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CONTENTS
Volume 53, Number 4, February25 2015
 

Abstract
In this paper, a two-layer partial interaction composite beams model considering the higher order shear deformation of sub-elements is built. Then, the governing differential equations and boundary conditions for static analysis of linear elastic higher order composite beams are formulated by means of principle of minimum potential energy. Subsequently, analytical solutions for cantilever composite beams subjected to uniform load are presented by Laplace transform technique. As a comparison, FEM for this problem is also developed, and the results of the proposed FE program are in good agreement with the analytical ones which demonstrates the reliability of the presented exact and finite element methods. Finally, parametric studies are performed to investigate the influences of parameters including rigidity of shear connectors, ratio of shear modulus and slenderness ratio, on deflections of cantilever composite beams, internal forces and stresses. It is revealed that the interfacial slip has a major effect on the deflection, the distribution of internal forces and the stresses.

Key Words
composite beams; Timoshenko beam theory; higher order shear deformation; shear effect; laplace transform; finite element method

Address
Guang-hui He and Xiao Yang: Department of Civil Engineering, Shanghai University, Shanghai, China

Abstract
This research investigates the thermoelastic transient behavior of a thermally loaded slab made of a thermal diode-like material which has two directional thermal conductivity values (low and high). Finite difference analysis is used to obtain the elastic response of the slab based on the temperature solutions. It is found that the rate of heat transfer through the thickness of the slab decreases with reducing the ratio between the low and high thermal conductivity values (R). In addition, reducing R makes the slab less responsive to the thermal load when heated from the direction associated with the low thermal conductivity value.

Key Words
thermal diode like material; thermoelastic transient response; finite difference analysis; low-tohigh thermal conductivity ratio

Address
Feras H. Darwish: Aeronautical Engineering Department, Jordan University of Science and Technology, Irbid 22110, Jordan
Mohammad A. Al-Nimr and Mohammad I. Hatamleh: Mechanical Engineering Department, Jordan University of Science and Technology, Irbid 22110, Jordan

Abstract
In this article, nonlinear finite element solutions of bending responses of functionally graded spherical panels are presented. The material properties of functionally graded material are graded in thickness direction according to a power-law distribution of volume fractions. A general nonlinear mathematical shallow shell model has been developed based on higher order shear deformation theory by taking the geometric nonlinearity in Green-Lagrange sense. The model is discretised using finite element steps and the governing equations are obtained through variational principle. The nonlinear responses are evaluated through a direct iterative method. The model is validated by comparing the responses with the available published literatures. The efficacy of present model has also been established by demonstrating a simulation based nonlinear model developed in ANSYS environment. The effects of power-law indices, support conditions and different geometrical parameters on bending behaviour of functionally graded shells are obtained and discussed in detail.

Key Words
FGM; nonlinear bending; Green-Lagrange nonlinearity; HSDT; FEM

Address
Vishesh Ranjan Kar and Subrata Kumar Panda: Department of Mechanical Engineering, National Institute of Technology, Rourkela, India

Abstract
Fracture analysis and remaining life prediction has been carried out for aluminium alloy (Al2014A) plate panels with concentric stiffener by varying sizes and positions under fatigue loading. Tension coupon tests and compact tension tests on 2014A have been carried out to evaluate mechanical properties and crack growth constants. Domain integral technique has been used to compute the Stress intensity factor (SIF) for various cases. Generalized empirical expressions for SIF have been derived for various positions of stiffener and size. From the study, it can be concluded that the remaining life for stiffened panel for particular size and position can be estimated by knowing the remaining life of corresponding unstiffened panel.

Key Words
stiffened panel; fracture analysis; stress intensity factor; remaining life; concentric stiffener

Address
A. Ramachandra Murthy, G.S. Palani, Smitha Gopinath and Nagesh R. Iyer: CSIR-Structural Engineering Research Centre, Taramani, Chennai, 600 113, India
Rakhi Sara Mathew: Saintgits College of Engineering, Pathamuttom P O, Kottayam, Kerala, 686 532, India

Abstract
In this paper optimization of volume fraction distribution in a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) and subjected to steady state thermal and mechanical loadings is considered. The finite element method with graded material properties within each element (graded finite elements) is used to model the structure. Volume fractions of constituent materials on a finite number of design points are taken as design variables and the volume fractions at any arbitrary point in the cylinder are obtained via cubic spline interpolation functions. The objective function selected as having the normalized effective stress equal to one at all points that leads to a uniform stress distribution in the structure. Genetic Algorithm jointed with interior penalty-function method for implementing constraints is effectively employed to find the global solution of the optimization problem. Obtained results indicates that by using the uniform distribution of normalized effective stress as objective function, considerably more efficient usage of materials can be achieved compared with the power law volume fraction distribution. Also considering uniform distribution of safety factor as design criteria instead of minimizing peak effective stress affects remarkably the optimum volume fractions.

