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CONTENTS
Volume 57, Number 2, January25 2016
 

Abstract
A general model of equations of the two-temperature theory of generalized thermoelasticity is applied to study the wave propagation in a fiber-reinforced magneto-thermoelastic medium in the context of the three-phase-lag model and Green-Naghdi theory without energy dissipation. The material is a homogeneous isotropic elastic half-space. The exact expression of the displacement components, force stresses, thermodynamic temperature and conductive temperature is obtained by using normal mode analysis. The variations of the considered variables with the horizontal distance are illustrated graphically. Comparisons are made with the results of the two theories in the absence and presence of a magnetic field as well as a two-temperature parameter. A comparison is also made between the results of the two theories in the absence and presence of reinforcement.

Key Words
fiber-reinforced; Green-Naghdi theory; three-phase-lag model; magnetic field

Address
Samia M. Said: Department of Mathematics, Faculty of Science, P.O. Box 44519, Zagazig University, Zagazig, Egypt
Mohamed I.A. Othman: Department of Mathematics, Faculty of Science, Taif University 888, Saudi Arabia

Abstract
One of the objectives of this study is to implement the direct calculation of the torsional moment of inertia for non-circular cross-sections, which is based on the St. Venant torsion formulation and the finite element method. Recently the proposed method provides a unique calculation of the torsional rigidity of simply and multiply connected cross-sections. Next, free vibration analyses of cylindrical and non-cylindrical helices with non-circular cross-sections are solved by a curved two-nodded mixed finite element based on the Timoshenko beam theory. Some thin-thick closed or open sections are handled and the natural frequencies of cylindrical and non-cylindrical helices are compared with the literature and the commercial finite element program SAP2000.

Key Words
mixed finite element; non-cylindrical helix; non-circular cross-sections; Poisson

Address
Nihal Eratli, Murat Yilmaz, Kutlu Darilmaz and Mehmet H. Omurtag: Department of Civil Engineering, Istanbul Technical University, Istanbul, Turkey

Abstract
The paper studies the natural oscillation of the three-layered solid sphere with a middle layer made of Functionally Graded Material (FGM). It is assumed that the materials of the core and outer layer of the sphere are homogeneous and isotropic elastic. The three-dimensional exact equations and relations of linear elastodynamics are employed for the investigations. The discrete-analytical method proposed by the first author in his earlier works is applied for solution of the corresponding eigenvalue problem. It is assumed that the modulus of elasticity, Poisson\'s ratio and density of the middle-layer material vary continuously through the inward radial direction according to power law distribution. Numerical results on the natural frequencies related to the torsional and spheroidal oscillation modes are presented and discussed. In particular, it is established that the increase of the modulus of elasticity (mass density) in the inward radial direction causes an increase (a decrease) in the values of the natural frequencies.

Key Words
functionally graded material; three-layered solid sphere; natural vibration; natural frequencies; torsional oscillation; spheroidal oscillation

Address
Surkay D. Akbarov: Department of Mechanical Engineering, Yildiz Technical University, Yildiz Campus,
34349, Besiktas, Istanbul, Turkey; Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan, AZ1141, Baku, Azerbaijan
Hatam H. Guliyev: Institute of Geology and Geophysics of the National Academy of Sciences of Azerbaijan, AZ1073, Baku, Azerbaijan
Nazmiye Yahnioglu: Department of Mathematical Engineering, Yildiz Technical University, Davutpasa Campus, 34220, Esenler Istanbul, Turkey

Abstract
A NLFE model was proposed to investigate the mechanical behavior of short columns, cast using plain or fibrous lightweight aggregate concrete (LWAC), and subjected to elevated temperatures of up to 700oC. The model was validated, before its predictions were extended to study the effect of other variables, not studied experimentally. The three-dimensional NLFE model was developed using ANSYS software and involved rational simulation of thermal mechanical behavior of plain and fibrous LWAC as well as longitudinal and lateral steel reinforcement. The prediction from the NLFE model of columns\' mechanical behavior, as represented by the stress-strain diagram and its characteristics, compared well with the experimental results. The predictions of the proposed models, considering wide range of lateral reinforcement ratios, confirmed the behaviors observed experimentally and stipulated the importance of steel confinement in preserving post-heating mechanical properties of plain and fibrous LWAC columns, being subjected to high temperature.

