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CONTENTS
Volume 81, Number 3, February10 2022
 


Abstract
Based upon differential quadrature method (DQM) and nonlocal strain gradient theory (NSGT), an investigation on the free vibrations of 2D plate systems with nano-dimensions has been provided taking into account the effects of different mechanical loadings. In order to capture different mechanical loadings, a general form of variable compressive load applied in the axial direction of the plate system has been introduced. The studied plate has been constructed from two types of particles which results in graded material properties and nanoscale pores. The established formulation for the plate is in the context of a novel shear deformable model and the equations have been solved via a semi-numerical trend. Presented results indicate the prominence of material composition, nonlocal coefficient, strain gradient coefficient and boundary conditions on vibrational frequencies of nano-size plate.

Key Words
2D plate model; compressive loads; differential quadrature method; free vibration; nonlocal effect

Address
Li Rao, Chao Lin and Chenglin Zhang: Physical Science and Technology College, Yichun University, Yichun 33600, Jiangxi, China

Abstract
Multiscale structure has attracted significant interest due to its high stiffness/strength to weight ratios and multifunctional performance. However, most of the existing concurrent topology optimization works are carried out under deterministic load conditions. Hence, this paper proposes a robust concurrent topology optimization method based on the bidirectional evolutionary structural optimization (BESO) method for the design of structures composed of periodic microstructures subjected to uncertain dynamic loads. The robust objective function is defined as the weighted sum of the mean and standard deviation of the module of dynamic structural compliance with constraints are imposed to both macro- and microscale structure volume fractions. The polynomial chaos expansion (PCE) method is used to quantify and propagate load uncertainty to evaluate the objective function. The effective properties of microstructure is evaluated by the numerical homogenization method. To release the computation burden, the decoupled sensitivity analysis method is proposed for microscale design variables. The proposed method is a non-intrusive method, and it can be conveniently extended to many topology optimization problems with other distributions. Several numerical examples are used to validate the effectiveness of the proposed robust concurrent topology optimization method.

Key Words
bi-directional evolutionary structural optimization method; homogenization method; load uncertainty; polynomial chaos expansion method; robust concurrent topology optimization

Address
Jinhu Cai: School of Mechanical Engineering and Automation, Beihang University, Beijing 100083, China
Zhijie Yang: State Key Laboratory of Virtual Reality and Systems, Beihang University, Beijing 100083, China
Chunjie Wang: School of Mechanical Engineering and Automation, Beihang University, Beijing 100083, China; State Key Laboratory of Virtual Reality and Systems, Beihang University, Beijing 100083, China
Jianzhong Ding: School of Mechanical Engineering and Automation, Beihang University, Beijing 100083, China

Abstract
This study aimed to analyze the dynamic punching shear performance of slab-column joints under cyclic loads with the use of double-hooked end (5D) steel fibers. Structural systems such as slab-column joints are widely found in infrastructures. The susceptibility to collapse of such structures when submitted to seismic loads is highly dependent on the structural performance of the slab-column connections. For this reason, the punching capacity of reinforced concrete (RC) structures has been the subject of a great number of studies. Steel fibers are used to achieve a certain degree of ductility under seismic loads. In this context, 5D steel hooked fibers provide high levels of fiber anchoring, tensile strength and ductility. However, only limited research has been carried out on the performance under cyclic loads of concrete structural members containing steel fibers. This study covers this gap with experimental testing of five different full-scale subassemblies of RC slab-column joints: one without punching reinforcement, one with conventional punching reinforcement and three with 5D steel fibers. The subassemblies were tested under cyclic loading, which consisted of applying increasing lateral displacement cycles, such as in seismic situations, with a constant axial load on the column. This set of cycles was repeated for increasing axial loads on the column until failure. The results showed that 5D steel fiber subassemblies: i) had a greater capacity to dissipate energy, ii) improved punching shear strength and stiffness degradation under cyclic loads; and iii) increased cyclic loading capacity.