Key Words
2D heterogeneous;volume fraction optimization; thermo-mechanical stresses;genetic algorithm

Address
Masoud Asgari: Faculty of Mechanical Engineering, K. N. Toosi University of Technology, Pardis Street, Molla-Sadra Avenue, Vanak Square, P.O. Box 19395-1999, Tehran, Iran

Abstract
In this paper, a new damage indicator based on mode shape data is introduced to identify damage in beam structures. In order to construct the indicator proposed, the mode shape, mode shape slope and mode shape curvature of a beam before and after damage are utilized. Mode shape data of the beam are first obtained here using a finite element modeling and then the slope and curvature of mode shape are evaluated via the central finite difference method. In order to assess the robustness of the proposed indicator, two test examples including a simply supported beam and a two-span beam are considered. Numerical results demonstrate that using the proposed indicator, the location of single and multiple damage cases having different characteristics can be accurately determined. Moreover, the indicator shows a better performance when compared with a well-known indicator found in the literature.

Key Words
damage detection; damage indicator; beam structure; mode shape data

Address
O. Yazdanpanah, S.M. Seyedpoor: Department of Civil Engineering, Shomal University, Amol, Iran
H. Akbarzadeh Bengar: Department of Civil Engineering, University of Mazandaran, Babolsar, Iran

Abstract
A nonlinear Finite Element (FE) algorithm is proposed to analyze the Reinforced Concrete (RC) columns subjected to Cyclic Loading (CL), Cyclic Oriented Lateral Force and Axial Loading (COLFAL), Monotonic Loading (ML) or Oriented Pushover Force and Axial Loading (OPFAL) in any direction. In the proposed algorithm, the following parameters are considered: uniaxial behavior of concrete and steel elements, the pseudo-plastic hinge produced in the critical sections, and global behavior of RC columns. In the proposed numerical simulation, the column is discretized into two Macro-Elements (ME) located between the pseudo-plastic hinges at critical sections and the inflection point. The critical sections are discretized into Fixed Rectangular Finite Elements (FRFE) in general cases of CL, COLFAL or ML and are discretized into Variable Oblique Finite Elements (VOFE) in the particular cases of ML or OPFAL. For pushover particular case, a fairly fast converging and properly accurate nonlinear simulation method is proposed to assess the behavior of RC columns. The proposed algorithm has been validated by the results of tests carried out on full-scale RC columns.

Key Words
Numerical simulation; reinforced concrete; columns; cyclic or monotonic loading

Address
Kabir Sadeghi: Civil Engineering Department, Girne American University, Karmi Campus, Girne, KKTC, via Mersin 10, Turkey

Abstract
Delaminations and cracks are common failures in structures. They may significantly reduce the stiffness of the structure and affect their vibration characteristics. In the present study, an analytical solution is developed to study the effect of an edge crack on the vibration characteristics of delaminated beams. The rotational spring model, the „free mode‟ and „constrained mode‟ assumptions in delamination vibration are adopted. This is the first study on how an edge crack affects the vibration characteristic of delaminated beams and new nondimensional parameters are developed accordingly. The crack may occur inside or outside the delaminated area and both cases are studied. Results show that the effect of delamination length and thickness-wise location on reducing the natural frequencies is aggravated by an increasing crack depth. The location of the crack also influences the effect of delamination, but such influence is different between crack occurring inside and outside the delaminated area. The difference of natural frequencies between „free mode‟ and „constrained mode‟ increases then decreases as the crack moves from one side of the delaminated region to the other side, peaking at the middle. The analytical results of this study can serve as the benchmark for FEM and other numerical solutions.

Key Words
vibration; beam; delamination; crack; natural frequency

Address
Yang Liu and Dong W. Shu: School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore

Abstract
We apply higher-order beam theory to analyze the deflections and stresses of a cantilevered single leaf flexure in bending. Our equations include shear deformation and the warping effect in bending. The results are compared with Euler-Bernoulli and Timoshenko beam theory, and are verified by finite element analysis (FEA). The results show that the higher-order beam theory is in a good agreement with the FEA results, with errors of less than 10%. These results indicate that the analysis of the deflections and stresses of a single leaf flexure should consider the shear and warping effects in bending to ensure high precision mechanism design.