Key Words
NLFE; fire; post-heating; mechanical properties; columns; lightweight concrete

Address
Yasmeen T. Obaidat: Civil Engineering Department, Yarmouk University, P.O. Box 566, Irbid, Jordan
Rami H. Haddad: Civil Engineering Department, Jordan University of Science and Technology, P.O. Box 22110, 22110 Irbid, Jordan

Abstract
The paper is devoted to study a mesh-free analysis method of structural elements of engineering structures based on B-spline Wavelet Basis Function. First, by employing the moving-least square method and the weighted residual method to solve the structural displacement field, the control equations and the stiffness equations are obtained. And then constructs the displacement field of the structure by using the m-order B-spline wavelet basis function as a weight function. In the end, the paper selects the plane beam structure and the structure with opening hole to carry out numerical analysis of deformation and stress. The Finite Element Method calculation results are compared with the results of the method proposed, and the calculation results of the relative error norm is compared with Gauss weight function as weight function. Therefore, the clarification verified the validity and accuracy of the proposed method.

Key Words
structural analysis; moving-least square method; meshless local MLPG method; B-Spline wavelet weight function

Address
Jianping Chen: School of Ship Engineering, Guangzhou Maritime Institute, Guangzhou, China; School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai, China
Wenyong Tang: School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai, China
Pengju Huang: School of Ship Engineering, Guangzhou Maritime Institute, Guangzhou, China
Li Xu: Fujian Chuanzheng Communications College, Fuzhou, China

Abstract
In this study, the three-dimensional finite element method is used to determine the stress intensity factor in Mode I and Mixed mode of a centered crack in an aluminum specimen repaired by a composite patch using contour integral. Various mesh densities were used to achieve convergence of the results. The effect of adhesive joint thickness, patch thickness, patch-specimen interface and layer sequence on the SIF was highlighted. The results obtained show that the patch-specimen contact surface is the best indicator of the deceleration of crack propagation, and hence of SIF reduction. Thus, the reduction in rigidity of the patch especially at adhesive layer-patch interface, allows the lowering of shear and normal stresses in the adhesive joint. The choice of the orientation of the adhesive layer-patch contact is important in the evolution of the shear and peel stresses. The patch will be more beneficial and effective while using the cross-layer on the contact surface.

Key Words
composite bonded patch; sequence of ply; adjacent cross-layer; contact surface of repair; stress intensity factor (SIF); finite element analysis

Address
Hadja Imane Beloufa, Djamel Ouinas: Laboratoire de Modelisation Numerique et Experimentale des Phenomenes Mecaniques, Faculty of Sciences and Technology, University Abdelhamid Ibn Badis of Mostaganem, 27000, Algeria
Mostapha Tarfaoui: Laboratoire Brestois de Mecaniqueet des Systemes, ENSTA Bretagne, 2 Rue Francois Verny, 29806 Brest Cedex 9, France
Noureddine Benderdouche: SEA2M, Faculty of Sciences and Technology, University Abdelhamid Ibn Badis of Mostaganem,
27000, Algeria

Abstract
A new first-order shear deformation theory is developed for dynamic behavior of functionally graded beams. The equations governing the axial and transverse deformations of functionally graded plates are derived based on the present first-order shear deformation plate theory. The governing equations and boundary conditions of functionally graded beams have the simple forms as those of isotropic plates. The influences of the volume fraction index and thickness-to-length ratio on the fundamental frequencies are discussed.The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

Key Words
functionally graded beam; first shear deformation theory; Hamilton

Address
Lazreg Hadji: Universite Ibn Khaldoun, BP 78 Zaaroura, 14000 Tiaret, Algerie
T. Hassaine Daouadji, M. Ait Amar Meziane, Y. Tlidji: Universite Ibn Khaldoun, BP 78 Zaaroura, 14000 Tiaret, Algerie; Laboratoire des Materiaux & Hydrologie, Universite de Sidi BelAbbes, 22000 Sidi Bel Abbes, Algerie
E.A. Adda Bedia: Laboratoire des Materiaux & Hydrologie, Universite de Sidi BelAbbes, 22000 Sidi Bel Abbes, Algerie

