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Abstract
To minimize the compliance of frame, a method to optimize the topology of bracing system in a frame is presented. The frame is first filled uniformly with a truss-like continuum, in which there are an infinite number of members. The frame and truss-like continuum are analysed by the finite element method altogether. By optimizing the distribution of members in the truss-like continuum over the whole design domain, the optimal bracing pattern is determined. As a result, the frame\'s lateral stiffness is enforced. Structural compliance and displacement are decreased greatly with a smaller increase in material volume. Since optimal bracing systems are described by the distribution field of members, rather than by elements, fewer elements are needed to establish the detailed structure. Furthermore, no numerical instability exists. Therefore it has high calculation effectiveness.

Key Words
topology optimization; compliance; bracing systems; truss-like continuum; lateral stiffness

Address
Kemin Zhou: College of Civil Engineering, Huaqiao University, Fujian, 361021, China

Abstract
An optimization method of patch shape was developed in this study, in order to improve repair of cracked plates. It aimed to minimize three objectives: stress intensity factor, patch volume and shear stresses in the adhesive film. The choice of these objectives ensures improving crack repair, gaining mass and enhancing the adhesion durability between the fractured plate and the composite patch. This was a multi-objective optimization combined with Finite elements calculations to find out the best distribution of patch height with respect to its width. The implementation of the method identified families of optimal shapes with specific geometric features around the crack tip and at the horizontal end of the patch. Considerable mass gain was achieved while improving the repair efficiency and keeping the adhesive shear stress at low levels.

Key Words
patch repair; stress intensity factor; adhesive shear; finite elements method; shape optimization

Address
Mohamed S. Bouchiba and Boualem Serier: Department of Mechanical Engineering, University of Sidi Bel Abbes, BP89 cite Arbi Ben M\'Hidi, Sidi Bel Abbes 22 000, Algeria

Abstract
In this paper, the recently developed meta-heuristic algorithm called tug of war optimization is applied to optimal design of castellated beams. Two common types of laterally supported castellated beams are considered as design problems: beams with hexagonal openings and beams with circular openings. Here, castellated beams have been studied for two cases: beams without filled holes and beams with end-filled holes. Also, tug of war optimization algorithm is utilized for obtaining the solution of these design problems. For this purpose, the minimum cost is taken as the objective function, and some benchmark problems are solved from literature.

Key Words
meta-heuristic algorithm; tug of war optimization; optimal design; hexagonal opening; cellular opening

Address
A. Kaveh and F. Shokohi: Centre of Excellence for Fundamental Studies in Structural Engineering, Iran University of Science and Technology, Narmak, Tehran, P.O. Box 16846-13114, Iran

Abstract
In this paper an efficient approach is introduced for design and analysis of double-layer grids including both geometrical and material nonlinearities, while the results are compared with those considering material nonlinearity. Optimum design procedure based on Enhanced Colliding Bodies Optimization method (ECBO) is applied to optimal design of two commonly used configurations of doublelayer grids. Two ranges of spans as small and big sizes with certain bays of equal length in two directions are considered for each type of square grids. ECBO algorithm obtains minimum weight grid through appropriate selection of tube sections available in AISC Load and Resistance Factor Design (LRFD). Strength constraints of AISC-LRFD specifications and displacement constraints are imposed on these grids.

Key Words
double-layer grids; nonlinear behavior; incremental nonlinear analysis; collapse; enhanced colliding bodies optimization

Address
A. Kaveh: Center of Excellence For Fundamental Studies in Structural Engineering, School of Civil Engineering, Iran University of Science and Technology, Narmak, Tehran -16, Iran M. Moradveisi: Road, Housing and Urban Development Research Center, Tehran P.O. Box 13145-1696, Iran

Abstract
The present paper focuses on size optimization of double layer barrel vaults considering nonlinear behavior. In order to tackle the optimization problem an improved colliding bodies optimization (ICBO) algorithm is proposed. The important task that should be achieved before optimization of structural systems is to determine the best form having the least cost. In this study, an attempt is done to find the best form then it is optimized considering linear and non-linear behaviors. In the optimization process based on nonlinear behavior, the geometrical and material nonlinearity effects are included. A large-scale double layer barrel vault is presented as the numerical example of this study and the obtained results indicate that the proposed ICBO has better computational performance compared with other algorithms.

Key Words
optimization; double layer barrel vault; nonlinear behavior; meta-heuristic

Address
Saeed Gholizadeh, Changiz Gheyratmand and Hamed Davoudi: Department of Civil Engineering, Urmia University, Urmia, West Azerbaijan Province, Iran

Abstract
Decks, interior beams, edge beams and girders are the parts of a steel floor system. If the deck is optimized without considering beam optimization, finding best result is simple. However, a deck with higher cost may increase the composite action of the beams and decrease the beam cost reducing the total cost. Also different number of floor divisions can improve the total floor cost. Increasing beam capacity by using castellated beams is other efficient method to save the costs. In this study, floor optimization is performed and these three issues are discussed. Floor division number and deck sections are some of the variables. Also for each beam, profile section of the beam, beam cutting depth, cutting angle, spacing between holes and number of filled holes at the ends of castellated beams are other variables. Constraints include the application of stress, stability, deflection and vibration limitations according to the load and resistance factor (LRFD) design. Objective function is the total cost of the floor consisting of the steel profile cost, cutting and welding cost, concrete cost, steel deck cost, shear stud cost and construction costs. Optimization is performed by enhanced colliding body optimization (ECBO), Results show that using castellated beams, selecting a deck with higher price and considering different number of floor divisions can decrease the total cost of the floor.

