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CONTENTS
Volume 66, Number 6, June25 2018
 

Abstract
Reliability assessment of complex structures using simulation methods is time-consuming. Thus, surrogate models are usually employed to reduce computational cost. AK-MCS is a surrogate-based Active learning method combining Kriging and Monte-Carlo Simulation for structural reliability analysis. This paper proposes three modifications of the AK-MCS method to reduce the number of calls to the performance function. The first modification is related to the definition of an initial Design of Experiments (DoE). In the original AK-MCS method, an initial DoE is created by a random selection of samples among the Monte Carlo population. Therefore, samples in the failure region have fewer chances to be selected, because a small number of samples are usually located in the failure region compared to the safe region. The proposed method in this paper is based on a uniform selection of samples in the predefined domain, so more samples may be selected from the failure region. Another important parameter in the AK-MCS method is the size of the initial DoE. The algorithm may not predict the exact limit state surface with an insufficient number of initial samples. Thus, the second modification of the AK-MCS method is proposed to overcome this problem. The third modification is relevant to the type of regression trend in the AK-MCS method. The original AK-MCS method uses an ordinary Kriging model, so the regression part of Kriging model is an unknown constant value. In this paper, the effect of regression trend in the AK-MCS method is investigated for a benchmark problem, and it is shown that the appropriate choice of regression type could reduce the number of calls to the performance function. A stepwise approach is also presented to select a suitable trend of the Kriging model. The numerical results show the effectiveness of the proposed modifications.

Key Words
structural reliability; surrogate model; Kriging; Monte-Carlo simulation; design of experiments

Address
Jafar Vahedi, Mohammad Reza Ghasemi and Mahmoud Miri: Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran

Abstract
This paper develops a nonlocal strain gradient plate model for vibration analysis of graphene sheets under thermal environments. For more accurate analysis of graphene sheets, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. Graphene sheet is modeled via a two-variable shear deformation plate theory needless of shear correction factors. Governing equations of a nonlocal strain gradient graphene sheet on elastic substrate are derived via Hamilton\'s principle. Differential quadrature method (DQM) is implemented to solve the governing equations for different boundary conditions. Effects of different factors such as temperature rise, nonlocal parameter, length scale parameter, elastic foundation and aspect ratio on vibration characteristics a graphene sheets are studied. It is seen that vibration frequencies and critical buckling temperatures become larger and smaller with increase of strain gradient and nonlocal parameter, respectively.

Key Words
thermal vibration; refined plate theory; graphene sheets; nonlocal strain gradient theory

Address
Farzad Ebrahimi and Mohammad Reza Barati: Mechanical Engineering Department, Faculty of Engineering, Imam Khomeini International University, Qazvin, P.O.B. 3414916818, Iran

Abstract
In this paper is studied the effect of considering the theory of Timoshenko in the vibration of AFG beams that support ground masses. As it is known, Timoshenko theory takes into account the shear deformation and the rotational inertia, provides more accurate results in the general study of beams and is mandatory in the case of high frequencies or non-slender beams. The Rayleigh-Ritz Method is employed to obtain approximated solutions of the problem. The accuracy of the procedure is verified through results available in the literature that can be represented by the model under study. The incidence of the Timoshenko theory is analyzed for different cases of beam slenderness, variation of its cross section and compositions of its constituent material, as well as different amounts and positions of the attached masses.

Key Words
vibration of beams; AFG beam; tapered beam; Timoshenko beam; attached masses; Rayleigh-Ritz method

Address
Carlos A. Rossit, Diana V. Bambill and Gonzalo J. Gilardi: Department of Engineering, Universidad Nacional del Sur(UNS) Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Avenida Alem 1253, (8000) Bahía Blanca, República Argentina

Abstract
Thin-walled mental tubes under lateral crushing are desirable and reliable energy absorbers against impact or blast loads. However, the early formations of plastic hinges in the thin cylindrical wall limit the energy absorption performance. This study investigates the energy absorption performance of a simple, light and efficient energy absorber called the ring stiffened tube. Due to the increase of section modulus of tube wall and the restraining effect of the T-stiffener flange, key energy absorption parameters (peak crushing force, energy absorption and specific energy absorption) have been significantly improved against the empty tube. Its potential application in the offshore blast wall design has also been investigated. It is proposed to replace the blast wall endplates at the supports with the energy absorption devices that are made up of the ring stiffened tubes and springs. An analytical model based on beam vibration theory and virtual work theory, in which the boundary conditions at each support are simplified as a translational spring and a rotational spring, has been developed to evaluate the blast mitigation effect of the proposed design scheme. Finite element method has been applied to validate the analytical model. Comparisons of key design criterions such as panel deflection and energy absorption against the traditional design demonstrate the effectiveness of the proposed design in blast alleviation.

