint has been built and verified using the full-scale test. The verified model is then used to investigate the mechanical behaviors of the joint subjected to cyclic loading with different static vertical loads. Column rocking mechanism and stress distributions of column foot were studied in detail, showing good agreement with the theoretical analysis. Mechanical behaviors of column foot joint and the effects of the vertical load on the seismic behavior of column foot were studied. Result showed that compression stress, restoring moment and stiffness increased with the increase of vertical load. An appropriate vertical load originated by the heavy upper structure would produce certain restoring moment and reset the rocking columns, ensuring the stability of the whole frame.

Key Words
traditional Chinese timber structure; column foot joint; vertical load; column rocking; mechanical behavior; finite element model

Address
Juan Wang and Na Yang:
1) School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China
2) Beijing\'s Key Laboratory of Structural Wind Engineering and Urban Wind Environment, Beijing Jiaotong University, Beijing 100044, China
Jun-Xiao He:
1) School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China
2) Beijing\'s Key Laboratory of Structural Wind Engineering and Urban Wind Environment, Beijing Jiaotong University, Beijing 100044, China
3) School of Computing, Engineering and Mathematics, Western Sydney University, Parramatta, NSW 2150, Australia
Qing-Shan Yang:
1) Beijing\'s Key Laboratory of Structural Wind Engineering and Urban Wind Environment, Beijing Jiaotong University, Beijing 100044, China
2) School of Civil Engineering, Chongqing University, Chongqing 400044, China

Abstract
Post-construction subgrade settlement especially differential settlement, has become a key issue in construction and operation of non-ballasted track on high-speed railway soil subgrade, which may also affect the dynamic performance of passing trains. To estimate the effect of differential subgrade settlement on the mechanical behaviors of the vehicle-slab track system, a detailed model considering nonlinear subgrade support and initial track state due to track self-weight is developed. Accordingly, analysis aiming at a typical high-speed vehicle coupled with a deteriorated slab track owing to differential subgrade settlement is carried out, in terms of two aspects: (i) determination of an initial mapping relationship between subgrade settlement and track deflections as well as contact state between track and subgrade based on a semi-analytical method; (ii) simulation of dynamic performance of the coupled system by employing a time integration approach. The investigation indicates that subgrade settlement results in additional track irregularity, and locally, the contact between the concrete track and the soil subgrade is prone to failure. Moreover, wheel-rail interaction is significantly exacerbated by the track degradation and abnormal responses occur as a result of the unsupported areas. Distributions of interlaminar contact forces in track system vary dramatically due to the combined effect of track deterioration and dynamic load. These may not only intensify the dynamic responses of the coupled system, but also have impacts on the long-term behavior of the track components.

Key Words
slab track; subgrade settlement; vehicle-track coupled dynamics; track deflections; contact failure

Address
Yu Guo, Wanming Zhai and Yu Sun: Train and Track Research Institute, State Key Laboratory of Traction Power, Southwest Jiaotong University, No. 111, First Section, North of Second Ring Road, Chengdu, People\'s Republic of China


Abstract
The objective of this work is to analyze geometrically nonlinear static analysis a simply supported laminated composite beam subjected to a non-follower transversal point load at the midpoint of the beam. In the nonlinear model of the laminated beam, total Lagrangian finite element model of is used in conjunction with the Timoshenko beam theory. The considered non-linear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. In the numerical results, the effects of the fiber orientation angles and the stacking sequence of laminates on the nonlinear deflections and stresses of the composite laminated beam are examined and discussed. Convergence study is performed. Also, the difference between the geometrically linear and nonlinear analysis of laminated beam is investigated in detail.

