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Abstract
In this paper, a multi-objective optimization of mixed convection air-cooling of two identical discrete heat sources mounted in an inclined channel is conducted to obtain the optimal design parameters, using Response Surface Methodology (RSM) and desirability function approach. Reynolds number (Re), inclination of the channel (r) and the width of the discrete heat source (b) are selected as the input parameters. The computational simulations are done for different Reynolds numbers (25-Re-250), inclination angles of the channel (0o-r-360o) and the width of the heat source (5-b-10 mm). A central composite design (CCD), which comes under the RSM approach, with design parameters was used for analysis of variance (ANOVA). A second-order regression models were developed to correlate the design parameters (Re, r and b) with mean Nusselt number (Nu) and maximum temperature (TMax). The optimum values of design parameters produce the lowest value of maximum temperature (TMax) with a higher mean Nusselt number (Nu) are Reynolds number (Re)=209.94, inclination angle of the channel (r)=330o and heat source width (b)=5.13 mm.

Key Words
air cooling; heat sources; mixed convection; multi-objective optimization; numerical simulation; RSM

Address
Moumtez Bensouici: Department of Science and Technology, Institute of Sciences and Technology, University Center of Mila, Mila 43000, Algeria; Laboratory of Applied Energetics and Pollution (LAEP), University of Constantine 1, Road of Ain El. Bey, Constantine 25000, Algeria Mohamed Walid Azizi: Department of Science and Technology, Institute of Sciences and Technology, University Center of Mila, Mila 43000, Algeria; Advanced Technologies in Mechanical Production Research Laboratory (LRTAPM), BadjiMokhtar - Annaba University, P.O Box 12, 23000 Annaba, Algeria Fatima Zohra Bensouici: Faculty of Pharmaceutical Process Engineering, University of Constantine 3, UVN05, Ali Mendjeli N V, Khroub, Constantine 25000, Algeria

Abstract
This study presents an optimal topology material distribution method in the framework of minimum compliance with a constraint on the total amount of multi-material using constant strain triangle (CST) elements and Moved and Regularized Heaviside Function (MRHF) filters. The sensitivity formulations for objective function and sensitivity for structures are derived in terms of multiphase design variables through triangle elements. Mathematical formulations of topology optimization problem solving the minimum compliance by using multiple materials are an alternating active-phase algorithm with a Gauss-Seidel version as an optimization model of optimality criteria. Moreover, MRHF that has the role of a filter in multiple materials is considered to produce obvious material distributions and improve the convergence of objective values. Some optimal topology results under the influence of rmin and filter are also investigated and verify the CST element-based multi-material topology optimization is appropriate to the use of MRHF and produces reasonable optimal results.

Key Words
constant strain triangle element (CST); finite element method; moved and regularized Heaviside function filter (MRHF); multiple materials; topology optimization

Address
Xuan Q. Nguyen, Thanh T. Banh and Dongkyu Lee: Department of Architectural Engineering, Sejong University, Seoul 05006, Republic of Korea

Abstract
The optimization conditions of the embedded nanocomposite multi-layer beams reinforced by ZnO nanoparticles are evaluated using a sinusoidal shear deformation theory. The adaptive improved harmony search (AIHS) optimization method is used as optimizer. Based on numerical method of differential quadrature, the buckling load is obtained. The optimum designs for nanocomposite reinforced sinusoidal multi-layer beams are evaluated using proposed AIHS based on the axial forces, applied voltage, volume fraction of ZnO nanoparticles, boundary conditions and geometrical parameters. The results demonstrated that optimum design conditions for a nanocomposite multi-layer beam under 50 GPa buckling constraint force are obtained as the length and thickness of multi-layer beam are 3.3326 m and 29.1125 cm. The applied voltage is the effective variables on the buckling of nanocomposite multi-layer beams.

Key Words
adaptive improved harmony search; optimization nanocomposite multi-layer beam; sinusoidal theory; ZnO nanoparticles

Address
Bin Wang: Civil Engineering and Transportation Engineering, Yellow River Conservancy Technical Institute, Kaifeng 475004, Henan, China Gongxing Yan: Scientific Research and Technical Service Office, Chongqing Vocational Institute of Engineering, Chongqing 402260, China Seyedmahmoodreza Allahyari: Department of Mechanical Engineering, Dariun Branch, Islamic Azad University, Dariun, Iran

