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CONTENTS
Volume 65, Number 4, February25 2018
 

Abstract
Dynamic analysis of complex and large structures may be costly from a numerical point of view. For coupled vibroacoustic finite element models, the importance of reducing the size becomes obvious because the fluid degrees of freedom must be added to the structural ones. In this paper, a component mode synthesis method is proposed for large vibroacoustic interaction problems. This method couples fluid subdomains and dynamical substructuring of Craig and Bampton type. The acoustic formulation is written in terms of the velocity potential, which implies several advantages: coupled algebraic systems remain symmetric, and a potential formulation allows a direct extension of Craig and Bampton\'s method to acoustics. Those properties make the proposed method easy to implement in an existing finite element code because the local numerical treatment of substructures and fluid subdomains is undifferentiated. Test cases are then presented for axisymmetric geometries. Numerical results tend to prove the validity and the efficiency of the proposed method.

Key Words
component mode synthesis; substructure; subdomain; vibroacoustic; finite element; fluid-structure interaction

Address
Rabii El Maani:
1) LMN, INSA de Rouen, Avenue de l\' Universite, 76800 Saint Etienne de Rouvray, France
2) LIMII, FST Settat, route de Casablanca, Settat, Maroc
Abdelkhalak El Hami: LMN, INSA de Rouen, Avenue de l\' Universite, 76800 Saint Etienne de Rouvray, France
Bouchaib Radi: LIMII, FST Settat, route de Casablanca, Settat, Maroc

Abstract
In this paper, a multi-layered finite element model for laminated glass plates is introduced. A layer-wise theory is applied to the analysis of laminated glass due to the combination of stiff and soft layers; the independent layers are connected via Lagrange multipliers. The von Kármán large deflection plate theory and the constant Poisson ratio for constitutive equations are assumed to capture the possible effects of geometric nonlinearity and the time/temperature-dependent response of the plastic foil. The linear viscoelastic behavior of a polymer foil is included by the generalized Maxwell model. The proposed layer-wise model was implemented into the MATLAB code and verified against detailed three-dimensional models in ADINA solver using different hexahedral finite elements. The effects of temperature, load duration, and creep/relaxation are demonstrated by examples.

Key Words
laminated glass plate; finite element method; layer-wise plate model; Lagrange multipliers; geometric nonlinearity; von Kármán assumptions; time/temperature-dependent behavior; generalized Maxwell model, Williams-Landel-Ferry equation; Newton method

Address
Alena Zemanova, Jan Zemana, Tomas Jandab and Michal Sejnohac: Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague,
Thákurova 7, 166 29 Prague 6, Czech Republic


Abstract
Dynamic behaviour of beam carrying masses has attracted attention of many researchers and engineers. Many studies on the analytical solution of beam with concentric tip mass have been published. However, there are limited works on vibration analysis of beam with an eccentric three dimensional object. In this case, bending and torsional deformations of beam are coupled due to the boundary conditions. Analytical solution of equations of motion of the system is complicated and lengthy. Therefore, in this study, Differential Transform Method (DTM) is applied to solve the relevant equations. First, the Timoshenko beam with 3D tip attachment whose centre of gravity is not coincident with beam end point is considered. The beam is assumed to undergo bending in two orthogonal planes and torsional deformation about beam axis. Using Hamilton\'s principle the equations of motion of the system along with the possible boundary conditions are derived. Later DTM is applied to obtain natural frequencies and mode shapes of the system. According to the relevant literature DTM has not been applied to such a system so far. Moreover, the problem is modelled by Ansys, the well-known finite element method, and impact test is applied to extract experimental modal data. Comparing DTM results with finite element and experimental results it is concluded that the proposed approach produces accurate results.