Key Words
nonlinear analysis; composite laminated beams; Timoshenko beam theory; total lagragian; finite element method

Address
Şeref D. Akbas: Department of Civil Engineering, Bursa Technical University, Yildirim Campus, Yildirim, Bursa 16330, Turkey

Abstract
In orthopedic surgery and in particular in total hip arthroplasty, the implant fixation is carried out using a surgical cement called polymethylmethacrylat (PMMA). This cement has to insure a good adhesion between implant and bone and a good load distribution to the bone. By its fragile nature, the cement can easily break when it is subjected to a high stress gradient by presenting a craze zone in the vicinity of inclusion. The focus of this study is to analyze the effect of inclusion in some zone of cement in which the loading condition can lead to the crack opening leading to their propagation and consequently the aseptic loosening of the THR. In this study, the fracture behavior of the bone cement including a strange body (bone remain) from which the onset of a crack is supposed. The effect of loading condition, the geometry, the presence of both crack and inclusion on the stress distribution and the fracture behavior of the cement. Results show that the highest stresses are located around the sharp tip of bony inclusion. Most critical cracks are located in the middle of the cement mantle when they are subjected to one leg standing state loading during walking.

Key Words
finite element method; total hip replacement; bone cement; biomechanics; bony inclusion; stress intensity factor; submodeling technique

Address
Cherfi Mohamed, Sahli Abderahmane and Smail Benbarek: Department of Mechanical Engineering, Laboratory Mechanics Physics of Materials (LMPM), University of Sidi Bel Abbes, BP 89, cite Ben M\'hidi, Sidi Bel Abbes, 22000, Algeria


Abstract
The bi-material elastic system consisting of the pre-stressed hollow cylinder and pre-stresses surrounding infinite elastic medium is considered and it is assumed that the mentioned initial stresses in this system are caused with the compressing or stretching uniformly distributed normal forces acting at infinity in the direction which is parallel to the cylinder\'s axis. Moreover, it is assumed that on the internal surface of the cylinder the ring load which moves with constant velocity acts and within these frameworks it is required to determine the influence of the aforementioned initial stresses on the critical velocity of the moving load. The corresponding investigations are carried out within the framework of the so-called three-dimensional linearized theory of elastic waves in initially stresses bodies and the axisymmetric stress-strain state case is considered. The

Key Words
critical velocity; initial stresses; moving load; interface stresses; hollow cylinder; surrounding elastic medium

Address
Surkay D. Akbarov:
1) Department of Mechanical Engineering, Yildiz Technical University, Yildiz Campus, 34349, Besiktas, Istanbul, Turkey
2) Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan, 37041, Baku, Azerbaijan
Mahir A. Mehdiyev:
1) Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan, 37041, Baku, Azerbaijan
2) Azerbaijan State University of Economics (UNEC), Department of Mathematics, 1001, Baku, Azerbaijan

Abstract
In this article, a higher shear deformation theory (HSDT) is improved to consider the influence of thickness stretching in functionally graded (FG) plates. The proposed HSDT has fewer numbers of variables and equations of motion than the first-order shear deformation theory (FSDT), but considers the transverse shear deformation influences without requiring shear correction coefficients. The kinematic of the present improved HSDT is modified by considering undetermined integral terms in in-plane displacements and a parabolic distribution of the vertical displacement within the thickness, and consequently, the thickness stretching influence is taken into account. Analytical solutions of simply supported FG plates are found, and the computed results are compared with 3D solutions and those generated by other HSDTs. Verification examples demonstrate that the developed theory is not only more accurate than the refined plate theory, but also comparable with the HSDTs which use more number of variables.

Key Words
functionally graded plates; bending; vibration; computational modeling

Address
Abdelhakim Bouhadra:
1) Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, civil Engineering Department, Algeria
2) Universite de Abbes Laghrour Khenchela, Faculte de Sciences & Technologie, Departement de Genie Civil, Algeria
Abdelouahed Tounsi:
1) Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
2) Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals,
31261 Dhahran, Eastern Province, Saudi Arabia
Abdelmoumen Anis Bousahla:
1) Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
2) Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes, Algeria
3) Centre Universitaire de Relizane, Algerie
Samir Benyoucef: Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
S.R. Mahmoud: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

Abstract
This study presents the reliability-based analysis of nonlinear structures using the analytical fragility curves excited by random earthquake loads. The stochastic method of ground motion simulation is combined with the random vibration theory to compute structural failure probability. The formulation of structural failure probability using random vibration theory, based on only the frequency information of the excitation, provides an important basis for structural analysis in places where there is a lack of sufficient recorded ground motions. The importance of frequency content of ground motions on probability of structural failure is studied for different levels of the nonlinear behavior of structures. The set of simulated ground motion for this study is based on the results of probabilistic seismic hazard analysis. It is demonstrated that the scenario events identified by the seismic risk differ from those obtained by the disaggregation of seismic hazard. The validity of the presented procedure is evaluated by Monte-Carlo simulation.

