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CONTENTS
Volume 39, Number 5, June10 2021
 


Abstract
There is not enough mixed finite element method (MFEM) model developed for static and dynamic analysis of functionally graded material (FGM) beams in the literature. The main purpose of this study is to develop a reliable and efficient computational modeling using an efficient functional in MFEM for free vibration and static analysis of FGM composite beams subject to high order shear deformation effects. The modeling of material properties was performed using mixture rule and Mori-Tanaka scheme which are more realistic determination techniques. This method based on the assumption that a two phase composite material consisting of matrix reinforced by spherical particles, randomly distributed in the beam. To explain the displacement components of the shear deformation effects, it was accepted that the shear deformation effects change sinusoidal. Partial differential field equations were obtained with the help of variational methods and then these equations were transformed into a novel functional for FGM beams with the help of Gâteaux differential derivative operator. Thanks to the Gâteaux differential method, the compatibility of the field equations was checked, and the field equations and boundary conditions were reflected to the function. A MFEM model was developed with a total of 10 degrees of freedom to apply the obtained functional. In the numerical applications section, free vibration and flexure problems solutions of FGM composite beams were compared with those predicted by other theories to show the effects of shear deformation, thickness changing and boundary conditions.

Key Words
functionally graded material; finite element method; high order shear deformation beam theory; free vibration

Address
Emrah Madenci: Department of Civil Engineering, Necmettin Erbakan University, 42140 Konya, Turkey

Abstract
There are recently some advances in solving numerically topology optimization problems for large-scaled trusses based on ground structure approach. A disadvantage of this approach is that the final design usually includes many bars, which is difficult to be produced in practice. One of efficient tools is a so-called filter scheme for the ground structure to reduce this difficulty and determine several distinct bars. In detail, this technique is valuable for practical uses because unnecessary bars are filtered out from the ground structure to obtain a well-defined structure during the topology optimization process, while it still guarantees the global equilibrium condition. This process, however, leads to a singular system of equilibrium equations. In this case, the minimization of least squares with Tikhonov regularization is adopted. In this paper, a proposed algorithm in controlling optimal Tikhonov parameter is considered in combination with the filter scheme due to its crucial role in obtaining solution to remove numerical singularity and saving computational time by using sparse matrix, which means that the discrete optimal topology solutions depend on choosing the Tikhonov parameter efficiently. Several numerical examples are investigated to demonstrate the efficiency of the filter parameter control algorithm in terms of the large-scaled optimal topology designs.

Key Words
truss topology optimization; ground structure approach, large-scaled; filter; Tikhonov regularization; iterative parameter-control algorithm

Address
Vi T. Nguyen and Dongkyu Lee: Department of Architectural Engineering, Sejong University, Seoul 05006, Republic of Korea

Abstract
Shear connectors are required to build composite (concrete and steel) beams. They are placed at the interface of concrete and steel to transfer shear and normal forces between two structural components. Such composite beams are sensitive to provide structural integrity when exposed to fire as they loss strength, stiffness, and ductility at elevated temperature. The present study is designed to investigate the shear resistance and the failure modes of the headed stud shear connectors at fire exposure and post-fire exposure. The study includes ordinary concrete and concrete with carbon nanotubes (CNTs) to build composite (concrete-steel) beams with structural steel. Experimental push tests were conducted on composite beams at ambient and elevated temperatures, such as 200, 400 & 600C. Moreover, push tests were performed on the composite beams after being exposed to 200, 400 & 600C. Push test results illustrated the reduction of ultimate shear capacity and stiffness of headed stud shear connectors as the temperature increased. Although similar values of ultimate shear were obtained for the headed stud connectors in both ordinary and CNT concrete, the CNT modified concrete reduced the concrete spalling and cracking compared to ordinary concrete and was observed to be effective at temperatures greater than 400C. All specimens showed a lower shear resistance at fire exposures compared to the corresponding post-fire exposures. Moreover, numerical simulation by Finite Element (FE) analyses were carried out at ambient temperature and at fire conditions. The FE analysis results show a good agreement with the experimental results. In the experimental studies, failure of all specimens occurred due to shear failure of headed stud, which was later validated by FE analyses using ABAQUS.

Key Words
shear; stud connector; steel concrete composite; push test; fire exposure; elevated temperatures

Address
Olivia Mirza and Kathryn Wilkins: School of Computing, Engineering & Mathematics, University of Western Sydney (UWS), Australia
Sukanta Kumer Shill: School of Engineering and Information Technology, the University of New South Wales, Australia;
School of engineering, Deakin University, Waurn ponds, Geelong VIC-3216, Australia
M.G. Rashed: School of Engineering and Information Technology, the University of New South Wales, Australia

