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CONTENTS
Volume 64, Number 4, November25 2017
 

Abstract
In this paper, a new nonlocal trigonometric shear deformation theory is proposed for thermal buckling response of nanosize functionally graded (FG) nano-plates resting on two-parameter elastic foundation under various types of thermal environments. This theory uses for the first time, undetermined integral variables and it contains only four unknowns, that is even less than the first shear deformation theory (FSDT). It is considered that the FG nano-plate is exposed to uniform, linear and sinusoidal temperature rises. Mori-Tanaka model is utilized to define the gradually variation of material properties along the plate thickness. Nonlocal elasticity theory of Eringen is employed to capture the size influences. Through the stationary potential energy the governing equations are derived for a refined nonlocal four-variable shear deformation plate theory and then solved analytically. A variety of examples is proposed to demonstrate the importance of elastic foundation parameters, various temperature fields, nonlocality, material composition, aspect and side-to-thickness ratios on critical stability temperatures of FG nano-plate.

Key Words
nonlocal elasticity theory; FG nanoplate; thermal buckling refined theory; elastic foundation

Address
Hafid Khetir: Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Faculté de Technologie, Département de Génie Civil, Université de Sidi Bel Abbes, Algeria

Mohamed Bachir Bouiadjra: Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Faculté de Technologie, Département de Génie Civil, Université de Sidi Bel Abbes, Algeria; Algerian National Thematic Agency of Research in Science and Technology (ATRST), Algeria

Mohammed Sid Ahmed Houari: Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Faculté de Technologie, Département de Génie Civil, Université de Sidi Bel Abbes, Algeria; Department of Civil Engineering, Université Mustapha Stambouli de Mascara, Mascara, Algeria

Abdelouahed Tounsi: Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals,31261 Dhahran, Eastern Province, Saudi Arabia; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Algerian National Thematic Agency of Research in Science and Technology (ATRST), Algeria

S.R. Mahmoud: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

Abstract
In this article, analytical solution for free vibration of micro composite laminated beam on elastic medium based on modified couple stress are presented. The surrounding elastic medium is modeled as the Winkler elastic foundation. The governing equations and boundary conditions are obtained by using the principle of minimum potential energy for Euler- Bernoulli beam. For investigating the effect of different parameters including material length scale, beam thickness, some numerical results on different cross ply laminated beams such as (90,0,90), (0,90,0), (90,90,90) and (0,0,0) are presented on elastic medium. Free vibration analysis of a simply supported beam is considered utilizing the Fourier series. Also, the fundamental frequency is obtained using the principle of Hamilton for four types of cross ply laminations with hinged-hinged boundary conditions and different beam theories. The fundamental frequency for different thin beam theories are investigated by increasing the slenderness ratio and various foundation coefficients. The results prove that the modified couple stress theory increases the natural frequency under the various foundation for free vibration of composite laminated micro beams.

Key Words
composite laminated beam; modified couple stress theory; elastic foundation; generalized differential quadrature

Address
Javad Ehyaei: Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, 3414916818, Qazvin, Iran

Reza Akbarizadeh: Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, 3414916818, Qazvin, Iran

Abstract
Probabilistic methods are used in engineering where a computational model contains random variables. The proposed method under development: Direct Optimized Probabilistic Calculation (DOProC) is highly efficient in terms of computation time and solution accuracy and is mostly faster than in case of other standard probabilistic methods. The novelty of the DOProC lies in an optimized numerical integration that easily handles both correlated and statistically independent random variables and does not require any simulation or approximation technique. DOProC is demonstrated by a collection of deliberately selected simple examples (i) to illustrate the efficiency of individual optimization levels and (ii) to verify it against other highly regarded probabilistic methods (e.g., Monte Carlo). Efficiency and other benefits of the proposed method are grounded on a comparative case study carried out using both the DOProC and MC techniques. The algorithm has been implemented in mentioned software applications, and has been used effectively several times in solving probabilistic tasks and in probabilistic reliability assessment of structures. The article summarizes the principles of this method and demonstrates its basic possibilities on simple examples. The paper presents unpublished details of probabilistic computations based on this method, including a reliability assessment, which provides the user with the probability of failure affected by statistically dependent input random variables. The study also mentions the potential of the optimization procedures under development, including an analysis of their effectiveness on the example of the reliability assessment of a slender column.

