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CONTENTS
Volume 44, Number 3, November10 2012
 

Abstract
Free vibration analysis of arbitrary quadrilateral thick plates with internal columns and elastic edge supports is presented by using the powerful pb-2 Ritz method and Reddy\'s third order shear deformation plate theory. The computing domain of arbitrary quadrilateral planform is mapped onto a standard square form by coordinate transformation. The versatile pb-2 Ritz functions defined by the product of a two-dimensional polynomial and a basic function are taken to be the admissible functions. Substituting these displacement functions into the energy functional and minimizing the total energy by differentiation, leads to a typical eigenvalue problem, which is solved by a standard eigenvalue solver. Stiffness and mass matrices are numerically integrated over the plate by using Gaussian quadrature. The accuracy and efficiency of the proposed method are demonstrated through several numerical examples by comparison and convergency studies. A lot of numerical results for reasonable natural frequency parameters of quadrilateral plates with different combinations of elastic boundary conditions and column supports at any locations are presented, which can be used as a benchmark for future studies in this area.

Key Words
free vibration; thick plate; arbitrary quadrilateral plate; third order shear deformation theory; pb-2 Ritz method; coordinate transformation

Address
L.H. Wu: Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, P.R. China

Abstract
Existing plane stress solutions for thin plates and disks have shown several qualitative features which are difficult to handle with the use of commercial numerical codes (non-existence of solutions, singular solutions, rapid growth of the plastic zone with a loading parameter). In order to understand the effect of temperature and pressure-dependency of the yield criterion on some of such features as well as on the distribution of residual stresses and strains, a semi-analytic solution for a thin hollow disk fixed to a rigid container and subject to thermal loading and subsequent unloading is derived. The material model is elastic-perfectly/plastic. The Drucker-Prager pressure-dependent yield criterion and the equation of incompressibity for plastic strains are adopted. The distribution of residual stresses and strains is illustrated for a wide range of the parameter which controls pressure-dependency of the yield criterion.

Key Words
thin disk; plane stress conditions; pressure-dependent yield criterion; thermal loading; residual stress and strain; semi-analytic solution

Address
S. Alexandrov: Department of Mechanical Engineering and Advanced Institute for Manufacturing with High-tech Innovations, National Chung Cheng University, Chia-Yi 62102, Taiwan; A.Yu Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow 119526, Russia
Y.R. Jeng: Department of Mechanical Engineering and Advanced Institute for Manufacturing with High-tech Innovations, National Chung Cheng University, Chia-Yi 62102, Taiwan
E. Lyamina: A.Yu Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow 119526, Russia

Abstract
Structural defects such as cracks are the source of local flexibilities and cause deficiencies in structural resistance. In the engineering constructions, structural elements sometimes are subjected to axial loading. Therefore, besides crack ratios and locations, influence of applied load on the stability and dynamical characteristics should also be explored. This study offers a numerical technique for the vibration and stability analysis of axially loaded cracked beams. The model merges finite element and component mode synthesis methods. Initially, stability analysis is completed and then dynamical characteristics of beams are found. Very good conformities between outcomes of the current study and those in literature, give the confidence that proposed method is reliable and effective.

Key Words
finite element analysis; damage; failure assessment; stability; axial load

Address
Murat Kisa: Department of Mechanical Engineering, Faculty of Engineering, Harran University, Sanliurfa, Turkey

Abstract
In this article, the multi-objective optimization of cylindrical aluminum tubes under axial impact load is presented. The specific absorbed energy and the maximum crushing force are considered as objective functions. The geometric dimensions of tubes including diameter, length and thickness are chosen as design variables. D/t and L/D ratios are constricted in the range of which collapsing of tubes occurs in concertina or diamond mode. The Non-dominated Sorting Genetic Algorithm-II is applied to obtain the Pareto optimal solutions. A back-propagation neural network is constructed as the surrogate model to formulate the mapping between the design variables and the objective functions. The finite element software ABAQUS/Explicit is used to generate the training and test sets for the artificial neural networks. To validate the results of finite element model, several impact tests are carried out using drop hammer testing machine.