Abstract
In this study free vibration analysis of a cracked Goland composite wing is investigated. The wing is modelled as a cantilevered beam based on Euler- Bernoulli equations. Also, composite material is modelled based on lamina fiber-reinforced. Edge crack is modelled by additional boundary conditions and local flexibility matrix in crack location, Castigliano's theorem and energy release rate formulation. Governing differential equations are extracted by Hamilton's principle. Using the separation of variables method, general solution in the normalized form for bending and torsion deflection is achieved then expressions for the cross-sectional rotation, the bending moment, the shear force and the torsional moment for the cantilevered beam are obtained. The cracked beam is modelled by separation of beam into two interconnected intact beams. Free vibration analysis of the beam is performed by applying boundary conditions at the fixed end, the free end, continuity conditions in the crack location of the beam and dynamic stiffness matrix determinant. Also, the effects of various parameters such as length and location of crack and fiber angle on natural frequencies and mode shapes are studied. Modal analysis results illustrate that natural frequencies and mode shapes are affected by depth and location of edge crack and coupling parameter.

Key Words
cracked wing; dynamic stiffness matrix; two interconnected Euler–Bernoulli beams

Address
Ali Reza Torabi: Fracture Research Laboratory, Faculty of New Science and Technologies, University of Tehran, Tehran, Iran
Shahrokh Shams and Mahdi Fatehi-Narab: Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran, P.C:1439957131

Abstract
In this paper the buckling analysis of the nanoplate made of arbitrary bi-directional functionally graded (BDFG) materials with small scale effects are investigated. To study the small-scale effects on buckling load, the Eringen's nonlocal theory is applied. Employing the principle of minimum potential energy, the governing equations are obtained. Generalize differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the buckling load of BDFG nanoplates. These models can degenerate into the classical models if the material length scale parameter is taken to be zero. Comparison between the results of GDQ method and other papers for buckling analysis of a simply supported rectangular nano FGM plate reveals the accuracy of GDQ method. At the end some numerical results are presented to study the effects of material length scale parameter, plate thickness, aspect ratio, Poisson's ratio boundary condition and side to thickness ratio on size dependent Frequency.

Key Words
buckling; bi-directional functionally graded (BDFG); nanoplate; nonlocal theory; size effect

Address
Maryam Emadi, Mohammad Zamani Nejad and Sima Ziaee:Department of Mechanical Engineering, Yasouj University, Yasouj, Iran
Amin Hadi:Cellular and Molecular Research Center, Yasuj University of Medical Sciences, Yasuj, Iran

Abstract
The composite steel reinforced concrete (SRC) columns have been widely used in Structural Engineering due to their good performances. Many studies have been done on the SRC columns' performances, but they focused on the ordinary types with conventional configurations and materials. In this study, nine new types of steel reinforced lightweight aggregate concrete (SRLAC) short columns with cross-shaped (+shaped and X-shaped) steel section were tested under monotonically axial compressive load; the studied parameters included steel section ratio, steel section configuration, ties spacing, lightweight aggregate concrete (LWAC) strength, and longitudinal bars ratio. From the results, it could be found that the specimens with larger ties ratio, concrete strength, longitudinal bars ratio, and steel section ratio achieved great strength and stiffness due to the excellent interaction between the concrete and steel. The well-confined concrete core could strengthen the steel section. The ductility and toughness of the specimens were influenced by the LWAC strength, steel section ratio, and longitudinal bars ratio; in addition, larger ties ratio with smaller LWAC strength led to better ductility and toughness. The load transfer between concrete and steel section largely depends on the LWAC strength, and the ultimate strength of the new types of SRLAC short columns could be approximately predicted, referring to the codes' formulas of ordinary types of steel reinforced concrete (SRC) columns. Among the used codes, the BS-5400-05 led to the most conservative results.

Key Words
lightweight aggregate concrete (LWAC); steel reinforced concrete (SRC) short column; axial behavior; high strength concrete; concrete encased composite (CEC) column; failure mode

Address
Mostafa M. A. Mostafa: Structural Engineering Department, School of Civil Engineering, Chang'an University, Xi'an, China
Civil Engineering Department, Faculty of Engineering, Al–Azhar University, Qena, Egypt
Tao Wu, Xi Liu and Bo Fu: Structural Engineering Department, School of Civil Engineering, Chang'an University, Xi'an, China


Abstract
This study deals with the Lateral-Torsional Buckling (LTB) of a mono-symmetric tapered I-beam, in which the cross-section is varying longitudinally. To obtain the buckling moment, two concentrated bending moments should be applied at the two ends of the structure. This structure is made of Functionally Graded Material (FGM). The Young' s and shear modules change linearly along the longitudinal direction of the beam. It is considered that this tapered beam is laterally restrained continuously, by using torsional springs. Furthermore, two rotational bending springs are employed at the two structural ends. To achieve the buckling moment, Ritz solution method is utilized. The response of critical buckling moment of the beam is obtained by minimizing the total potential energy relation. The lateral and torsional displacement fields of the beam are interpolated by harmonic functions. These functions satisfy the boundary conditions. Two different support conditions are considered in this study. The obtained formulation is validated by solving benchmark problems. Moreover, some numerical studies are implemented to show the accuracy, efficiency and high performance of the proposed formulation.