Key Words
Direct Optimized Probabilistic Calculation; DOProC; probabilistic method; random variable; reliability assessment; probability of failure; Monte Carlo

Address
Petr Janas: Department of Structural Mechanics, Faculty of Civil Engineering, VSB - Technical University of Ostrava, Ludvika Podeste 1875/17, 708 33 Ostrava-Poruba, Czech Republic

Martin Krejsa: Department of Structural Mechanics, Faculty of Civil Engineering, VSB - Technical University of Ostrava, Ludvika Podeste 1875/17, 708 33 Ostrava-Poruba, Czech Republic

Jiri Sejnoha: Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague,
Thakurova 7, 166 29 Prague 6, Czech Republic

Vlastimil Krejsa: Department of Structural Mechanics, Faculty of Civil Engineering, VSB - Technical University of Ostrava, Ludvika Podeste 1875/17, 708 33 Ostrava-Poruba, Czech Republic

Abstract
Concrete technologists have used ultrasonic pulse velocity test for decades to evaluate the properties of concrete. However, the presented research work focuses on the use of ultrasonic pulse velocity test to study the degradation in steelconcrete bond subjected to increasing loading. A detailed experimental investigation was conducted by testing five identical beam specimens under increasing loading. The loading was increased from zero till failure in equal increments. From the experimentation, it was found that as the reinforced concrete beams were stressed from control unloaded condition till complete failure, the propagating ultrasonic wave velocity reduced. This reduction in wave velocity is attributed to the initiation, development, and propagation of internal cracking in the concrete surrounding the steel reinforcement. Using both direct and semidirect methods of testing, results of reduction in wave velocity with evidence of internal cracking at steel-concrete interface are presented. From the presented results and discussion, it can be concluded that the UPV test method can be successfully employed to identify zones of poor bonding along the length of reinforced concrete beam. The information gathered by such testing can be used by engineers for localizing repairs thereby leading to saving of time, labor and cost of repairs. Furthermore, the implementation strategy along with real-world challenges associated with the application of the proposed technique and area of future development have also been presented.

Key Words
ultrasonic pulse velocity test; bond evaluation; increasing loading; internal cracking; implementation strategy; real-world challenges

Address
Muhammad Saleem: Department of Basic Engineering, College of Engineering, Imam Abdulrahman Bin Faisal University,
P.O. Box 1982, Dammam 31451, Eastern Province, Kingdom of Saudi Arabia

Abstract
Explicit expressions for rapid prediction of inelastic design quantities (considering cracking of concrete) from corresponding elastic quantities, are presented for multi-storey composite frames (with steel columns and steel-concrete composite beams) subjected to service load. These expressions have been developed from weights and biases of the trained neural networks considering concrete stress, relative stiffness of beams and columns including effects of cracking in the floors below and above. Large amount of data sets required for training of neural networks have been generated using an analyticalnumerical procedure developed by the authors. The neural networks have been developed for moments and deflections, for first floor, intermediate floors (second floor to ante-penultimate floor), penultimate floor and topmost floor. In the case of moments, expressions have been proposed for exterior end of exterior beam, interior end of exterior beam and both interior ends of interior beams, for each type of floor with a total of twelve expressions. Similarly, in the case of deflections, expressions have been proposed for exterior beam and interior beam of each type of floor with a total of eight expressions. The proposed expressions have been verified by comparison of the results with those obtained from the analytical-numerical procedure. This methodology helps to obtain the inelastic design quantities from the elastic quantities with simple calculations and thus would be very useful in preliminary design.

Key Words
composite frames; cracking; neural network; service load; tension stiffening

Address
M.P. Ramnavas: Department of Civil Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India

K.A. Patel: Department of Civil Engineering, Institute of Infrastructure, Technology, Research And Management (IITRAM), Ahmedabad 380026, India

Sandeep Chaudhary:Discipline of Civil Engineering, Indian Institute of Technology Indore, Simrol, Indore 453552, India

A.K. Nagpal: Department of Civil Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India