Key Words
ring stiffened tube; blast wall; flexible support; energy absorption; analytical model; finite element analysis

Address
JinJing Liao:
1) Atkins Australasia Pty Ltd., Level 8, 50 St Geroges Terrace, Perth WA 6000, Australia
2) School of Civil, Environmental and Mining Engineering, The University of Western Australia, 35 Stirling Hwy, Crawley WA 6009, Australia
Guowei Ma
1) School of Civil and Transportation Engineering, Hebei University of Technology, Tianjin 300401, China
2) School of Civil, Environmental and Mining Engineering, The University of Western Australia, 35 Stirling Hwy, Crawley WA 6009, Australia

Abstract
This paper studies thermal buckling and post-buckling behaviors of functionally graded materials (FGM) tubes subjected to a uniform temperature rise and resting on elastic foundations via a refined beam model. Compared to the Timoshenko beam theory, the number of unknowns of this model are the same and no correction factors are required. The material properties of the FGM tube vary continuously in the radial direction according to a power function. Two ends of the tube are assumed to be simply supported and in-plane boundary conditions are immovable. Energy variation principle is employed to establish the governing equations. A two-step perturbation method is adopted to determine the critical thermal buckling loads and post-buckling paths of the tubes with arbitrary radial non-homogeneity. Through detailed parametric studies, it can be found that the tube has much higher buckling temperature and post-buckling strength when it is supported by an elastic foundation.

Key Words
functionally graded materials; tubes; thermal buckling; post-buckling; elastic foundation

Address
Gui-Lin She, Yi-Ru Ren, Wan-Shen Xiao and Haibo Liu: State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, China

Abstract
The current study presents a new technique in the framework of the nonlocal elasticity theory for a comprehensive buckling analysis of Euler-Bernoulli nano-beams made up of bidirectional functionally graded material (BDFGM). The mechanical properties are considered by exponential and arbitrary variations for axial and transverse directions, respectively. The various circumstances including tapering, resting on two-parameter elastic foundation, step-wise or continuous variations of axial loading, various shapes of sections with various distribution laws of mechanical properties and various boundary conditions like the multi-span beams are taken into account. As far as we know, for the first time in the current work, the buckling analyses of BDFGM nano-beams are carried out under mentioned circumstances. The critical buckling loads and mode shapes are calculated by using energy method and a new technique based on calculus of variations and collocation method. Fast convergence and excellent agreement with the known data in literature, wherever possible, presents the efficiency of proposed technique. The effects of boundary conditions, material and taper constants, foundation moduli, variable axial compression and small-scale of nano-beam on the buckling loads and mode shapes are investigated. Moreover the analytical solutions, for the simpler cases are provided in appendices.

Key Words
buckling analysis; nonlocal elasticity theory; bidirectional functionally graded material; two-parameter elastic foundation; variable axial compression; tapered nano-beam; multi-span nano-beam

Address
Abbas Heydari: Young Researchers and Elite Club, Ardabil Branch, Islamic Azad University, Ardabil, Iran
Mahdi Shariati:
1) Faculty of Civil Engineering, University of Tabriz, Tabriz, Iran
2) Department of Civil Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia
3) UTM Construction Research Centre, Faculty of Civil Engineering, Institute for Smart Infrastructure and Innovative Construction, UTM, 81310 Johor Bahru, Johor, Malaysia

Abstract
Aiming at widely used high-pier bridges in Sichuan-Tibet Railway, this paper presents an investigation to design and evaluate the seismic vibration reduction effects of several measures, including viscous damper (VD), friction pendulum bearing (FPB), and tuned mass damper (TMD). Primarily, according to the detailed introduction of the concerned bridge structure, dynamic models of high-pier bridges with different seismic vibration reduction (SVR) measures are established. Further, the designs for these SVR measures are performed, and the optimal parameters of these measures are investigated. On this basis, the vibration reduction effects of these measures are analyzed and assessed subject to actual earthquake excitations in Wenchuan Earthquake (M=8.0), and the most appropriate SVR measure for high-pier bridges in Sichuan-Tibet Railway is determined at the end of the work. Results show that the height of pier does not obviously affect the performances of the concerned SVR measures. Comprehensively considering the vibration absorption performance, installation and maintenance of all the employed measures in this paper, TMD is the best one to absorb vibrations induced by earthquakes.