Key Words
Lateral-torsional buckling; tapered member; mono-symmetric I-beam; FGM; Ritz solution

Address
Mohammad Rezaiee-Pajand, Amir R. Masoodi and Ali Alepaighambar: Department of Civil Engineering, Ferdowsi University of Mashhad, Iran

Abstract
The main purpose of the present work was to study the dynamic instability of a three-layered, thick composite sandwich beam with the functionally graded (FG) flexible core subjected to an axial compressive follower force. Flutter instability of a sandwich cantilever beam was analyzed using the high-order theory of sandwich beams, for the first time. The governing equations in general for sandwich beams with an FG core were extracted and could be used for all types of sandwich beams with any types of face sheets and cores. A polynomial function is considered for the vertical distribution of the displacement field in the core layer along the thickness, based on the results of the first Frosting's higher order model. The governing partial differential equations and the equations of boundary conditions of the dynamic system are derived using Hamilton's principle. By applying the boundary conditions and numerical solution methods of squares quadrature, the beam flutter phenomenon is studied. In addition, the effects of different geometrical and material parameters on the flutter threshold were investigated. The results showed that the responses of the dynamic instability of the system were influenced by the follower force, the coefficients of FGs and the geometrical parameters like the core thickness. Comparison of the present results with the published results in the literature for the special case confirmed the accuracy of the proposed theory. The results showed that the follower force of the flutter phenomenon threshold for long beams tends to the corresponding results in the Timoshenko beam.

Key Words
flutter analysis; follower force; FGM core; cantilever beam; GDQ numerical method

Address
Fahimeh Rashed Saghavaz and GHolamhassan Payganeh: Department of Mechanical Engineering, Shahid Rajaee Teacher Training University (SRTTU), Tehran, Iran
Keramat Malekzadeh Fard: Aerospace research institute, Malekashtar university of Technology, Tehran, Iran

Abstract
The aim of this work is to study the hygro-thermo-mechanical bending responses of simply supported FG plate resting on a Winkler-Pasternak elastic foundation. The effect transverse shear strains is taken into account in which the zero transverse shear stress condition on the top and bottom surfaces of the plate is ensured without using any shear correction factors. The developed model contains only four unknowns variable which is reduced compared to other HSDTs models. The material properties of FG-plate are supposed to vary across the thickness of the plate according to power-law mixture. The differential governing equations are derived based on the virtual working principle. Numerical outcomes of bending analysis of FG plates under hygro-thermo-mechanical loads are performed and compared with those available in the literature. The effects of the temperature, moisture concentration, elastic foundation parameters, shear deformation, geometrical parameters, and power-law-index on the dimensionless deflections, axial and transverse shear stresses of the FG-plate are presented and discussed.

Key Words
FG plates; Winkler–Pasternak foundations; shear and normal strains; hygrothermal and mechanical response

Address
Bouzid Merazka, Abdelhakim Bouhadra and Abderrahmane Menasria: Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria;
Department of Civil Engineering, Faculty of Science &Technology, Abbes Laghrour University, Khenchela, Algeria
Mahmoud M. Selim: Department of Mathematics, Al-Aflaj College of Science and Humanities, Prince Sattam bin Abdulaziz University,
Al-Aflaj 710-11912 Saudi Arabia
Abdelmoumen Anis Bousahla: Laboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbés, Algeria
Fouad Bourada: Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria;
Département des Sciences et de la Technologie, université de Tissemsilt, BP 38004 Ben Hamouda, Algérie
Abdeldjebbar Tounsi and Kouider Halim Benrahou: Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
Abdelouahed Tounsi: Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria;
YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea;
Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran,
Eastern Province, Saudi Arabia
Mesfer Mohammad Al-Zahrani: Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran,
Eastern Province, Saudi Arabia







Abstract
There is a growing need of seismic retrofit of existing non-seismically designed structures in Korea after the 2016 Gyeongju and 2017 Pohang earthquakes, especially school buildings which experienced extensive damage during those two earthquakes. To this end, a steel multi-slit damper (MSD) was developed in this research which can be installed inside of partition walls of school buildings. Full-scale two-story RC frames were tested with and without the proposed dampers. The frames had structural details similar to school buildings constructed in the 1980s in Korea. The details of the experiments were described in detail, and the test results were validated using the analysis model. The developed seismic retrofit strategy was applied to a case study school building structure, and its seismic performance was evaluated before and after retrofit using the MSD. The results show that the developed retrofit strategy can improve the seismic performance of the structure to satisfy a given target performance level.

Key Words
seismic retrofit; slit dampers; energy dissipation; seismic performance; hysteretic damper

Address
Mohammad Mahdi Javidan, Mohammad Seddiq Eskandari Nasab and Jinkoo Kim: Department of Civil & Architectural Engineering, Sungkyunkwan University, Suwon, Republic of Korea


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