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CONTENTS
Volume 35, Number 1, April10 2020
 

Abstract
This article deals with the buckling analysis in the plates containing carbon nanotubes (CNTs) subject to axial load. In order to control the plate smartly, a piezoelectric layer covered the plate. The plate is located in elastic medium which is modeled by spring elements. The Mori-Tanaka low is utilized for calculating the equivalent mechanical characteristics of the plate. The structure is modeled by a thick plate and the governing equations are deduced using Hamilton\'s principle under the assumption of higher-order shear deformation theory (HSDT). The Navier method is applied to obtain the bulking load. The effects of the applied voltage to the smart layer, agglomeration and volume percent of CNT nanoparticles, geometrical parameters and elastic medium of the structure are assessed on the buckling response. It has been demonstrated that by applying a negative voltage, the buckling load is increased significantly.

Key Words
smart plate; buckling load; piezoelectric layer; elastic medium; analytical method

Address
Ahmad Farrokhian: Mechanical Engineering group, Pardis College, Isfahan University of Technology, Isfahan 84156-83111, Iran

Abstract
To investigate the stress-strain relation of PVC-FRP Confined Concrete (PFCC) column with RC ring beam joint subjected to eccentric compression, the experiment of 13 joint specimens, which were designed with principle of \"strong joint and weak column\", were presented. Several variable parameters, such as reinforcement ratio, width and height of ring beam, FRP strips spacing and eccentricity, were considered. The specimens were eventually damaged by the crushing of concrete, the fracture of PVC tube and several FRP strips. With the FRP strips spacing or eccentricity increased, the ultimate carrying capacity of specimens declined. The strain of FRP strips and axial strain of PVC tube decreased as FRP strips spacing decreased. The decrease of eccentricity would slow down the development of strain of FRP strips and axial strain of PVC tube. The slope of stress-strain curve of PFCC column decreased as FRP strips spacing or eccentricity increased. The ultimate strain of PFCC column reduced as FRP strips spacing increased, while the effect of eccentricity on the ultimate strain of PFCC was not distinct. Considering the influence of eccentricity on the stress-strain relation, a modified stress-strain model for conveniently predicting the weak PFCC column and strong RC ring beam joint under eccentric compression was proposed and it was in good agreement with the experimental data.

Key Words
stress-strain relation; eccentric compression; carrying capacity; PVC-FRP; column; beam; joint

Address
Feng Yu, Nannan Zhang, Yuan Fang, Jie Liu and Guosheng Xiang: Department of Civil engineering and Anhui University of Technology, Maxiang Road 59, Maanshan, China

Abstract
Cross-beams of modern through truss bridges are connected to truss chord at its nodes and between them. It results in variable rotational end restraint for cross-beams, thus variable bending moment distribution. This feature is captured in three-dimensional modelling of through truss bridge structure. However, for preliminary design or rapid assessment of service load effects such technique of analysis may not be available. So an analytical method of assessment of rotational end restraint for cross-beam of through truss bridges was worked out. Two cases – nodal cross-beam and inter-nodal cross-beam – were analyzed. Flexural and torsional stiffness of truss members, flexural stiffness of deck members and axial stiffness of wind bracing members in the vicinity of the analyzed cross-beam were taken into account. The provision for reduced stiffness of the X-type wind bracing was made. Finally, general formula for assessment of rotational end restraint was given. Rotational end restraints for cross-beams of three railway through truss bridges were assessed basing on the analytical method and the finite element method (three-dimensional beam-element modelling). Results of both methods show good agreement. The analytical method is able to reflect effects of some structural irregularities. On the basis of the obtained results the general values of rotational end restraint for nodal and inter-nodal cross-beams of railway through truss bridges were suggested.

Key Words
rotational end restraint; cross-beam; through truss bridge

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


Abstract
In this study, free vibration analysis of laminated composite parabolic thick plate frames by using finite element method is introduced. Governing equations of an eigenvalue problem are obtained from First Order Shear Deformation Theory (FSDT). Finite element method is employed to obtain natural frequency values from the governing differential equations. The frames consist of two flat square plates and one singly curved plate. Parameters like radii of curvature, aspect ratio, ply orientation and boundary conditions are investigated to understand their effect on dynamic behavior of such a structure. In addition, multi-bay structures of such geometry with different stacking order are also taken into account. The composite frame structures are also modeled and simulated via ANSYS to verify the accuracy of the present study.

