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CONTENTS
Volume 54, Number 4, May25 2015
 

Abstract
This paper presents a comparative study of analytical method and finite element method (FEM) for analysis of a continuous contact problem. The problem consists of two elastic layers loaded by means of a rigid circular punch and resting on semi-infinite plane. It is assumed that all surfaces are frictionless and only compressive normal tractions can be transmitted through the contact areas. Firstly, analytical solution of the problem is obtained by using theory of elasticity and integral transform techniques. Then, finite element model of the problem is constituted using ANSYS software and the two dimensional analysis of the problem is carried out. The contact stresses under rigid circular punch, the contact areas, normal stresses along the axis of symmetry are obtained for both solutions. The results show that contact stresses and the normal stresses obtained from finite element method (FEM) provide boundary conditions of the problem as well as analytical results. Also, the contact areas obtained from finite element method are very close to results obtained from analytical method; disagree by 0.03-1.61%. Finally, it can be said that there is a good agreement between two methods.

Key Words
contact problem; finite element model; rigid punch; semi-infinite plane; singular integral equation

Address
Erdal Oner: Department of Civil Engineering, Bayburt University, 69000, Bayburt, Turkey
Murat Yaylaci: Department of Civil Engineering, Recep Tayyip Erdoğan University, 53100, Rize, Turkey
Ahmet Birinci: Department of Civil Engineering, Karadeniz Technical University, 61080, Trabzon, Turkey

Abstract
A numerical approach is presented for the analysis of the forced vibration of a rigid surface foundation with arbitrary shape. In the analysis, the foundation is discretized into a number of sub squareelements. The dynamic response within each sub-element is described by the Green‟s function, which is obtained by the Fourier-Bessel transform and Precise Integration Method (PIM). Incorporating the displacement boundary condition and force equilibrium of the foundation, it obtains a system of linear algebraic equation in terms of the contact forces within each sub-element. Solving the equation leads to the desired dynamic impedance functions of the foundation. Numerical results are obtained for foundation not only with simple geometrical configurations, such as rectangular and circular foundation, but also the case of irregularly shaped foundation. Several comparisons between the proposed approach and other methods are made. Very good agreement is reached. Also, parametric studies are carried out on the dynamic response of foundation. Addressed in this study are the effects of Poisson‟s ratio, material damping and contact condition of soil-foundation interface. Several conclusions are drawn the significance of the factors.

Key Words
elastic multi-layered half space; Green‟s function; wavenumber domain; spatial domain; Precise Integration Method (PIM); impedance functions

Address
Lin Chen: Lehrstuhl für Baustatik und Baudynamik, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany

Abstract
In this study, the authors present an analytical approach to find the axisymmetric buckling load of two joined isotropic conical shells under axial compression. The problem of two joined conical shells may be considered as the generalized form of joined cylindrical and conical shells with constant or stepped thicknesses. Thickness of each cone is constant; however it may be different from the thickness of the other cone. The boundary conditions are assumed to be simply supported with rigid rings. The governing equations for the conical shells are obtained and solved with an analytical approach. A simple closed-form expression is obtained for the buckling load of two joined truncated conical shells. Results are compared and validated with the numerical results of finite element method. The variation of buckling load with changes in the thickness and semi-vertex angles of the two cones is studied. Finally, application of the results in practical design and range of engineering validity are investigated.

Key Words
joined conical shells; buckling; analytical solution; design application

Address
M.A. Kouchakzadeh: Department of Aerospace Engineering and Center of Excellence in Aerospace Systems, Sharif University of Technology, P.O. Box 11155-8639, Tehran, Iran
M. Shakouri: Department of Aerospace Engineering, Sharif University of Technology, P.O. Box 11155-8639, Tehran, Iran

Abstract
This study aims at comparing the optimum design of two common types open web expanded beams: with hexagonal openings, also called castellated beams and beams with circular openings referred to as cellular beams. The minimum weights of both beams are taken as the objective functions while the design constraints are respectively implemented from The Steel Construction Institute Publication Numbers 5 and 100. The design methods adopted in these publications are consistent with BS5950 parts. The formulation of the design problem considering the limitations of the above mentioned turns out to be a discrete programming problem. Improved harmony search algorithm is suggested to compare the optimum design of mentioned web-expanded beams to analysis the performance of both beams. The design algorithms based on the technique select the optimum Universal Beam sections, dimensional properties of hexagonal and circular holes and total number of openings along the beam as design variables.