Key Words
single leaf flexure; higher-order beam theory; shear deformation; bending; stress analysis

Address
Nghia Huu Nguyen and Dong-Yeon Lee: School of Mechanical Engineering, Yeungnam University, Gyeongsan 712-749, Republic of Korea

Abstract
RC buildings constitute the prevailing type of construction in earthquake-prone region like Kathmandu Valley. Most of these building constructions were based on conventional methods. In this context, the present paper studied the seismic behaviour of existing RC buildings in Kathmandu Valley. For this, four representative building structures with different design and construction, namely a building: (a) representing the non-engineered construction (RC1 and RC2) and (b) engineered construction (RC3 and RC4) has been selected for analysis. The dynamic properties of the case study building models are analyzed and the corresponding interaction with seismic action is studied by means of non-linear analyses. The structural response measures such as capacity curve, inter-storey drift and the effect of geometric nonlinearities are evaluated for the two orthogonal directions. The effect of plan and vertical irregularity on the performance of the structures was studied by comparing the results of two engineered buildings. This was achieved through non-linear dynamic analysis with a synthetic earthquake subjected to X, Y and 45o loading directions. The nature of the capacity curve represents the strong impact of the P-delta effect, leading to a reduction of the global lateral stiffness and reducing the strength of the structure. The non-engineered structures experience inter-storey drift demands higher than the engineered building models. Moreover, these buildings have very low lateral resistant, lesser the stiffness and limited ductility. Finally, a seismic safety assessment is performed based on the proposed drift limits. Result indicates that most of the existing buildings in Nepal exhibit inadequate seismic performance.

Key Words
non-engineered buildings; performance evaluation; P-Delta effect; seismic vulnerability

Address
Hemchandra Chaulagain: Civil Engineering Department, University of Aveiro, 3810-193 Aveiro, Portugal; Oxford College of Engineering and Management, Gaindakot, Nawalparashi, Nepal
Hugo Rodrigues: School of Technology and Management, Polytechnic Institute of Leiria, Leiria, Portugal
Enrico Spacone: University of Chieti-Pescara, Department PRICOS – Architettura, 65127 Pescara, Italy
Humberto Varum: Department of Civil Engineering, Faculty of Engineering, University of Porto, Porto, Portugal

Abstract
In this paper, we propose a new method for taking into account uncertainties based on the projection on polynomial chaos. The new approach is used to determine the dynamic response of a spur gear system with uncertainty associated to gear system parameters and this uncertainty must be considered in the analysis of the dynamic behavior of this system. The simulation results are obtained by the polynomial chaos approach for dynamic analysis under uncertainty. The proposed method is an efficient probabilistic tool for uncertainty propagation. It was found to be an interesting alternative to the parametric studies. The polynomial chaos results are compared with Monte Carlo simulations.

Key Words
uncertainty; spur gear system; polynomial chaos; random variable; Monte Carlo simulation; gear parameter

Address
A. Guerine: Department of Mechanical Engineering, INSA of Rouen, University Road, Saint Etienne de Rouvray, France, Department of Mechanical Engineering, National School of Engineers of Sfax, Soukra Road, Sfax, Tunisia
A. El Hami: Department of Mechanical Engineering, INSA of Rouen, University Road, Saint Etienne de Rouvray, France
T. Fakhfakh, M. Haddar: Department of Mechanical Engineering, National School of Engineers of Sfax, Soukra Road, Sfax, Tunisia

Abstract
Natural frequencies of the structural systems should be far away from the excitation frequency in order to avoid or reduce the destructive effects of dynamic loads on structures. To accomplish this goal, a structural optimization on size and shape has been performed considering frequency constraints. Such an optimization problem has highly nonlinear property. Thus, the quality of the solution is not independent of the optimization technique to be applied. This study presents the performance evaluation of the recently proposed meta-heuristic algorithm called Teaching Learning Based Optimization (TLBO) as an optimization engine in the weight optimization of the truss structures under frequency constraints. Some examples regarding the optimization of trusses on shape and size with frequency constraints are solved. Also, the results obtained are tabulated for comparison. The results demonstrated that the performance of the TLBO is satisfactory. Additionally, TLBO is better than other methods in some cases.

Key Words
teaching learning based optimization; frequency constraints; shape and size optimization; trusses

Address
Tayfun Dede and Vedat Togan: Department of Civil Engineering, Karadeniz Technical University, 61080 Trabzon, Turkey


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