Key Words
vibration analysis; parabolic frames; composite structures; first order shear deformation theory; finite element analysis

Address
uzhan Das and Can Gonenli: The Graduate School of Natural and Applied Sciences, Dokuz Eylul University,
Tinaztepe Campus, Buca – İzmir, 35390 Turkey
Hasan Ozturk: Department of Mechanical Engineering, Dokuz Eylul University, Tinaztepe Campus, Buca – İzmir, 35390 Turkey



Abstract
In this paper, the dynamic behaviour of an inclined functionally graded material (FGM) beam with different boundary conditions under a moving mass is investigated based on the first-order shear deformation theory (FSDT). The material properties vary continuously along the beam thickness based on the power-law distribution. The system of motion equations is derived by using Hamilton\'s principle. The finite element method (FEM) is adopted to develop a general solution procedure. The moving mass is considered on the top surface of the beam instead of supposing it on the mid-plane. In order to consider the Coriolis, centrifugal accelerations and the friction force, the contact force method is used. Moreover, the effects of boundary conditions, the moving mass velocity and various material distributions are studied. For verification of the present results, a comparative fundamental frequency analysis of an FGM beam is conducted and the dynamic transverse displacements of the homogeneous and FGM beams traversed by a moving mass are compared with those in the existing literature. There is a good accord in all compared cases. In this study for the first time in dynamic analysis of the inclined FGM beams, the Coriolis and centrifugal accelerations of the moving mass are taken into account, and it is observed that these accelerations can be ignored for the low-speeds of the moving mass. The new provided results for dynamics of the inclined FGM beams traversed by a moving mass can be significant for the scientific and engineering community in the area of FGM structures.

Key Words
inclined Timoshenko beam; FGM; moving mass; Coriolis; centrifugal; friction; FEM

Address
Vahid Shokouhifard and Parviz Malekzadeh : Department of Mechanical Engineering, Persian Gulf University, Bushehr, 7516913798, Iran
Saeedreza Mohebpour:Department of Mechanical Engineering, Persian Gulf University, Bushehr, 7516913798, Iran;
Department of Aerospace Engineering, Ryerson University, Toronto, ON, M5B 2K3, Canada
Hekmat Alighanbari: Department of Aerospace Engineering, Ryerson University, Toronto, ON, M5B 2K3, Canada



Abstract
The present paper outlined a procedure for geometrically nonlinear dynamic analysis of functionally graded graphene platelets-reinforced (GPLR-FG) nanocomposite cylinder subjected to mechanical shock loading. The governing equation of motion for large deformation problems is derived using meshless local Petrov-Galerkin (MLPG) method based on total lagrangian approach. In the MLPG method, the radial point interpolation technique is employed to construct the shape functions. A micromechanical model based on the Halpin-Tsai model and rule of mixture is used for formulation the nonlinear functionally graded distribution of GPLs in polymer matrix of composites. Energy dissipation in analyses of the structure responding to dynamic loads is considered using the Rayleigh damping. The Newmark-Newton/Raphson method which is an incremental-iterative approach is implemented to solve the nonlinear dynamic equations. The results of the proposed method for homogenous material are compared with the finite element ones. A very good agreement is achieved between the MLPG and FEM with very fine meshing. In addition, the results have demonstrated that the MLPG method is more effective method compared with the FEM for very large deformation problems due to avoiding mesh distortion issues. Finally, the effect of GPLs distribution on strength, stiffness and dynamic characteristics of the cylinder are discussed in details. The obtained results show that the distribution of GPLs changed the mechanical properties, so a classification of different types and volume fraction exponent is established. Indeed by comparing the obtained results, the best compromise of nanocomposite cylinder is determined in terms of mechanical and dynamic properties for different load patterns. All these applications have shown that the present MLPG method is very effective for geometrically nonlinear analyses of GPLR-FG nanocomposite cylinder because of vanishing mesh distortion issue in large deformation problems. In addition, since in proposed method the distributed nodes are used for discretization the problem domain (rather than the meshing), modeling the functionally graded media yields to more accurate results.

Key Words
functionally graded materials; meshless local Petrov-Galerkin method; shock loading; geometrically nonlinear analysis; graphene platelets reinforced nanocomposite

Address
Mohammad Hossein Ghadiri Rad: Civil Engineering Department, Quchan University of Technology, Quchan, Iran
Farzad Shahabian: Civil Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Seyed Mahmoud Hosseini: Industrial Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

Abstract
Developed from conventional concrete filled steel tubular (CFST) members, concrete-encased CFST has attracted growing attention in building and bridge practices. In actual construction, the inner CFST is erected prior to the casting of the outer reinforced concrete part to support the construction preload, after which the whole composite member is under sustained service load. The complex loading sequence leads to highly nonlinear material interaction and consequently complicated structural performance. This paper studies the full-range behaviour of concrete-encased CFST columns with initial preload on inner CFST followed by sustained service load over the whole composite section. Validated against the reported data obtained from specifically designed tests, a finite element analysis model is developed to investigate the detailed structural behaviour in terms of ultimate strength, load distribution, material interaction and strain development. Parametric analysis is then carried out to evaluate the impact of significant factors on the structural behaviour of the composite columns. Finally, a simplified design method for estimating the sectional capacity of concrete-encased CFST is proposed, with the combined influences of construction preload and sustained service load being taken into account. The feasibility of the developed method is validated against both the test data and the simulation results.