Key Words
structural optimization; web-expanded beams; castellated beams; cellular beams; harmony search algorithm

Address
Ferhat Erdal: Department of Civil Engineering, Akdeniz University, 07058, Antalya, Turkey

Abstract
This paper presents a nonlocal shear deformation beam theory for bending, buckling, and vibration of functionally graded (FG) nanobeams using the nonlocal differential constitutive relations of Eringen. The developed theory account for higher-order variation of transverse shear strain through the depth of the nanobeam, and satisfy the stress-free boundary conditions on the top and bottom surfaces of the nanobeam. A shear correction factor, therefore, is not required. In addition, this nonlocal nanobeam model incorporates the length scale parameter which can capture the small scale effect and it has strong similarities with Euler–Bernoulli beam model in some aspects such as equations of motion, boundary conditions, and stress resultant expressions. The material properties of the FG nanobeam are assumed to vary in the thickness direction. The equations of motion are derived from Hamilton\'s principle. Analytical solutions are presented for a simply supported FG nanobeam, and the obtained results compare well with those predicted by the nonlocal Timoshenko beam theory.

Key Words
nanobeam; nonlocal elasticity theory; bending; buckling; vibration; functionally graded materials

Address
Amine Zemri: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
Mohammed Sid Ahmed Houari: Departement de Genie Civil, Universite de Mascara, Algeria; Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil, Algeria
Abdelmoumen Anis Bousahla: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Universite de Sidi Bel Abbes, Algeria
Abdelouahed Tounsi: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Universite de Sidi Bel Abbes, Algeria; Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Universite de Sidi Bel Abbes, Algeria

Abstract
This study investigates the identification of added mass and its location in the glass fiber reinforced polymer (GFRP) beam structures. The main emphasis of this paper is to ascertain the importance of inclusion of rotational degrees of freedom (dofs) in the introduction of added mass or damage identification. Two identification indices that include the rotational dofs have been introduced in this paper: the modal force index (MFI) and the modal rotational curvature index (MRCI). The MFI amplifies damage signature using undamaged numerical stiffness matrix which is related to changes in the altered mode shapes from the original mode shapes. The MRCI is obtained by using a higher derivative of rotational mode shapes. Experimental and numerical results are compared with the existing methods leading to a conclusion that the contributions of the rotational modes play a key role in the identification of added mass. The authors believe that the similar results are likely in the case of damage identification also.

Key Words
modal force index (MFI); modal rotational curvature index (MRCI); rotational mode shape; added mass; glass fiber reinforced polymer (GFRP)

Address
Prakash Rajendran and Sivakumar M Srinivasan: Department of Applied Mechanics, Indian Institute of Technology Madras, Active Materials Structures and Systems Lab, Chennai 600 036, Tamil Nadu, India

Abstract
This study presents critical buckling load optimization of the axially graded layered uniform columns. In the first place, characteristic equations for the critical buckling loads for all boundary conditions are obtained using the transfer matrix method. Then, for each case, square of this equation is taken as a fitness function together with constraints. Due to explicitly unavailable objective function for the critical buckling loads as a function of segment length and volume fraction of the materials, especially for the column structures with higher segment numbers, initially, prescribed value is assumed for it and then the design variables satisfying constraints are searched using Differential Evolution (DE) optimization method coupled with eigen-value routine. For constraint handling, Exterior Penalty Function formulation is adapted to the optimization cycle. Different boundary conditions are considered. The results reveal that maximum increments in the critical buckling loads are attained about 20% for cantilevered and pinned-pinned end conditions and 18% for clamped-clamped case. Finally, the strongest column structure configurations will be determined. The scientific and statistical results confirmed efficiency, reliability and robustness of the Differential Evolution optimization method and it can be used in the similar problems which especially include transcendental functions.

Key Words
axially graded; uniform column; buckling; optimization; differential evolution

Address
Veysel Alkan: Department of Mechanical Engineering, Pamukkale University, Kinikli, 20070, Denizli, Turkey

Abstract
This study evaluates prediction models for three EDPs (engineering demand parameters) using data from three symmetrical structures with RC walls designed according to the currently enforced Romanian seismic design code P100-1/2013. The three analyzed EDPs are: the maximum interstorey drift, the maximum top displacement and the maximum shear force at the base of the RC walls. The strong ground motions used in this study consist of three pairs of recordings from the Vrancea intermediate-depth earthquakes of 1977, 1986 and 1990, as well as two other pairs of recordings from significant earthquakes in Turkey and Greece (Erzincan and Aigion). The five pairs of recordings are rotated in a clockwise direction and the values of the EDPs are recorded. Finally, the relation between various IMs (intensity measures) of the strong ground motion records and the EDPs is studied and two prediction models for EDPs are also evaluated using the analysis of residuals.