Key Words
high-pier bridge; Sichuan-Tibet Railway; seismic effect; vibration reduction; TMD

Address
Zhaowei Chen:
1) School of Mechanotronics & Vehicle Engineering, Chongqing Jiaotong University, Chongqing, China
2) MOE Key Laboratory of High-speed Railway Engineering, Southwest Jiaotong University, Chengdu, China
Zhaoling Han: State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu, China
Hui Fang: Electric Power Research Institute, State Grid Chongqing Electric Power Company, Chongqing, China
Kai Wei: MOE Key Laboratory of High-speed Railway Engineering, Southwest Jiaotong University, Chengdu, China

Abstract
In this paper, we study the Carbon/Glass hybrid laminated composite plates, where the buckling behavior is examined using an accurate and simple refined higher order shear deformation theory. This theory takes account the shear effect, where shear deformation and shear stresses will be considered in determination of critical buckling load under different boundary conditions. The most interesting feature of this new kind of hybrid laminated composite plates is that the possibility of varying components percentages, which allows us for a variety of plates with different materials combinations in order to overcome the most difficult obstacles faced in traditional laminated composite plates like (cost and strength). Numerical results of the present study are compared with three-dimensional elasticity solutions and results of the first-order and the other higher-order theories issue from the literature. It can be concluded that the proposed theory is accurate and simple in solving the buckling behavior of hybrid laminated composite plates and allows to industrials the possibility to adjust the component of this new kind of plates in the most efficient way (reducing time and cost) according to their specific needs.

Key Words
hybrid plates; laminated composite plates; higher-order shear deformation theory; transverse shear; buckling

Address
Adim Belkacem:
1) Departement des Sciences et Technologies, Centre Universitaire El Wancharissi - Tissemsilt, Algerie
2) Laboratoire de Geomatique et Developpement Durable, Universite Ibn Khaldoun de Tiaret Algerie
Hassaine Daouadji Tahar, Rabahi Abderrezak, Benhenni Mohamed Amine and Zidour Mohamed:
1) Laboratoire de Geomatique et Développement Durable, Universite Ibn Khaldoun de Tiaret Algerie
2) Departement de Genie Civil, Universite Ibn Khaldoun Tiaret; BP 78 Zaaroura, 14000 Tiaret, Algerie
Abbes Boussad: Laboratoire GRESPI - Campus du Moulin de la Housse BP 1039 - 51687 Reims Cedex 2, France

Abstract
This study deals with free vibrations analysis with stretching effect of nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs) resting on an elastic foundation. Four different carbon nanotubes (CNTs) distributions including uniform and three types of functionally graded distributions of CNTs through the thickness are considered. The rule of mixture is used to describe the effective material properties of the nanocomposite beams. The significant feature of this model is that, in addition to including the shear deformation effect and stretching effect it deals with only 4 unknowns without including a shear correction factor. The governing equations are derived through using Hamilton\'s principle. Natural frequencies are obtained for nanocomposite beams. The mathematical models provided in this paper are numerically validated by comparison with some available results. New results of free vibration analyses of CNTRC beams based on the present theory with stretching effect is presented and discussed in details. The effects of different parameters of the beam on the vibration responses of CNTRC beam are discussed.

Key Words
free vibration; stretching effect; CNTRC beams; elastic foundation

Address
Lazreg Hadji:
1) Department of Civil Engineering, Ibn Khaldoun University, BP 78 Zaaroura, 14000 Tiaret, Algeria
2) Laboratory of Geomatics and Sustainable Development, Ibn Khaldoun University of Tiaret, Algeria
Mohamed Ait Amar Meziane: Department of Civil Engineering, Ibn Khaldoun University, BP 78 Zaaroura, 14000 Tiaret, Algeria
Abdelkader Safa: Department of Civil Engineering, Ahmed Zabana University, 48000 Relizane, Algeria

Abstract
This paper presents a detailed theoretical study of the sleeved compression members based on a mechanical model. In the mechanical model, the core protrusion above sleeve and the contact force between the core and sleeve are specially taken into account. Via the theoretical analyses, load-displacement relationships of the sleeved compression members are obtained and verified by the experimental results. On the basis of the core moment distribution changing with the increase of the applied axial load, failure mechanism of the sleeved compression members is assumed and proved to be consistent with the experimental results in terms of the failure modes and the ultimate bearing capacities. A parametric study is conducted to quantify how essential factors including the core protrusion length above sleeve, stiffness ratio of the core to sleeve, core slenderness ratio and gap between the core and sleeve affect the mechanical behaviors of the sleeved compression members, and it is concluded that the constrained effect of the sleeve is overestimated neglecting the core protrusion; the improvement of ultimate bearing capacity for the sleeved compression member is considered to be decreasing with the decrease of the core slenderness ratio and for the sleeved compression member with core of small slenderness ratio, small gap and small stiffness ratio are preferred to obtain larger ultimate bearing capacity and stiffness.

Key Words
theoretical study; sleeved compression member; load-displacement relationship; failure mechanism; parametric study; buckling constraint

Address
Chenhui Zhang and Changgen Deng: College of Civil Engineering, Tongji University, Shanghai 200092, China


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