Key Words
differential transform method (DTM); bending and torsional vibration; tip mass; Timoshenko beam; natural frequencies; mode shapes

Address
Hilal Doganay Kati and Hakan Gokdag: Department of Mechanical Engineering, Bursa Technical University, Bursa, Turkey

Abstract
An exact solution for the title problem was obtained in closed-form fashion considering general boundary conditions. The expressions of moment, shear and shear coefficient (or shear factor) of cross section under the effect of arbitrary temperature distribution were first derived. In view of these relationships, the differential equations of Timoshenko beam under the effect of temperature were obtained and solved. Second, the characteristic equations of Timoshenko beam carrying several spring-mass systems under the effect of temperature were derived based on the continuity and force equilibrium conditions at attaching points. Then, the correctness of proposed method was demonstrated by a Timoshenko laboratory beam and several finite element models. Finally, the influence law of different temperature distribution modes and parameters of spring-mass system on the modal characteristics of Timoshenko beam had been studied, respectively.

Key Words
temperature; spring-mass system; mode shape; frequency; Timoshenko beam

Address
Hanbing Liu, Hua Wang, Guojin Tan, Wensheng Wang and Ziyu Liu: College of Transportation, Jilin University, Renmin Street No.5988, Changchun 130022, China

Abstract
Concentric braced frames are commonly used in steel structures to withstand lateral forces. One of the drawbacks of these systems is the possibility that the braces are buckled under compressive loads, which leads to sudden reduction of the bearing capacity of the structure. To overcome this deficiency, the idea of the Buckling Restrained Brace (BRB) has been proposed in recent years. The length of a BRB steel core can have a significant effect on its overall behavior, since it directly influences the energy dissipation capability of the member. In this study, numerical methods have been utilized for investigation of the optimum length of BRB steel cores. For this purpose, BRBs with different lengths placed into several two-dimensional framing systems with various heights were considered. Then, the Response History Analysis (RHA) was performed, and finally, the optimum steel core length of BRBs and its effect on the responses of the overall system were investigated. The results show that the shortest length where failure does not occur is the best length that can be proposed as the optimum steel core length of BRBs. This length can be obtained through a formula which has been derived and verified in this study by both analytical and numerical methods.

Key Words
buckling restrained braces; steel core; optimum length; seismic loads; failure

Address
Masoud Mirtaheri and Saeed Sehat: Department of Civil Engineering, K.N. Toosi University of Technology, Tehran, Iran
eissam Nazeryan: Department of Civil Engineering, Sharif University of Technology, Tehran, Iran

Abstract
In this paper, He\'s Variational Approach (VA) is used to solve high nonlinear vibration equations. The proposed approach leads us to high accurate solution compared with other numerical methods. It has been established that this method works very well for whole range of initial amplitudes. The method is sufficient for both linear and nonlinear engineering problems. The accuracy of this method is shown graphically and the results tabulated and results compared with numerical solutions.

Key Words
variational approach (VA); nonlinear oscillators; Runge-Kutta\'s algorithm

Address
Mahmoud Bayat: Young Researchers and Elite Club, Roudehen Branch, Islamic Azad University, Roudehen, Iran
Mahdi Bayat: Department of Civil Engineering, Roudehen Branch, Islamic Azad University, Roudehen, Iran
Iman Pakar: Young Researchers and Elite club, Mashhad Branch, Islamic Azad University, Mashhad, Iran

Abstract
The Conjugate Finite-Step Length\" (CFSL) algorithm is proposed to improve the efficiency and robustness of first order reliability method (FORM) for reliability analysis of highly nonlinear problems. The conjugate FORM-based CFSL is formulated using the adaptive conjugate search direction based on the finite-step size with simple adjusting condition, gradient vector of performance function and previous iterative results including the conjugate gradient vector and converged point. The efficiency and robustness of the CFSL algorithm are compared through several nonlinear mathematical and structural/mechanical examples with the HL-RF and \"Finite-Step-Length\" (FSL) algorithms. Numerical results illustrated that the CFSL algorithm performs better than the HL-RF for both robust and efficient results while the CFLS is as robust as the FSL for structural reliability analysis but is more efficient.

Key Words
reliability analysis; conjugate search direction; conjugate finite-step length; failure probability

Address
Behrooz Keshtegar: Department of Civil Engineering, Faculty of Engineering, University of Zabol, P.B. 9861335856 Zabol, Iran

Abstract
In present work, both the hyperbolic shear deformation theory and stress function concept are used to study the mechanical and thermal stability responses of functionally graded (FG) plates resting on elastic foundation. The accuracy of the proposed formulation is checked by comparing the computed results with those predicted by classical plate theory (CPT), first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Moreover, results demonstrate that the proposed formulation can achieve the same accuracy of the existing HSDTs which have more number of governing equations.