Abstract
A new analytical derivation of the elastodynamic point load solutions for an isotropic multilayered half-space is presented by means of the precise integration method (PIM) and the approach of dual vector. The time-harmonic external load is prescribed either on the external boundary or in the interior of the solid medium. Starting with the axisymmetric governing motion equations in a cylindrical coordinate system, a second order ordinary differential matrix equation can be gained by making use of the Hankel integral transform. Employing the technique of dual vector, the second order ordinary differential matrix equation can be simplified into a first-order one. The approach of PIM is implemented to obtain the solutions of the ordinary differential matrix equation in the Hankel integral transform domain. The PIM is a highly accurate algorithm to solve sets of first-order ordinary differential equations and any desired accuracy of the dynamic point load solutions can be achieved. The numerical simulation is based on algebraic matrix operation. As a result, the computational effort is reduced to a great extent and the computation is unconditionally stable. Selected numerical trials are given to validate the accuracy and applicability of the proposed approach. More examples are discussed to portray the dependence of the load-displacement response on the isotropic parameters of the multi-layered media, the depth of external load and the frequency of excitation.

Key Words
time-harmonic point load; precise integration method; Hankel integral transform; dual vector; stratified soil

Address
Gao Lin: School of Hydraulic Engineering, Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, China
Pengchong Zhang: School of Hydraulic Engineering, Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, China
Jun Liu: School of Hydraulic Engineering, Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, China; State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China; State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
Wenyuan Wang: School of Hydraulic Engineering, Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, China

Abstract
This paper illustrates an experimental study on a self compacting polymer concrete called isobeton made of polyurethane foam and expanded clay. Several experiments were conducted to characterize the physic-mechanical properties of the considered material. Application of the Linear Elastic Fracture Mechanics (LEFM) and determining the toughness of two isobetons based on Belgian and Italian clay, was conducted to determine the stress intensity factor KIC and the rate of releasing energy GIC. The material considered was tested under static and dynamic loadings for two different samples with 10x10x40 and 10x15x40 cm dimensions. The result obtained by the application of the Linear Elastic Fracture Mechanics (LEFM) shows that is optimistic and fulfilled the physic-mechanical requirement of the study.

Key Words
polymer concrete; polyurethane; expanded clay; linear elastic fracture mechanics; flexion

Address
K. Boudjellal, M. Bouabaz and M. Belachia: Department of Civil Engineering, LMGHU Laboratory, University 20 août 1955-Skikda, Algeria

Abstract
In this work, random homogenization analysis for the effective thermal properties of a three-dimensional composite material with unidirectional fibers is presented by combining the equivalent inclusion method with Random Factor Method (RFM). The randomness of the micro-structural morphology and constituent material properties as well as the correlation among these random parameters are completely accounted for, and stochastic effective thermal properties as thermal expansion coefficients as well as their correlation are then sought. Results from the RFM and the Monte-Carlo Method (MCM) are compared. The impact of randomness and correlation of the micro-structural parameters on the random homogenized results is revealed by two methods simultaneously, and some important conclusions are obtained.

Key Words
random homogenization; randomness and correlation; Random Factor Method; random effective thermal proterties; Monte-Carlo Method

Address
Juan Ma: Key Laboratory of Electronic Equipment Structure Design, Ministry of Education, Xidian University, Xi\'an, 710071, P.R. China; Institute of Continuum Mechanics, Leibniz Universität Hannover, 30167 Hannover, Germany
Peter Wriggers: Institute of Continuum Mechanics, Leibniz Universität Hannover, 30167 Hannover, Germany
Liangjie Li: Key Laboratory of Electronic Equipment Structure Design, Ministry of Education, Xidian University, Xi\'an, 710071, P.R. China


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