Abstract
The current investigation deals with assessing the search performance of a recently developed, parameter-free, and self-adaptive search algorithm so-called Interactive Fuzzy Search Algorithm (IFSA) in solving weight minimization of the constrained structural optimization problems with discrete variables. The proposed IFSA combines the navigation pattern of the Interactive Search Algorithm (ISA) with the decision-making competence of fuzzy reasoning. The fuzzy module of the proposed IFSA permanently monitors the search process and adjusts each agent's search behavior by considering the governing condition of the current problem. In structural optimization, due to construction limitations, it is more realistic to select the sizing variables from a discrete domain. Thus, in this study, to empirically evaluate the search capability of the IFSA, it is applied to solve a suite of structural optimization problems with the discrete design variables. The attained outcomes are compared with the ISA and some other related methods addressed in the relevant literature. The acquired accuracy level and demanded number of objective function evaluations indicates that the IFSA, comparatively, using lower computational cost could found lighter structural systems. Also, the comparison of the attained standard deviation values shows that the IFSA demonstrates higher stability during the optimization process. These superior outcomes designate that the fuzzy decision-making mechanism of the IFSA could work properly in dynamically adapting the search behavior of the algorithm with the governing condition of the current problem. Consequently, the promising gained results reveal that IFSA can effectively be applied in solving the structural optimization problems with discrete search domains.

Key Words
fuzzy logic; hybrid methods; metaheuristic methods; structural optimization

Address
Ali Mortazavi: Graduate School of Natural and Applied Science, Ege University, Izmir, Turkey

Abstract
The frequency-based method is the most commonly used method for measuring cable tension. However, the calculation formulas for the conventional frequency-based method are generally based on the ideally hinged or fixed boundary conditions without a comprehensive consideration of the inclination angle, sag-extensibility, and flexural stiffness of cables, leading to a significant error in cable tension identification. This study aimed to propose a frequency-based method of cable tension identification considering the complex boundary conditions at the two ends of cables using the particle swarm optimization (PSO) algorithm. First, the refined stay cable model was established considering the inclination angle, flexural stiffness, and sag-extensibility, as well as the rotational constraint stiffness and lateral support stiffness for the unknown boundaries of cables. The vibration mode equation of the stay cable model was discretized and solved using the finite difference method. Then, a multiparameter identification method based on the PSO algorithm was proposed. This method was able to identify the tension, flexural stiffness, axial stiffness, boundary rotational constraint stiffness, and boundary lateral support stiffness according to the measured multiorder frequencies in a synchronous manner. The feasibility and accuracy of this method were validated through numerical cases. Finally, the proposed approach was applied to the tension identification of the anchor span strands of a suspension bridge (Jindong Bridge) in China. The results of cable tension identification using the proposed method and the existing methods discussed in previous studies were compared with the on-site pressure ring measurement results. The comparison showed that the proposed approach had a high accuracy in cable tension identification. Moreover, the synchronous identification of the flexural stiffness, axial stiffness, boundary rotational constraint stiffness, and boundary lateral support stiffness was highly beneficial in improving the results of cable tension identification.

Key Words
boundary constraint stiffness; cable tension; finite difference method; frequency-based method; multiparameter identification; particle swarm optimization algorithm

Address
Wen-ming Zhang, Zhi-wei Wang, Dan-dian Feng and Zhao Liu: The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University, Nanjing 211189, China

Abstract
In this paper, the porosity distribution of functionally graded porous (FGP) beams are optimized using the genetic algorithm to achieve the maximum ratio of the normalized buckling load to the beam's weight. The analytical forms for critical buckling loads of the FGP beams under different end conditions are determined analytically using principle virtual work based on the Euler and Timoshenko beam theories. The effects of Nano Graphene Platelets (NGPs) on the critical buckling load of the nanocomposite FGP beams are also taken into account. The sensitivity analyses show that porosity will reduce the buckling load-to-weight ratio of porous beams to conventional beams in some cases. Based on the optimization results, the optimum distribution of the porosity and NGPs' volume fraction are proposed for several porosity coefficients. The obtained results indicate that the optimum distribution for porosity has a symmetric sandwich-like shape while the optimum distribution for NGPs' volume fraction is uniform.

Key Words
buckling strength; functionally graded porous beams; nanographene plate reinforcement; optimization; porosity distribution

Address
Mojtaba Farrokh and Mohammad Taheripur: Advanced Structures Research Lab., K. N. Toosi University of Technology, P.O. Box 16765-3381, Tehran, Iran

Abstract
Shell bridges have attracted extensive interest in engineering research and practice. This paper aims to evaluate the effects of longitudinal and transverse curvatures on the optimal design of the shell bridge. For this purpose, a slant-legged steel shell footbridge with the same initial and target volumes of steel was chosen to build parametric geometric models with different curvature radii, and then topology optimization was carried out using the bi-directional evolutionary structural optimization (BESO) technique to obtain optimized designs with high structural stiffness. Furthermore, linear static analysis and eigenvalue analysis demonstrate that the displacement, von Mises effective stress, and the first-order vertical vibration frequency satisfied all the requirements of design regulations. Numerical results indicate that not only the longitudinal curvature but also the transverse curvature have a significant effect on the optimized designs of steel shell footbridge. While the mean compliance increased with the transverse curvature radius, it first decreased and then increased with the longitudinal curvature radius.