Key Words
reliability; fragility curve; tail-equivalent linearization; failure probability; random vibration; point-source

Address
Mohammad-Rashid Salimi and Azad Yazdani: Department of Civil Engineering, University of Kurdistan, Sanandaj, Iran

Abstract
This study investigates the response of functionally graded (FG) gas pipe under unsteady internal pressure and temperature. The pipe is proposed to be manufactured from FGMs rather than custom carbon steel, to reduce the erosion, corrosion, pressure surge and temperature variation effects caused by conveying of gases. The distribution of material graduations are obeying power and sigmoidal functions varying with the pipe thickness. The sigmoidal distribution is proposed for the 1st time in analysis of FG pipe structure. A Two-dimensional (2D) plane strain problem is proposed to model the pipe cross-section. The Fourier law is applied to describe the heat flux and temperature variation through the pipe thickness. The time variation of internal pressure is described by using exponential-harmonic function. The proposed problem is solved numerically by a two-dimensional (2D) plane strain finite element ABAQUS software. Nine-node isoparametric element is selected. The proposed model is verified with published results. The effects of material graduation, material function, temperature and internal pressures on the response of FG gas pipe are investigated. The coupled temperature and displacement FEM solution is used to find a solution for the stress displacement and temperature fields simultaneously because the thermal and mechanical solutions affected greatly by each other. The obtained results present the applicability of alternative FGM materials rather than classical A106Gr.B steel. According to proposed model and numerical results, the FGM pipe is more effective in natural gas application, especially in eliminating the corrosion, erosion and reduction of stresses.

Key Words
finite element method; FG Pipe; natural gas industry; nonlinear transient analysis; unsteady pressure and temperature

Address
Ahmed E. Soliman and Amal E. Alshorbagy: Department of Mechanical Design and Production, Faculty of Engineering, Zagazig University, Egypt
Mohamed A. Eltaher:
1) Department of Mechanical Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia
2) Department of Mechanical Design and Production, Faculty of Engineering, Zagazig University, Egypt
Mohamed A. Attia:
1) Department of Mechanical Design and Production, Faculty of Engineering, Zagazig University, Egypt
2) Department of Mechanical Engineering, College of Engineering, Shaqra University, Dawadmi, Saudi Arabia

Abstract
Cracking can lead to unexpected sudden failure of normally ductile metals subjected to a tensile stress, especially at elevated temperature. This article is raised to study the application of a composite material instead of the traditional carbon steel material used in the natural gas transmission pipeline because the cracks occurs in the pipeline initiate at its internal surface which is subjected to internal high fluctuated pressure and unsteady temperature according to actual operation conditions. Functionally graded material (FGM) is proposed to benefit from the ceramics durability and its surface hardness against erosion. FGM properties are graded at the radial direction. Finite element method (FEM) is applied and solved by ABAQUS software including FORTRAN subroutines adapted for this case of study. The stress intensity factor (SIF), temperatures and stresses are discussed to obtain the optimum FGM configuration under the actual conditions of pressure and temperature. Thermoelastic analysis of a plane strain model is adopted to study SIF and material response at various crack depths.