Key Words
functionally graded materials; mechanical-thermal buckling; plate; hyperbolic shear deformation theory; stress function

Address
Ali Houari and Mohamed Benguediab: Departement de Genie Mecanique, Faculte de Technologie, Universite Sidi Bel Abbes, Algerie
Ahmed Bakora: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
Abdelouahed Tounsi:
1) Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
2) Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes, Algeria

Abstract
This paper is concerned with thermo-mechanical vibration behavior of flexoelectric/piezoelectric nanobeams under uniform and linear temperature distributions. Flexoelectric/piezoelectric nanobeams have higher natural frequencies compared to conventional piezoelectric ones, especially at lower thicknesses. Both nonlocal and surface effects are considered in the analysis of flexoelectric/piezoelectric nanobeams for the first time. Hamilton\'s principle is employed to derive the governing equations and the related boundary conditions which are solved applying a Galerkin-based solution. Comparison study is also performed to verify the present formulation with those of previous data. Numerical results are presented to investigate the influences of the flexoelectricity, nonlocal parameter, surface elasticity, temperature rise, beam thickness and various boundary conditions on the vibration frequencies of thermally affected flexoelectric/piezoelectric nanobeam.

Key Words
vibration; flexoelectric/piezoelectric nanobeam; surface effect; nonlocal elasticity theory

Address
Farzad Ebrahimi and Mohammad Reza Barati: Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, P.O.B. 16818-34149, Iran

Abstract
The controlling and prediction of spring back is one of the most important factors in sheet metal forming processes which require high dimensional precision. The relationship between effective parameters and spring back phenomenon is highly nonlinear and complicated. Moreover, the objective function is implicit with regard to the design variables. In this paper, first the influence of some effective factors on spring back in U-die bending process was studied through some experiments and then regarding the robustness of artificial neural network (ANN) approach in predicting objectives in mentioned kind of problems, ANN was used to estimate a prediction model of spring back. Eventually, the spring back angle was optimized using the Imperialist Competitive Algorithm (ICA). The results showed that the employment of ANN provides us with less complicated and time-consuming analytical calculations as well as good results with reasonable accuracy.

Key Words
U-die bending process; spring back angle; artificial neural network; imperialist competitive algorithm

Address
Mojtaba Sheikhi Azqandi: Department of Mechanical Engineering, Bozorgmehr University of Qaenat, Qaen, Iran
Navid Nooredin: Khorasan Steel Complex Co., Neishabour, Iran
Ali Ghoddosian: Faculty of Mechanical Engineering, Semnan University, Semnan, Iran

Abstract
In this paper, an efficient higher-order shear deformation theoryis presented to analyze thermomechanical bending of temperature-dependentfunctionally graded (FG) plates resting on an elastic foundation. Further simplifying supposition are made to the conventional HSDT so that the number of unknowns is reduced, significantly facilitating engineering analysis. These theory account for hyperbolic distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Nonlinearthermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived fromthe principle of virtual displacements. Analytical solutions for the thermomechanical bending analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier\'s method). Non-dimensional results are compared for temperature-dependent FG plates and validated with those of other shear deformation theories. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature field on the thermomechanical bending characteristics. It can be concluded that the present theory is not only accurate but also simple in predicting the thermomechanical bending responses of temperature-dependentFG plates.

Key Words
functionally graded plate; higher-order plate theory; thermomechanical bending; temperature-dependent properties

Address
Amina Attia:
1) Department of Civil Engineering, Material and Hydrology Laboratory, Faculty of Technology, University of Sidi Bel Abbes, Algeria
2) Departement de Genie Civil, Institut des Sciences et de la Technologie, Centre Universitaire d\'Ain-Temouchent, Algerie
Abdelmoumen Anis Bousahla:
1) Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes, Algeria
2) Centre Universitaire Ahmed Zabana de Relizane, Algerie
Abdelouahed Tounsi:
1) Department of Civil Engineering, Material and Hydrology Laboratory, Faculty of Technology, University of Sidi Bel Abbes, Algeria
2) Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals,
31261 Dhahran, Eastern Province, Saudi Arabia
S.R. Mahmoud: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
Afaf S. Alwabli: Department of Biology, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