Key Words
concrete-encased CFST; construction preload; sustained service load; numerical analysis; sectional capacity

Address
Gen Li and Luming Shen: 1School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia
Chao Hou: Department of Ocean Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, P. R. China
Lin-Hai Han: Department of Civil Engineering, Tsinghua University, Beijing, 100086, P. R. China

Abstract
The goal of this study is to fill this apparent gap in the area about investigating the effect of porosity distributions on vibrational behavior of FG sectorial plates resting on a two-parameter elastic foundation. The response of the elastic medium is formulated by the Winkler/Pasternak model. The internal pores and graphene platelets (GPLs) are distributed in the matrix either uniformly or non-uniformly according to three different patterns. The model is proposed with material parameters varying in the thickness of plate to achieve graded distributions in both porosity and nanofillers. The elastic modulus of the nanocomposite is obtained by using Halpin-Tsai micromechanics model. The annular sector plate is assumed to be simply supported in the radial edges while any arbitrary boundary conditions are applied to the other two circular edges including simply supported, clamped and free. The 2-D differential quadrature method as an efficient and accurate numerical approach is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and those reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. It is observed that the maximum vibration frequency obtained in the case of symmetric porosity and GPL distribution, while the minimum vibration frequency is obtained using uniform porosity distribution. Results show that for better understanding of mechanical behavior of nanocomposite plates, it is crucial to consider porosities inside the material structure.

Key Words
sectorial plates; vibration; pores and graphene platelets; Halpin-Tsai micromechanics model; elastic foundation

Address
Anqiang Jia: School of Architecture, Tianjin University, Tianjin 300072, China;
Institute of Urban and Rural Construction, Hebei Agricultural University, Baoding, Hebei 071001, China
Haiyan Liu: College of Sciences, Hebei Agricultural University, Baoding, Hebei 071001, China
Lijian Ren and Yingxia Yun: School of Architecture, Tianjin University, Tianjin 300072, China
Vahid Tahouneh: Young Researchers and Elite Club, Islamshahr Branch, Islamic Azad University, Islamshahr, Iran


Abstract
In typical, structural topology optimization plays a significant role to both increase stiffness and save mass of structures in the resulting design. This study contributes to a new numerical approach of topologically optimal design of Mindlin-Reissner plates considering Winkler foundation and mathematical formulations of multi-directional variable thickness of the plate by using multi-materials. While achieving optimal multi-material topologies of the plate with multi-directional variable thickness, the weight information of structures in terms of effective utilization of the material at the appropriate thickness location may be provided for engineers and designers of structures. Besides, numerical techniques of the well-established mixed interpolation of tensorial components 4 element (MITC4) is utilized to overcome a well-known shear locking problem occurring to thin plate models. The well-founded mathematical formulation of topology optimization problem with variable thickness Mindlin-Reissner plate structures by using multiple materials is derived in detail as one of main achievements of this article. Numerical examples verify that variable thickness Mindlin-Reissner plates on Winkler foundation have a significant effect on topologically optimal multi-material design results.

Key Words
multiphase material topology optimization; Mindlin-Reissner plate theory; variable thickness; mixed interpolation of tensorial components (MITC4); Winkler foundation

Address
Thanh T. Banh, Xuan Q. Nguyen and Dongkyu Lee: Department of Architectural Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 05006, Republic of Korea
Michael Herrmann: Department of Civil and Environmental Engineering, University of California, Berkeley, CA 94720 United States of America
Structure GmbH, 70176 Stuttgart, Germany
Filip C. Filippou: Department of Civil and Environmental Engineering, University of California, Berkeley, CA 94720 United States of America


Abstract
In the present research, thermo-elastic buckling of small scale functionally graded material (FGM) nano-size plates with clamped edge conditions rested on an elastic substrate exposed to uniformly, linearly and non-linearly temperature distributions has been investigated employing a secant function based refined theory. Material properties of the FGM nano-size plate have exponential gradation across the plate thickness. Using Hamilton\' s rule and non-local elasticity of Eringen, the non-local governing equations have been stablished in the context of refined four-unknown plate theory and then solved via an analytical method which captures clamped boundary conditions. Buckling results are provided to show the effects of different thermal loadings, non-locality, gradient index, shear deformation, aspect and length-to-thickness ratios on critical buckling temperature of clamped exponential graded nano-size plates.

Key Words
thermal buckling; refined theory; exponential graded material; functionally graded material

Address
Mohammed Abdulraoof Abdulrazzaq, Raad M. Fenjan, Ridha A. Ahmed and Nadhim M. Faleh: Al-Mustansiriah University, Engineering Collage P.O. Box 46049, Bab-Muadum, Baghdad 10001, Iraq

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