Key Words
strong ground motion records; interstorey drift; top displacement; shear force; prediction model

Address
Florin Pavel: Department of Reinforced Concrete Structures, Technical University of Civil Engineering Bucharest, Bd. Lacul Tei no. 122-124, Sector 2, 020396, Bucharest, Romania
Andrei Pricopie: Department of Strength of Materials, Technical University of Civil Engineering Bucharest, Bd. Lacul Tei no. 122-124, Sector 2, 020396, Bucharest, Romania


Abstract
In this study, a 2-D finite element formulation in the frame of nonlocal integral elasticity is presented. Subsequently, the bending problem of a nanobeam under different types of loadings and boundary conditions is solved based on classical beam theory and also 3-D elasticity theory using nonlocal finite elements (NL-FEM). The obtained results are compared with the analytical and numerical results of nonlocal differential elasticity. It is concluded that the classical beam theory and the nonlocal differential elasticity can separately lead to significant errors for the problem under consideration as distinct from 3-D elasticity and nonlocal integral elasticity respectively.

Key Words
nonlocal integral elasticity; nonlocal differential elasticity; finite element; beam; bending

Address
M. Taghizadeh and H.R. Ovesy: Department of Aerospace Engineering and Centre of Excellence in Computational Aerospace Engineering, Amirkabir University of Technology, Tehran, 15875-4413, Iran
S.A.M. Ghannadpour: Department of Aerospace Engineering, Faculty of New Technologies and Engineering, Shahid Beheshti University, GC, 1983963113, Tehran, Iran

Abstract
In the paper we study dynamic response of a finite, simply supported Timoshenko beam subject to a moving continuously distributed forces. Three problems have been considered. The dynamic response of the Timoshenko beam under a uniform distributed load moving with a constant velocity v has been considered as the first problem. Obtained solutions allow to find the response of the beam under the interval of the finite length a uniformly distributed moving load. Part of the solutions are presented in a closed form instead of an infinite series. As the second problem the steady-state vibrations of the beam under uniformly distributed mass m1 moving with the constant velocity has been considered. The vibrations of the beam caused by the interval of the finite length randomly distributed load moving with constant velocity is considered as the last problem. It is assumed that load process is space-time stationary stochastic process.

Key Words
Timoshenko beam; moving force; vibrations

Address
Olga Szyiko-Bigus: Institute of Civil Engineering, Wrociaw University of Technology, 50-421 Wrociaw, ul. Na Grobli 15, Poland
Pawei Sniady: Faculty of Environmental Engineering and Geodesy, Wrociaw University of Environmental and Life Science, pl. Grunwaldzki 24, 50-363 Wrociaw, Poland

Abstract
Constructing the influence lines of forces of statically indeterminate structures is a traditional issue in structural engineering and mechanics. However, the existing kinematic method for establishing these force influence lines is an indirect or mixed approach by combining the force method with the theorem of reciprocal displacements, which is yet inconsistent with the kinematic method for statically determinate structure. This paper proposes the direct kinematic method in conjunction with the load-displacement differential relation for exactly constructing influence lines of reaction and internal forces of indeterminate structures. Firstly, through applying the principle of virtual displacement, the formula for influence lines of reaction and internal forces of indeterminate structure via direct kinematic method is derived based on the released structure. Then, a computational approach with a clear concept and unified procedure as well as wide applicability based on the load-displacement differential relation of beam is suggested to achieve conveniently the closed-form expression of force influence lines, and exactly draw them. Finally, three representative examples for constructing force influence lines of statically indeterminate beams and frame illustrate the superiority of the proposed method.

Key Words
statically indeterminate structure; influence lines of reaction and internal forces; closed-form solution; direct kinematic method; principle of virtual displacement

Address
Dixiong Yang: Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, China; State Key Laboratory Base of Eco-hydraulic Engineering in Arid Area, Xi\'an University of Technology, Xi\'an 710048, China
Guohai Chen and Zongliang Du: Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, China

Abstract
In this paper, seismic energy response of inelastic steel structures under earthquake excitations is investigated. For this purpose, a numerical procedure based on nonlinear dynamic analysis is developed by considering material, geometric and connection nonlinearities. Material nonlinearity is modeled by the inversion of Ramberg-Osgood equation. Nonlinearity caused by the interaction between the axial force and bending moment is also defined considering stability functions, while the geometric nonlinearity caused by axial forces is described using geometric stiffness matrix. Cyclic behaviour of steel connections is taken into account by employing independent hardening model. Dynamic equation of motion is solved by Newmark\'s constant acceleration method in the time history domain. Energy response analysis of space frames is performed by using this proposed numerical method. Finally, for the first time, the distribution of the different energy types versus time at the duration of the earthquake ground motion is obtained where in addition error analysis for the numerical solutions is carried out and plotted depending on the relative error calculated as a function of energy balance versus time.

Key Words
seismic energy response; inelastic steel structure; earthquake ground motion; Ramberg-Osgood equation; independent hardening model; stability functions

Address
Kadir Ozakgul: Department of Civil Engineering, Istanbul Technical University, Maslak 34469, Istanbul, Turkey


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