Key Words
cylindrical tube; axial crushing; energy absorption; neural networks; optimization

Address
M. Mirzaei: Department of Mechanical Engineering, Islamic Azad University, Damavand Branch, Dmavand, Iran
H. Akbarshahi, M. Shakeri and M. Sadighi: Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran

Abstract
Large amplitude free vibration and thermal post-buckling of shear flexible Functionally Graded Material (FGM) beams is studied using finite element formulation based on first order Timoshenko beam theory. Classical boundary conditions are considered. The ends are assumed to be axially immovable. The von-Karman type strain-displacement relations are used to account for geometric non-linearity. For all the boundary conditions considered, hardening type of non-linearity is observed. For large amplitude vibration of FGM beams, a comprehensive study has been carried out with various lengths to height ratios, maximum lateral amplitude to radius of gyration ratios, volume fraction exponents and boundary conditions. It is observed that, for FGM beams, the non-linear frequencies are dependent on the sign of the vibration amplitudes. For thermal post-buckling of FGM beams, the effect of shear flexibility on the structural response is discussed in detail for different volume fraction exponents, length to height ratios and boundary conditions. The effect of shear flexibility is observed to be predominant for clamped beam as compared to simply supported beam.

Key Words
functionally graded materials; large amplitude vibrations; post-buckling; finite element analysis; shear flexibility; von-Karman geometric non-linearity; Newton-Raphson method

Address
K. Sanjay Anandrao and R.K. Gupta: Advanced Systems Laboratory, Kanchanbagh, Hyderabad-500058, India
P. Ramchandran: DRDL, Kanchanbagh, Hyderabad-500058, India
G. Venkateswara Rao: Department of Mechanical Engineering, Vardhaman College of Engineering, Shamshabad, Hyderabad-501218, India

Abstract
The stiffness of a suspension system is provided by the bushings and the stiffness of the wheel center controls the suspension\'s elasto-kinematic (e-k) specification. So the stiffness of the wheel center is very important, but the stiffness of the wheel center is very hard to measure. The paper give a new method that we can use the stiffness of the bushings to calculate the equivalent stiffness of the wheel center, which can quickly and widely be used in all kinds of suspension structure. This method can also be used to optimize and design the suspension system. In the example we use the method to calculate the equivalent stiffness of the wheel center which meets the symmetric and positive conditions of the stiffness matrix.

Key Words
stiffness of the wheel center; stiffness of bushing; suspension structure

Address
Pinbin Zhao, Guo-feng Yao, Min Wang, Xumin Wang and Jianhui Li: Mechanical Department, Nanling Campus, Jilin University, Changchun 130022, P. R. China

Abstract
In recent years, the need for optimal design of structures under time-history loading aroused great attention in researchers. The main problem in this field is the extremely high computational demand of time-history analyses, which may convert the solution algorithm to an illogical one. In this paper, a new framework is developed to solve the size optimization problem of steel truss structures subjected to ground motions. In order to solve this problem, the covariance matrix adaptation evolution strategy algorithm is employed for the optimization procedure, while a generalized regression neural network is utilized as a meta-model for fitness approximation. Moreover, the computational cost of time-history analysis is decreased through a wavelet analysis. Capability and efficiency of the proposed framework is investigated via two design examples, comprising of a tower truss and a footbridge truss.

Key Words
size optimization; space truss structure; time-history analysis; the covariance matrix adaptation evolution strategy (CMA-ES); generalized regression neural network (GRNN); wavelet analysis (WA)

Address
A. Kaveh, M. Fahimi-Farzam and M. Kalateh-Ahani: Centre of Excellence for Fundamental Studies in Structural Engineering, Iran University of Science and Technology, Narmak, Tehran 16, Iran

Abstract
In this study the investigation of large deflections subject in compliant mechanisms is presented using homotopy perturbation method (HPM). The main purpose is to propose a convenient method of solution for the large deflection problem in compliant mechanisms in order to overcome the difficulty and complexity of conventional methods, as well as for the purpose of mathematical modeling and optimization. For simplicity, a cantilever beam of linear elastic material under horizontal, vertical and bending moment end point load is considered. The results show that the applied method is very accurate and capable for cantilever beams and can be used for a large category of practical problems for the aim of optimization. Also the consequence of effective parameters on the large deflection is analyzed and presented.

Key Words
compliant beam; homotopy perturbation method; large deflection; slope variation; nonlinear problem

Address
A. Khavaji, D.D. Ganji, N. Roshan, M. Hatami and A. Hasanpour: Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran
R. Moheimani: School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran


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