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CONTENTS
Volume 55, Number 3, August10 2015
 

Abstract
The existence of initial imperfections in manufacturing or assembly of double-layer space structures having hundreds or thousands of members is inevitable. Many of the imperfections, such as the initial curvature of the members and residual stresses in members, are all random in nature. In this paper, the probabilistic effect of initial curvature imperfections in the load bearing capacity of double-layer grid space structures with different types of supports have been investigated. First, for the initial curvature imperfection of each member, a random number is generated from a gamma distribution. Then, by employing the same probabilistic model, the imperfections are randomly distributed amongst the members of the structure. Afterwards, the collapse behavior and the ultimate bearing capacity of the structure are determined by using nonlinear push down analysis and this procedure is frequently repeated. Ultimately, based on the maximum values of bearing capacity acquired from the analysis of different samples, structure\'s reliability is obtained by using Monte Carlo simulation method. The results show the sensitivity of the collapse behavior of double-layer grid space structures to the random distribution of initial imperfections and supports type.

Key Words
double-layer grids; random initial curvature imperfections; reliability; Monte Carlo simulation method; progressive collapse

Address
Mehrzad Tahamouli Roudsari and Mehrdad Gordini: Department of Civil Engineering, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran

Abstract
A graded harmonic finite element formulation based on three-dimensional elasticity theory is developed for the structural analysis of 2D functionally graded axisymmetric structures. The mechanical properties of the axisymmetric solid structures composed of two different metals and ceramics are assumed to vary in radial and axial directions according to power law variations as a function of the volume fractions of the constituents. The material properties of the graded element are calculated at the integration points. Effects of material distribution profile on the static deformation, natural frequency and dynamic response analyses of particular axisymmetric solid structures are investigated by changing the power law exponents. It is observed that the displacements, stresses and natural frequencies are severely affected by the variation of axial and radial power law exponents. Good accuracy is obtained with fewer elements in the present study since Fourier series expansion eliminates the need of finite element mesh in circumferential direction and continuous material property distribution within the elements improves accuracy without refining the mesh size in axial and radial directions.

Key Words
computational mechanics; finite element method (FEM); functionally graded; numerical methods; parametric analysis

Address
Ali I. Karakas and Ayse T. Daloglu: Department of Civil Engineering, Karadeniz Technical University, 61080 Trabzon, Turkey

Abstract
Free vibration of non-uniform embedded nanoplates based on classical (Kirchhoff\'s) plate theory in conjunction with nonlocal elasticity theory has been studied. The nanoplate is assumed to be rested on two-parameter Winkler-Pasternak elastic foundation. Non-uniform material properties of nanoplates have been considered by taking linear as well as quadratic variations of Young\'s modulus and density along the space coordinates. Detailed analysis has been reported for all possible cases of such variations. Trial functions denoting transverse deflection of the plate are expressed in simple algebraic polynomial forms. Application of the present method converts the problem into generalised eigen value problem. The study aims to investigate the effects of non-uniform parameter, elastic foundation, nonlocal parameter, boundary condition, aspect ratio and length of nanoplates on the frequency parameters. Three- dimensional mode shapes for some of the boundary conditions have also been illustrated. One may note that present method is easier to handle any sets of boundary conditions at the edges.

Key Words
classical plate theory; Rayleigh-Ritz method; nonlocal elasticity theory; mode shapes

Address
S. Chakraverty and Laxmi Behera: Department of Mathematics, National Institute of Technology Rourkela, Odisha 769008, India

Abstract
Damaged steel-concrete composite girders can be repaired and retrofitted by epoxy-bonded carbon fiber-reinforced polymer (CFRP) sheets to the critical areas of tension flanges. This paper presents the results of a study on the behavior of damaged steel-concrete composite girders repaired with CFRP sheets under static loading. A total of seven composite girders made of I20A steel sections and 80mm-thick by 900mm-wide concrete slabs were prepared and tested. CFRP sheets and prestressed CFRP sheets were used to repair the specimens. The specimens lost the cross-sectional area of their tension flanges with 30%, 50% and 100%. The results showed that CFRP sheets had no significant effect on the yield loads of strengthened composite girders, but had significant effect on the ultimate loads. The yield loads, elastic stiffness, and ultimate bearing capacities of strengthened composite girders had been changed as a result of prestressed CFRP sheets, the utilization ratio of CFRP sheets could be effectively improved by applying prestress to CFRP sheets. Both the yield loads and ultimate bearing capacities had been changed as a result of steel beam\' sflange damage level and CFRP sheets could cover the girders\' shortage of bearing capacity with 30% and 50% flange damage, respectively.