Abstract
High-rise buildings are generally sensitive to strong winds. The evaluation of wind loads for the structural design, structural health monitoring (SHM), and vibration control of high-rise buildings is of primary importance. Nevertheless, it is difficult or even infeasible to measure the wind loads on an existing building directly. In this regard, a new inverse method for evaluating wind loads on high-rise buildings is developed in this study based on a discrete-time Kalman filter. The unknown structural responses are identified in conjunction with the wind loads on the basis of limited structural response measurements. The algorithm is applicable for estimating wind loads using different types of wind-induced response. The performance of the method is comprehensively investigated based on wind tunnel testing results of two high-rise buildings with typical external shapes. The stability of the proposed algorithm is evaluated. Furthermore, the effects of crucial factors such as cross-section shapes of building, the wind-induced response type, errors of structural modal parameters, covariance matrix of noise, noise levels in the response measurements and number of vibration modes on the identification accuracy are examined through a detailed parametric study. The research outputs of the proposed study will provide valuable information to enhance our understanding of the effects of wind on high-rise buildings and improve codes of practice.

Key Words
force identification; wind load; high-rise building; Kalman filter; structural response; wind tunnel test

Address
Lun-hai Zhi: School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan 430070, China

Pan Yu: School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan 430070, China

Jian-wei Tu: Key Laboratory of Roadway Bridge and Structural Engineering, Wuhan University of Technology, Wuhan 430070, China

Bo Chen: Key Laboratory of Roadway Bridge and Structural Engineering, Wuhan University of Technology, Wuhan 430070, China

Yong-gui Li: School of Civil Engineering, Hunan University of Science and Technology, Xiangtan 411201, China

Abstract
The dynamic tests of recycled aggregate concrete (RAC) are carried out, the rate-dependent mechanical models of RAC are proposed. The dynamic mechanical behaviors of RAC frame structure are investigated by adopting the numerical simulation method of the finite element. It is indicated that the lateral stiffness and the hysteresis loops of RAC frame structure obtained from the numerical simulation agree well with the test results, more so for the numerical simulation which is considered the strain rate effect than for the numerical simulation with strain rate excluded. The natural vibration frequency and the lateral stiffness increase with the increase of the strain rate. The dynamic model of the lateral stiffness is proposed, which is reasonably applied to describe the effect of the strain rate on the lateral stiffness of RAC frame structure. The effect of the strain rate on the structural deformation and capacity of RAC is analyzed. The analyses show that the inter-story drift decreases with the increase of the strain rate. However, with the increasing strain rate, the structural capacity increases. The dynamic models of the base shear coefficient and the overturning moment of RAC frame structure are developed. The dynamic models are important and can be used to evaluate the strength deterioration of RAC structure under dynamic loading.

Key Words
recycled aggregate concrete (RAC); dynamic characteristic; strain rate effect; natural frequency; lateral stiffness; hysteresis loops; inter-story drift; shear coefficient; overturning moment

Address
Changqing Wang: School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China; College of Civil Engineering, Tongji University, Shanghai 200092, China

Jianzhuang Xiao: College of Civil Engineering, Tongji University, Shanghai 200092, China

Abstract
An isolated building, composed of superstructure and isolation system which have very different damping properties, is typically non-classical damping system. This results in inapplicability of traditional response spectrum method for isolated buildings. A multidimensional response spectrum method based on complex mode superposition is herein introduced, which properly takes into account the non-classical damping feature in the structure and a new method is developed to estimate velocity spectra from the commonly used displacement or pseudo-acceleration spectra based on random vibration theory. The error of forced decoupling method, an approximated approach, is discussed in the viewpoint of energy transfer. From the baseisolated benchmark model, as a numerical example, application of the procedure is illustrated companying with comparison study of time-history method, forced decoupling method and the proposed method. The results show that the proposed method is valid, while forced decoupling approach can\'t reflect the characteristics of isolated buildings and may lead to insecurity of structures.