Key Words
BESO method; curvature radius; optimal design; shell bridge; steel shell; topology optimization

Address
Shiming Liu: School of Civil Engineering and Communication, North China University of Water Resources and Electric Power, Zhengzhou 450045, China; Centre for Innovative Structures and Materials, School of Engineering, RMIT University, Melbourne 3001, Australia; International Joint Research Lab for Eco-building Materials and Engineering of Henan Province, North China University of Water Resources and Electric Power, Zhengzhou 450045, China Bin Huang: School of Civil Engineering and Communication, North China University of Water Resources and Electric Power, Zhengzhou 450045, China Yi Min Xie: Centre for Innovative Structures and Materials, School of Engineering, RMIT University, Melbourne 3001, Australia

Abstract
This study presents topology optimization of plate structures by employing isogeometrical level set method. For structural analysis of plates, the IsoGeometric Analysis (IGA) approach is applied and Non-Uniform Rational B-Splines (NURBS) basis functions are used for approximation of the design domain geometry as well as the unknown deformation field. In this paper, the level set function is parametrized with Radial Basis Functions (RBFs), which is more efficient than the conventional level set method. This approach along with an approximate re-initialization scheme can maintain a smooth level set function during the optimization process and has less dependency on initial designs because of its ability to nucleate new holes inside the design domain. Due to capability of IGA method in modeling complex design domains while maintaining high accuracy in analysis, combination of IGA with RBFs level set method provides a very useful and effective technique for topology optimization problems. Several numerical examples are prepared to demonstrate the efficiency and accuracy of the method and obtained optimum topologies are compared with the results of other methods in literature.

Key Words
isogeometric analysis; level set method; radial basis functions; topology optimization of plates

Address
A. Halaku and S.M. Tavakkoli: Civil Engineering Department, Shahrood University of Technology, Shahrood, Iran

Abstract
In this work, the optimization of the effective parameters on the thermal buckling of a square composite plate with various stacking sequence containing quasi- triangular cutout in the center using particle swarm optimization (PSO) to achieve the maximum resistance of plate against thermal buckling load is done. It is assumed that the plate is under a uniform temperature distribution. The stability equations are based on the first order shear deformation theory. The thermal buckling analysis and the PSO algorithm are performed using the code developed in MATLAB software. In this study, the design variables are: fiber angle, bluntness of cutout corners, cutout orientation, and cutout size to plate size ratio, which are determined by using the PSO algorithm to optimize the parameters for the highest critical buckling temperature. The results showed that the plate with a quasi-triangular cutout has more resistance to thermal buckling than the plate with a circular cutout. It was also found that the thermal buckling of a composite plate is dependent on various parameters and the maximum thermal buckling load can be achieved by the appropriate selection of these parameters.

Key Words
composite plates; critical buckling temperature; finite element method; particle swarm optimization; quasitriangular cutout

Address
S. Mahdavi, A.R. Shaterzadeh and M. Jafari: Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology, Shahrood, Iran

Abstract
A method to minimize the economic cost of the structural design of spatial reinforced concrete (RC) frame structures is presented. SAP2000 is used as computational engine, taking into account modelling aspects such as static soilstructure interaction (SSSI). The optimization problem is formulated to properly reflect an actual design problem, limiting e.g., the size of reinforcement bars to commercially available sections. The resulting discrete optimization problem is solved by using Biogeography-Based Optimization (BBO), an evolutionary algorithm selected for its convergence properties. Strategies to reduce the computational cost of the optimization procedure are proposed and an extensive tuning of the parameters of the BBO algorithm is performed, using a novel utility metric, evaluated for models of six simple RC frame structures. The parameters to deal with more complex structures are selected based on the use of utility landscapes. The resulting tuned optimization algorithm allows to reduce the direct cost of the construction of a particular structure project with 21% (15% when SSSI is not taken into account), compared to a design based on traditional criteria. The effect of considering SSSI on the cost of the superstructure is also evaluated, showing that this is an aspect that should not be neglected during modeling.

Key Words
Biogeography-Based optimization; evolutionary algorithm; parameter tuning; reinforcement concrete structures; static soil-structure interaction; structural optimization

Address
Iván A. Negrin: Department of Civil Engineering, Faculty of Construction, Marta Abreu Central University, Santa Clara, Cuba Dirk Roose: Department of Computer Science, KU Leuven, Belgium Ernesto L. Chagoyén: Department of Civil Engineering, Faculty of Construction, Marta Abreu Central University, Santa Clara, Cuba Geert Lombaert: Department of Civil Engineering, KU Leuven, Belgium

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