Key Words
5D steel fiber; cyclic load; double hooked end steel fiber; dynamic punching; slab-column joint; steel fiber reinforced concrete

Address
Yezid A. Alvarado: Pontificia Universidad Javeriana, Calle 40 # 5-50 Ed. José Gabriel Maldonado, Bogotá, Colombia
Benjamin Torres: Department of Civil Engineering, University of Alicante, San Vicente del Raspeig, Ap. 99, 03080, Spain
Manuel Buitrago: ICITECH, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
Daniel M. Ruiz, Sergio Y. Torres, Ramon A. Alvarez: Pontificia Universidad Javeriana, Calle 40 # 5-50 Ed. José Gabriel Maldonado, Bogotá, Colombia

Abstract
As infrastructure ages and traffic load increases, serious public concerns have arisen for the well-being of bridges. The current health monitoring practice focuses on large-scale bridges rather than short span bridges. However, it is critical that more attention should be given to these behind-the-scene bridges. The relevant information about the construction methods and as-built properties are most likely missing. Additionally, since the condition of a bridge has unavoidably changed during service, due to weathering and deterioration, the material properties and boundary conditions would also have changed since its construction. Therefore, it is not appropriate to continue using the design values of the bridge parameters when undertaking any analysis to evaluate bridge performance. It is imperative to update the model, using finite element (FE) analysis to reflect the current structural condition. In this study, a FE model is established to simulate a concrete culvert bridge in New South Wales, Australia. That model, however, contains a number of parameter uncertainties that would compromise the accuracy of analytical results. The model is therefore updated with a neural network (NN) optimisation algorithm incorporating Monte Carlo (MC) simulation to minimise the uncertainties in parameters. The modal frequency and strain responses produced by the updated FE model are compared with the frequency and strain values on-site measured by sensors. The outcome indicates that the NN model updating incorporating MC simulation is a feasible and robust optimisation method for updating numerical models so as to minimise the difference between numerical models and their real-world counterparts.

Key Words
finite element model updating; neural network optimization; short span bridge; unidentified construction method

Address
S.T.K. Lin, Y. Lu: Department of Civil Engineering, Monash University, Melbourne, VIC, Australia
M.M. Alamdari: School of Civil and Environmental Engineering, University of New South Wales, Sydney, NSW, Australia
N.L.D. Khoa: Data61, Commonwealth Scientific and Industrial Research Organisation (CSIRO), Sydney, NSW, Australia

Abstract
Externally bonded ultrahigh performance fiber-reinforced concrete (UHPFRC) is commonly used as a strengthening material for reinforced concrete (RC) structures. This study reports the results of an experimental program investigating the bonding behavior between concrete and prefabricated UHPFRC plates. The overall experimental program is consisting of five RC specimens, which are strengthened using the different lengths and widths of prefabricated UHPFRC plates. These specimens were analyzed using the pull-pull double-shear test. The performance of each strengthened specimen is presented, discussed and compared in terms of failure mode, maximum load, load-slip relationship, fracture energy and strain distribution. Specimen C-25-160-300 which bonded along the whole width of 160 mm recorded the highest maximum load (109.2 kN) among all the analysed specimens. Moreover, a 3D numerical finite element model (FEM) is proposed to simulate the bond behavior between concrete and UHPFRC plates. Moreover, this study reviews the analytical models that can predict the relationship between the maximum bond stress and slip for strengthened concrete elements. The proposed FEM is verified against the experimental program and then used to test 36 RC specimens strengthened with prefabricated UHPFRC plates with different concrete grades and UHPFRC plate widths. The obtained results together with the review of analytical models helped in the formation of a design equation for estimating the bond stress between concrete and prefabricated UHPFRC plates.