Key Words
fracture mechanics; functionally graded pipe; finite element; pressure fluctuation; radial crack; stress intensity factor; thermoelastic analysis

Address
Ahmed E. Soliman and Amal E. Alshorbagy: Department of Mechanical Design and Production, Faculty of Engineering, Zagazig University, Egypt
Mohamed A. Eltaher:
1) Department of Mechanical Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia
2) Department of Mechanical Design and Production, Faculty of Engineering, Zagazig University, Egypt
Mohamed A. Attia:
1) Department of Mechanical Design and Production, Faculty of Engineering, Zagazig University, Egypt
2) Department of Mechanical Engineering, College of Engineering, Shaqra University, Dawadmi, Saudi Arabia

Abstract
In the present paper, we have considered a layered medium of two semi-infinite nonlocal elastic solids with intermediate transversely isotropic magnetothermoelastic solid. The intermediate slab is of uniform thickness with the effects of two temperature, rotation and Hall current and with and without energy dissipation. A plane longitudinal or transverse wave propagating through one of the nonlocal elastic solid half spaces, is made incident upon transversely isotropic slab and it results into various reflected and refracted waves. The amplitude ratios of various reflected and refracted waves are obtained by using appropriate boundary conditions. The effect of nonlocal parameter on the variation of various amplitude ratios with angle of incidence are depicted graphically. Some cases of interest are also deduced.

Key Words
interface; reflection; transmission; transversely isotropic thermoelastic; nonlocal elastic half space; amplitude ratios

Address
Parveen Lata: Department of Basic and Applied Sciences, Punjabi University, Patiala, Punjab, India

Abstract
This paper proposes a transfer matrix method for the bending vibration of two types of tapered beams subjected to axial force, and it is applied to analyze tapered beams with an edge or multiple edge open cracks. One beam type is assumed to be reduced linearly in the cross-section height along the beam length. The other type is a tapered beam in which the cross-section height and width with the same taper ratio is linearly reduced simultaneously. Each crack is modeled as two sub-elements connected by a rotational spring, and the method can evaluate the effect of cracking on the desired number of eigenfrequencies using a minimum number of subdivisions. Among the power series available for the solutions, the roots of the differential equation are computed using the Frobenius method. The computed results confirm the accuracy of the method and are compared with previously reported results. The effectiveness of the proposed methods is demonstrated by examining specific examples, and the effects of cracking and axial loading are carefully examined by a comparison of the single and double tapered beam results.

Key Words
transfer matrix method; Frobenius method; crack; axial force; tapered beam

Address
Jung Woo Lee and Jung Youn Lee: Department of Mechanical System Engineering, Kyonggi University, 154-42, Gwanggyosan-ro, Yeongtong-gu, Suwon-si, Gyeonggi-do, 16227, Republic of Korea


Abstract
Many practical engineering problems are associated with nonlinear systems subjected to nonstationary random excitations. Equivalent linearization methods are commonly used to seek for approximate solutions to this kind of problems. Compared to various approaches developed in the frequency and mixed time-frequency domains, though directly solving the system equation of motion in the time domain would improve computation efficiency, only limited studies are available. Considering the fact that the orthogonal functions have been widely used to effectively improve the accuracy of the approximated responses and reduce the computational cost in various engineering applications, an orthogonal-function-based equivalent linearization method in the time domain has been proposed in the current paper for nonlinear systems subjected to nonstationary random excitations. In the numerical examples, the proposed approach is applied to a SDOF system with a set-up spring and a SDOF Duffing oscillator subjected to stationary and nonstationary excitations. In addition, its applicability to nonlinear MDOF systems is examined by a 3DOF Duffing system subjected to nonstationary excitation. Results show that the proposed method can accurately predict the nonlinear system response and the formulation of the proposed approach allows it to be capable of handling any general type of nonstationary random excitations, such as the seismic load.

Key Words
equivalent linearization; nonstationary excitation; orthogonal functions; nonlinearity; random vibration

Address
Amir Younespour:
1) Department of Civil and Environmental Engineering, University of Tabriz, Tabriz, Iran
2) Department of Civil and Environmental Engineering, University of Windsor, Windsor, Ontario, Canada
Shaohong Cheng: Department of Civil and Environmental Engineering, University of Windsor, Windsor, Ontario, Canada
Hosein Ghaffarzadeh: Department of Civil and Environmental Engineering, University of Tabriz, Tabriz, Iran


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