Key Words
response spectrum method; CCQC rule; complex mode superposition approach; forced decoupling method; velocity response spectra; the base-isolated benchmark building

Address
Huating Chen:Earthquake Engineering Research & Test Center, Guangzhou University, Guangzhou, China

Ping Tan: Earthquake Engineering Research & Test Center, Guangzhou University, Guangzhou, China

Haitao Ma: Earthquake Engineering Research & Test Center, Guangzhou University, Guangzhou, China

Fulin Zhou: Earthquake Engineering Research & Test Center, Guangzhou University, Guangzhou, China

Abstract
The present paper deals with a theoretical study of delamination fracture in the Crack Lap Shear (CLS) functionally graded beam configuration. The basic purpose is to analyze the fracture with taking into account the material non-linearity. The mechanical behavior of CLS was described by using a non-linear stress-strain relation. It was assumed that the material is functionally graded along the beam height. The fracture was analyzed by applying the J-integral approach. The curvature and neutral axis coordinate of CLS beam were derived in order to solve analytically the J-integral. The non-linear solution of Jintegral obtained was verified by analyzing the strain energy release rate with considering material non-linearity. The effects of material gradient, crack location along the beam height and material non-linearity on fracture behavior were evaluated. The Jintegral non-linear solution derived is very suitable for parametric studies of longitudinal fracture in the CLS beam. The results obtained can be used to optimize the functionally graded beam structure with respect to the fracture performance. The analytical approach developed in the present paper contributes for the understanding of delamination fracture in functionally graded beams exhibiting material non-linearity.

Key Words
functionally graded beams; fracture; material non-linearity; analytical modeling

Address
Victor I. Rizov: Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy,
1 Chr. Smirnensky blvd., 1046-Sofia, Bulgaria

Abstract
This paper proposes a new direct numerical integration algorithm for solving equation of motion in structural dynamics problems with nonlinear stiffness. The new implicit method\'s degree of accuracy is higher than that of existing methods due to the higher order of the acceleration. Two parameters are defined, leading to a new family of unconditionally stable methods, which helps to take greater time steps in integration and eliminate concerns about the duration of solving. The method developed can be utilized for a number of solid plane finite elements, examples of which are given to compare the proposed method with existing ones. The results indicate the superiority of the proposed method.

Key Words
structural dynamics; direct time integration; numerical procedure; accuracy; unconditionally stable; nonlinear equation of motion

Address
Saeed Mohammadzadeh: School of Civil Engineering, University of Tehran, Tehran, Iran

Mehdi Ghassemieh: School of Civil Engineering, University of Tehran, Tehran, Iran

Yeonho Park: Department of Civil Engineering, University of Texas, Arlington, USA

Abstract
In this paper, a receding contact problem for an elastic layer resting on a half plane is considered. The layer is pressed by two rectangular stamps placed symmetrically. It is assumed that the contact surfaces are frictionless and only compressive traction can be transmitted through the contact surfaces. In addition the effect of body forces is neglected. Firstly, the problem is solved analytically based on theory of elasticity. In this solution, the problem is reduced into a system of singular integral equations in which half contact length and contact pressures are unknowns using boundary conditions and integral transform techniques. This system is solved numerically using Gauss-Jacobi integral formulation. Secondly, two dimensional finite element analysis of the problem is carried out using ANSYS. The dimensionless quantities for the contact length and the contact pressures are calculated under various stamp size, stamp position and material properties using both solutions. The analytic results are verified by comparison with finite element results.

Key Words
receding contact; half plane; contact pressure; stamp; finite element method

Address
Pembe Merve Karabulut, Gokhan Adiyamana and Ahmet Birinci: Department of Civil Engineering, Karadeniz Technical University, Trabzon, Turkey

Abstract
Dynamic response of functionally graded Carbon nanotubes (FG-CNT) reinforced pipes conveying viscous fluid under accelerated moving load is presented. The mixture rule is used for obtaining the material properties of nano-composite pipe. The radial force induced by viscous fluid is calculated by Navier–Stokes equation. The material properties of pipe are considered temperature-dependent. The structure is simulated by Reddy higher-order shear deformation shell theory and the corresponding motion equations are derived by Hamilton\'s principal. Differential quadrature (DQ) method and the Integral Quadrature (IQ) are applied for analogizing the motion equations and then the Newmark time integration scheme is used for obtaining the dynamic response of structure. The effects of different parameters such as boundary conditions, geometrical parameters, velocity and acceleration of moving load, CNT volume percent and distribution type are shown on the dynamic response of pipe. Results indicate that increasing CNTs leads to decrease in transient deflection of structure. In accelerated motion of the moving load, the maximum displacement is occurred later with respect to decelerated motion of moving load.

Key Words
dynamic response; FG-CNT pipe; moving load; viscous fluid; DQ-IQ method

Address
F. Vakili Tahami: Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran

H. Biglari: Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran

M. Raminnea: Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran


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