Key Words
structural optimization; steel floor optimization; composite castellated beams; enhanced colliding bodies optimization; floor division number

Address
A. Kaveh and M.H. Ghafari: Centre of Excellence for Fundamental Studies in Structural Engineering, Iran University of Science and Technology, Narmak, Tehran, P.O. Box 16846-13114, Iran

Abstract
Helicopters are essential for supporting offshore oil and gas activities around the world. To ensure accessibility for helicopters, helideck structures must satisfy the safety requirements associated with various environmental and accidental loads. Recently, offshore helideck structures have used aluminium because of its light weight, low maintenance requirements, cost effectiveness and easy installation. However, section designs of aluminum pancakes tend to modify and/or change from the steel pancakes. Therefore, it is necessary to optimize section design and evaluate the safety requirements for aluminium helideck. In this study, a design procedure was developed based on section optimization techniques with experimental studies, industrial regulations and nonlinear finite element analyses. To validate and verify the procedure, a new aluminium section was developed and compared strength capacity with the existing helideck section profiles.

Key Words
safety helideck; nonlinear structural response analysis; optimization; aluminium pancake; accidental load

Address
Jung Kwan Seo, Dae Kyeom Park : The Korea Ship and Offshore Research Institute (The Lloyd\'s Register Foundation Research Centre of Excellence), Pusan National University, Busan, Korea Sung Woo Jo : Department of Naval Architect and Ocean Engineering, Pusan National University, Busan, Korea Joo Shin Park,Jeong Bon Koo, Yeong Su Ha, Ki Bok Jang : Central Research Institute, Samsung Heavy Industries Co., Ltd., Geoje, Republic of Korea

Abstract
This study tries to examine the effect of different parameters on stress analysis of infinite plates with central quasi-triangular cutout using particle swarm optimization (PSO) algorithm and also an attempt has been made to introduce general optimum parameters in order to achieve the minimum amount of stress concentration around this type of cutout on isotropic and orthotropic plates. Basis of the presented method is expansion of analytical method conducted by Lekhnitskii for circular and elliptical cutouts. Design variables in this study include fiber angle, load angle, curvature radius of the corner of the cutout, rotation angle of the cutout and at last material of the plate. Also, diagrams of convergence and duration time of the desired problem are compared with Simulated Annealing algorithm. Conducted comparison is indicative of appropriateness of this method in optimization of the plates. Finite element numerical solution is employed to examine the results of present analytical solution. Overlap of the results of the two methods confirms the validity of the presented solution. Results show that by selecting the aforementioned parameters properly, less amounts of stress can be achieved around the cutout leading to an increase in load-bearing capacity of the structure.

Key Words
particle swarm optimization; infinite plates; quasi-triangular cutout; analytical solution

Address
Mohammad Jafari, Seyed A. Mahmodzade Hoseynia and Mohammad H. Bayati Chaleshtari: Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, P.O.B. 3619995161 Shahrood, Iran

Abstract
The main contribution of the present paper is to propose an intelligent fuzzy inference system approach for modeling the debonding strength of masonry elements retrofitted with Fiber Reinforced Polymer (FRP). To achieve this, the hybrid of meta-heuristic optimization methods and adaptive-network-based fuzzy inference system (ANFIS) is implemented. In this study, particle swarm optimization with passive congregation (PSOPC) and real coded genetic algorithm (RCGA) are used to determine the best parameters of ANFIS from which better bond strength models in terms of modeling accuracy can be generated. To evaluate the accuracy of the proposed PSOPC-ANFIS and RCGA-ANFIS approaches, the numerical results are compared based on a database from laboratory testing results of 109 sub-assemblages. The statistical evaluation results demonstrate that PSOPC-ANFIS in comparison with ANFIS-RCGA considerably enhances the accuracy of the ANFIS approach. Furthermore, the comparison between the proposed approaches and other soft computing methods indicate that the approaches can effectively predict the debonding strength and that their modeling results outperform those based on the other methods.

Key Words
debonding strength; Fiber Reinforced Polymer; adaptive-network-based fuzzy inference system; particle swarm optimization; real coded genetic algorithm

Address
Mohsen Khatibinia: Department of Civil Engineering, University of Birjand, Birjand, Iran Mohammad Reza Mohammadizadeh: Department of Civil Engineering, Hormozgan University, Bandar Abbas, Iran

Abstract
In the present study, a numerical model for probability analysis of optimal design of fatigue non-uniform crack growth behaviour of a cracked aluminium 2024 T3 plate repaired with a bonded composite patch is investigated. The proposed 3D numerical model has advanced in literatures, which gathers in a unique study: problems of reliability, optimization, fatigue, cracks and repair of plates subjected to tensile loadings. To achieve this aim, a finite element modelling is carried out to determine the evolution of the stress intensity factor at the crack tip Paris law is used to predict the fatigue life for a give n crack. To have an optimal volume of our patch satisfied the practical fatigue life, a procedure of optimization is proposed. Finally, the probabilistic analysis is performed in order to a show that optimized patch design is influenced by uncertainties related to mechanical and geometrical properties during the manufacturing process.

Key Words
composites; fatigue; optimizations; numerical methods; structural reliability; simulation, fracture mechanics

Address
H. Errouane, N. Deghoul, Z. Sereir :Laboratoire Structures de Composites et Materiaux innovants, Faculte de Genie Mecanique, Universite des Sciences et de la Technologie d\'Oran, BP 1505 El M\'naouer, USTMB, Oran, Algerie A. Chateauneuf:Clermont Universite, Blaise Pascal, EA 3867, LaMI, BP 10448, 63000 Clermont-Ferrand, France

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