Key Words
bond stress-slip model; concrete; de-bonding, interface; finite element model (FEM); prefabricated plates; ultrahigh performance fiber-reinforced concrete (UHPFRC)

Address
Walid Mansour: Civil Engineering Department, Faculty of Engineering, Kafrelsheikh University, Box 33511, Kafrelsheikh, Egypt
Mohammed A. Sakr: Department of Structural Engineering, Tanta University, Tanta, Egypt
Ayman A. Seleemah: Department of Structural Engineering, Tanta University, Tanta, Egypt
Bassam A. Tayeh: Department of Civil Engineering Department, Faculty of Engineering, Islamic University of Gaza, Palestine
Tarek M. Khalifa: Department of Structural Engineering, Tanta University, Tanta, Egypt

Abstract
Visco-Plastic Damper (VPD) as a passive energy dissipation device with dual behavior has been recently numerically studied. It consists of two bent steel plates and segments with a viscoelastic solid material in between, combining and improving characteristics of both displacement-dependent and velocity-dependent devices. In order to trust the performance of VPD, for the 1st time this paper experimentally investigates prototype damper behavior under a wide range of frequency and amplitude of dynamic loading. A high-axial damping rubber is innovatively proposed as the viscoelastic layer designed to withstand large axial strains and dissipate energy accordingly. Test results confirmed all assumptions about VPD. The behavior of VPD subjected to low levels of excitation is elastic while with increasing levels of excitation, a significant source of energy dissipation is provided through the yielding of the steel elements in addition to the viscoelastic energy dissipation. The results showed energy dissipation of 99.35 kN.m under a dynamic displacement with 14.095 mm amplitude and 0.333 Hz frequency. Lateral displacement at the middle of the device was created with an amplification factor obtained ranging from 2.108 to 3.242 in the rubber block. Therefore, the energy dissipation of viscoelastic material of VPD was calculated 18.6 times that of the ordinary viscoelastic damper.

Key Words
equivalent viscous damping ratio; finite element analysis; metallic yielding devices; passive control devices; viscoelastic damper

Address
Ahmad Modhej: Department of Civil Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
Seyed Mehdi Zahrai: School of Civil Engineering, College of Engineering, University of Tehran, P.O. Box 11155-4563, Iran; Civil Engineering Department, University of Ottawa, Canada

Abstract
It is well known that after finding the displacement in the structural mechanics, strain and stress can be obtained in the straight-forward process. The main purpose of this paper is to unify the displacement functions for solving the solid body. By performing mathematical operations, three sets of these key relationships are found in this paper. All of them are written in the Cartesian Coordinates and in terms of a simple function. Both analytical and numerical approaches are utilized to validate the correctness of the presented formulations. Since all required conditions for the bodies with self-equilibrated loadings are satisfied accurately, the authors' relations can solve these kinds of problems. This fact is studied in-depth by solving some numerical examples. It is found that a very simple function can be used for each formulation instead of ten different and complex displacement potentials defined by previous studies.

Key Words
Beltrami-Michell equations; Beltrami's stress tensor; displacement potentials; Maxwell stress functions; Morera stress functions

Address
Mohammad Rezaiee-Pajand: Department of Civil Engineering, Ferdowsi University of Mashhad, Iran
Arash Karimipour: Department of Civil Engineering, Member of Center for Transportation Infrastructure System (CTIS),
University of Texas at El Paso (UTEP), USA

Abstract
Steel fibre-reinforced concrete (SFRC) is an emerging class of composite for construction. However, a reliable method to assess the flexural behaviour of SFRC structural member is in lack. An analytical technique is proposed for determining the moment-curvature response of concrete beams reinforced with steel fibres and longitudinal bars (R/SFRC members). The behaviour of the tensile zone of such members is highly complex due to the interaction between the residual (tension softening) stresses of SFRC and the tension stiffening stresses. The current study suggests a transparent and mechanically sound method to combine these two stress concepts. Tension stiffening is modelled by the reinforcement-related approach assuming that the corresponding stresses act in the area of tensile reinforcement. The effect is quantified based on the analogy between the R/SFRC member and the equivalent RC member having identical geometry and materials except fibres. It is assumed that the resultant tension stiffening force for the R/SFRC member can be calculated as for the equivalent RC member providing that the reinforcement strain in the cracked section of these members is the same. The resultant tension stiffening force can be defined from the moment-curvature relation of the equivalent RC member using an inverse technique. The residual stress is calculated using an existing model that eliminates the need for dedicated mechanical testing. The proposed analytical technique was validated against test data of R/SFRC beams and slabs.