Abstract
This article investigates buckling behavior of a multi-phase nanocrystalline nanobeam resting on Winkler-Pasternak foundation in the framework of nonlocal couple stress elasticity and a higher order refined beam model. In this model, the essential measures to describe the real material structure of nanocrystalline nanobeams and the size effects were incorporated. This non-classical nanobeam model contains couple stress effect to capture grains micro-rotations. Moreover, the nonlocal elasticity theory is employed to study the nonlocal and long-range interactions between the particles. The present model can degenerate into the classical model if the nonlocal parameter, and couple stress effects are omitted. Hamilton\'s principle is employed to derive the governing equations and the related boundary conditions which are solved applying an analytical approach. The buckling loads are compared with those of nonlocal couple stress-based beams. It is showed that buckling loads of a nanocrystalline nanobeam depend on the grain size, grain rotations, porosities, interface, elastic foundation, shear deformation, surface effect, nonlocality and boundary conditions.

Key Words
buckling; higher-order theory; nanocrystalline nanobeam; nonlocal couple stress theory

Address
Farzad Ebrahimi and Mohammad Reza Barati: Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran P.O.B. 16818-34149

Abstract
Reinforced concrete (RC) columns, as the primary load-bearing structural components in buildings, may need to be strengthened due to material deteriorations, changes in usage, new building codes or new design requirements. The use of post compressed plates (PCP) to strengthen existing RC columns has been proven experimentally and practically to be effective in solving stress-lagging effects between the original column and the new strengthening jacket caused by the pre-existing loads. This paper presents a comprehensive summary and review of PCP strengthening techniques to strengthen preloaded RC columns. The failure mode, deformability, and ductility of the strengthened RC columns are reviewed.

Key Words
RC columns; strengthening; preloaded; post compressed plates; ultimate load capacity

Address
L. Wang: College of Civil Engineering, Nanjing Tech University, China
RKL. Su: Department of Civil Engineering, The University of Hong Kong, Hong Kong, China

Abstract
Because of sandwich structures with low weight and high stiffness have much usage in various industries such as civil and aerospace engineering, in this article, buckling and free vibration analyses of coupled micro composite sandwich plates are investigated based on sinusoidal shear deformation (SSDT) and most general strain gradient theories (MGSGT). It is assumed that the sandwich structure rested on an orthotropic elastic foundation and make of four composite face sheets with temperature-dependent material properties that they reinforced by carbon and boron nitride nanotubes and two flexible transversely orthotropic cores. Mathematical formulation is presented using Hamilton\'s principle and governing equations of motions are derived based on energy approach and applying variation method for simply supported edges under electro-magneto-thermo-mechanical, axial buckling and pre-stresses loadings. In order to predict the effects of various parameters such as material length scale parameter, length to width ratio, length to thickness ratio, thickness of face sheets to core thickness ratio, nanotubes volume fraction, pre-stress load and orthotropic elastic medium on the natural frequencies and critical buckling load of double-bonded micro composite sandwich plates. It is found that orthotropic elastic medium has a special role on the system stability and increasing Winkler and Pasternak constants lead to enhance the natural frequency and critical buckling load of micro plates, while decrease natural frequency and critical buckling load with increasing temperature changes. Also, it is showed that pre-stresses due to help the axial buckling load causes that delay the buckling phenomenon. Moreover, it is concluded that the sandwich structures with orthotropic cores have high stiffness, but because they are not economical, thus it is necessary the sandwich plates reinforce by carbon or boron nitride nanotubes specially, because these nanotubes have important thermal and mechanical properties in comparison of the other reinforcement.

Key Words
buckling and free vibration analyses; double-bonded micro composite sandwich plates; most general strain gradient theory; sinusoidal shear deformation plate theory; orthotropic foundation

Address
M.Mohammadimehr, E. Shabani Nejad and M. Mehrabi: Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, P. O. Box: 87175-53153, Iran


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