Key Words
damaged composite girders; carbon fiber-reinforced polymer; prestressing; strengthening

Address
Lianguang Wang, Wenyu Hou and Huafeng Han: Department of Civil Engineering, College of Resources and Civil Engineering, Northeastern University Shenyang, China
Junhua Huo: Liaoning Provincial College of Communications Shenyang, China

Abstract
A new structural dynamic fuzzy reliability analysis under stochastic loads which are applied several times is proposed in this paper. The fuzzy reliability prediction models based on time responses with and without strength degeneration are established using the stress-strength interference theory. The random loads are applied several times and fuzzy structural strength is analyzed. The efficiency of the proposed method is demonstrated numerically through an example. The results have shown that the proposed method is practicable, feasible and gives a reasonably accurate prediction. The analysis shows that the probabilistic reliability is a special case of fuzzy reliability and fuzzy reliability of structural strength without degeneration is also a special case of fuzzy reliability with structural strength degeneration.

Key Words
fuzzy; dynamic reliability; probability; stochastic loads

Address
Yongfeng Fang: School of Mechanical Engineering, Guizhou University of Science Engineering, Bijie, 551700, China
Jianbin Xiong: School of Computer and Electronic Information, Guangdong University of Petrochemical Technology, Maoming, 525000, China
Kong Fah Tee: Department of Civil Engineering, University of Greenwich, Kent, ME4 4TB, UK

Abstract
Dolphin echolocation (DE) optimization algorithm is a recently developed meta-heuristic in which echolocation behavior of Dolphins is utilized for seeking a design space. The computational performance of meta-heuristic algorithms is highly dependent to its internal parameters. But the computational time of adjusting these parameters is usually extensive. The DE is an efficient optimization algorithm as it includes few internal parameters compared with other meta-heuristics. In the present paper a modified Dolphin echolocation (MDE) algorithm is proposed for optimization of steel frame structures. In the MDE the step locations are determined using one-dimensional chaotic maps and this improves the convergence behavior of the algorithm. The effectiveness of the proposed MDE algorithm is illustrated in three benchmark steel frame optimization test examples. Results demonstrate the efficiency of the proposed MDE algorithm in finding better solutions compared to standard DE and other existing algorithms.

Key Words
steel structure; optimization; Dolphin echolocation; meta-heuristic

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

Abstract
Triangular pyramid and Quadrangular pyramid elements for partial double-layer spherical reticulated shells of pyramidal system are investigated in the present study. Macro programs for six typical partial double-layer spherical reticulated shells of pyramidal system are compiled by using the ANSYS Parametric Design Language (APDL). Internal force analysis of six spherical reticulated shells is carried out. Distribution regularity of the stress and displacement are studied. A shape optimization program is proposed by adopting the sequence two-stage algorithm (RDQA) in FORTRAN environment based on the characteristics of partial double-layer spherical reticulated shells of pyramidal system and the ideas of discrete variable optimization design. Shape optimization is achieved by considering the objective function of the minimum total steel consumption, global and locality constraints. The shape optimization of six spherical reticulated shells is calculated with the span of 30m~120m and rise to span ratio of 1/7~1/3. The variations of the total steel consumption along with the span and rise to span ratio are discussed with contrast to the results of shape optimization. The optimal combination of main design parameters for six spherical reticulated shells is investigated, i.e., the number of the optimal grids. The results show that: (1) The Kiewitt and Geodesic partial double-layer spherical reticulated shells of triangular pyramidal system should be preferentially adopted in large and medium-span structures. The range of rise to span ratio is from 1/6 to 1/5. (2) The Ribbed and Schwedler partial double-layer spherical reticulated shells of quadrangular pyramidal system should be preferentially adopted in small-span structures. The rise to span ratio should be 1/4. (3) Grids of the six spherical reticulated shells can be optimized after shape optimization and the total steel consumption is optimized to be the least.

Key Words
pyramidal system; APDL; parametric modeling; RDQA; shape optimization

Address
J. Wu: Geotechnical and Structural Engineering Research Center, Shandong University, Ji\'nan 250061, Shandong, China; Institute of Engineering Mechanics, Shandong Jianzhu University, Ji\'nan 250101, Shandong, China
X.Y. Lu: Institute of Engineering Mechanics, Shandong Jianzhu University, Ji\'nan 250101, Shandong, China
S.C. Li: Geotechnical and Structural Engineering Research Center, Shandong University, Ji\'nan 250061, Shandong, China
D.L. Zhang: Shandong Agriculture and Engineering University Ji\'nan 250100, Shandong, China
Y.G. Xue, L.P. Li and Y.G. Xue: Geotechnical and Structural Engineering Research Center, Shandong University, Ji\'nan 250061, Shandong, China

Abstract
There are so many applications of perforated pates with various penetration patterns. If they are penetrated regularly, it can be represented by solid plate with equivalent material properties, which has a benefit of finite element modelling and reducing computation time for the analysis. Because the equivalent material properties suggested already are not proper to be applicable for the dynamic analysis, it is necessary to extract the equivalent material properties for the dynamic analysis. Therefore, in this study, the equivalent modulus of elasticity are obtained for the perforated plate with a triangular penetration pattern by comparing the natural frequencies of the perforated plate with those of solid plate, which are represented with respect to the ligament efficacy. Using the equivalent material properties suggested, the modal analyses of the partially perforated rectangular plate with a triangular penetration pattern are performed and its applicability is shown by comparing natural frequencies of perforated and homogeneous solid plates from finite element method and analytical method.