Key Words
deformation; moment-curvature; steel fibre-reinforced concrete; tension stiffening

Address
Gintaris Kaklauskas: Department of Reinforced Concrete Structures and Geotechnics, Vilnius Gediminas Technical University, Sauletekio av. 11, 10223 Vilnius, Lithuania
Aleksandr Sokolov: Laboratory of Innovative Building Structures, Vilnius Gediminas Technical University, Sauletekio av. 11, 10223 Vilnius, Lithuania
Ashkan Shakeri: Department of Reinforced Concrete Structures and Geotechnics, Vilnius Gediminas Technical University, Sauletekio av. 11, 10223 Vilnius, Lithuania
Pui-Lam Ng: Institute of Building Materials, Vilnius Gediminas Technical University, Linkmenų g. 28, 08217 Vilnius, Lithuania; Department of Civil Engineering, The University of Hong Kong, Pokfulan 999077 Hong Kong, China
Joaquim A.O. Barros: Institute for Sustainability and Innovation in Structural Engineering, University of Minho, Campus de Azurém 4800-058 Guimarães, Portugal; Institute of Science and Innovation for Bio-Sustainability, University of Minho, Campus de Azurém 4804-533 Guimarães, Portugal

Abstract
In this study, combined size and shape optimization of spatial truss tower structures are presented by using new optimization algorithms named Rao-1, and Rao-2. The nodal displacements, allowable stress and buckling for compressive members are taken into account as structural constraints for truss towers. The discrete and continuous design variables are used as design variables for size and shape optimization. To show the efficiency of the proposed optimization algorithm, 25-bar, and 39-bar 3D truss towers are solved for combined size and shape optimization. The 72-bar, and 160-bar 3D truss towers are solved only by size optimization. The optimal results obtained from this study are compared to those given in the literature to illustrate the efficiency and robustness of the proposed algorithm. The structural analysis and the optimization process are coded in MATLAB programming.

Key Words
allowable stress; buckling; Rao algorithms; size and shape optimization; tower structures

Address
Maksym Grzywiński: Faculty of Civil Engineering, Czestochowa University of Technology, 42-200 Czestochowa, Poland

Abstract
Shallow footings usually belonged to the category of thick plate structures. For accurate analysis of thick plates, the contribution of out-of-plane components of the stress tensor should be considered in the formulation. Most of the available shallow footing models are based on the classical plate theories, which usually neglect the effects of the out-of-plane stresses. In this study, a mixed-field plate finite element model (FEM) is developed for the analysis of shallow footings rested on soil foundations. In addition to displacement field variables, the out-of-plane components of the stress tensor are also assumed as a priori unknown variables. For modeling the interaction effect of the soil under and outside of the shallow footings, the modified Vlasov theory is used. The tensionless nature of the supporting soil foundation is taken into account by adopting an incremental, iterative procedure. The equality requirement of displacements at the interface between the shallow footing and soil is fulfilled using the penalty approach. For validation of the present mixed FEM, the obtained results are compared with the results of 3D FEM and previous results published in the literature. The comparisons show the present mixed FEM is an efficient and accurate tool for solving the problems of shallow footings rested on subsoil.

Key Words
mixed finite element; out-of-plane stresses; tensionless foundation; Vlasov model

Address
M. Lezgy-Nazargah: Department of Civil Engineering, Faculty of Engineering, Hakim Sabzevari University, Sabzevar 9617976487-397, Iran
A. Mamazizi: Department of Civil Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj 66177-15175, Iran
H. Khosravi: Department of Civil Engineering, Faculty of Engineering, Hakim Sabzevari University, Sabzevar 9617976487-397, Iran


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