Key Words
partially perforated plate; rectangular plate; effective modulus of elasticity; finite element analysis; Rayleigh-Ritz method; ligament efficiency

Address
Myung J. Jhung: Korea Institute of Nuclear Safety, Yuseong-gu, Daejeon, 305-338, Republic of Korea
Kyeong H. Jeong: Korea Atomic Energy Research Institute, Yuseong-gu, Daejeon, 305-353, Republic of Korea

Abstract
It is intended to perform buckling analysis of steel gabled frames with tapered members and flexible connections. The method is based on the exact solutions of the governing differential equations for stability of a gabled frame with I-section elements. Corresponding buckling load and subsequently effective length factor are obtained for practical use. For several popular frames, the influences of the shape factor, taper ratio, span ratio, flexibility of connections and elastic rotational and translational restraints on the critical load, and corresponding equivalent effective length coefficient are studied. Some of the outcomes are compared against available solutions, demonstrating the accuracy, efficiency and capabilities of the presented approach.

Key Words
gabled frame; tapered member; I-section; flexible connection; critical load; effective length factor; buckling

Address
Mohammad Rezaiee-Pajand, Farzad Shahabian and Mohsen Bambaeechee: Department of Civil Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Iran

Abstract
Bolted joints are essential elements of mechanical structures and metal constructions. Although their static behaviour is fairly well known, their dynamic behaviour due to shocks and vibrations has been less studied, because of the large size of the finite element models needed for a detailed simulation. This work presents four different simplified models suitable for studying the dynamic behaviour of an elementary bolted joint. Three of them include contact elements to allow sliding of the screw head and the nut on the assembled parts, and the last one allows rotation between screw and nut. A penalty approach based on the Coulomb friction model is used to model contact. The results show that these models effectively represent the dynamic behaviour, with different accuracy depending on the model details. The last model simulates the self loosening of a bolt subjected to transversal vibrations.

Key Words
bolted joint; dynamic study; finite element model; friction; bolt model; self loosening

Address
Olfa Ksentini, Mohamed Slim Abbes and Mohamed Haddar: Laboratory of Mechanics, Modelisation and Manufacturing, National School of Engineers of Sfax, Sfax University, BP 1173-3038,Sfax, Tunisia
Olfa Ksentini, Bertrand Combes and Alain Daidie: Institute Clement Ader, University of Toulouse, National Institute of Applied Sciences of Toulouse, 31077 Toulouse, France

Abstract
In this paper, a new and simplified method is presented in which the natural frequencies of the uniform and non-uniform beams are calculated through simple mathematical relationships. The various vibration problems such as: Rayleigh beam under variable axial force, axial vibration of a bar with and without end discrete spring, torsional vibration of a bar with an attached mass moment of inertia, flexural vibration of the beam with laterally distributed elastic springs and also flexural vibration of the beam with effects of viscose damping are investigated. The governing differential equations are first obtained and then; according to a harmonic vibration, are converted into single variable equations in terms of location. Through repetitive integrations, the governing equations are converted into weak form integral equations. The mode shape functions of the vibration are approximated using a power series. Substitution of the power series into the integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of a non-trivial solution for system of equations. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained with those obtained from other published references and results of available finite element software.

Key Words
natural frequency; Rayleigh beam; axial vibration; torsional vibration; flexural vibration; weak form integral equation

Address
Mehrdad Mohammadnejad: Department of Civil Engineering, Faculty of Engineering, Birjand University of Technology, Birjand, Iran

Abstract
The use of ground granulated blast furnace slag (GGBFS) from steel industries waste is showing perspective application in civil engineering as partial substitute to cement. Use of such waste conserves natural resources and minimizes the space required for landfill. The GGBFS used in the present work is of ultra fine size and hence serves as micro filler. In this paper strength and durability characteristics of ultra fine slag based high strength concrete (HSC) (with a characteristic compressive strength of 50 MPa) were studied. Cement was replaced with ultra fine slag in different percentages of 5, 10, and 15% to study the compressive strength, porosity, resistances against sulfate attack, sorptivity and chloride ion penetration. The experiments to study compressive strength were conducted for different ages of concrete such as 7, 28, 56, and 90 days. From the detailed investigations with 16 mix combinations, 10% ultra fine slag give better results in terms of strength and durability characteristics.

Key Words
ultra fine slag; compressive strength; sorptivity; porosity; sulfate attack; chloride ion penetration

Address
Pichaiya Sharmila and Govindasamy Dhinakaran: School of Civil Engineering, Sastra University, Thanjavur 613401 Tamil Nadu, India


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