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CONTENTS
Volume 55, Number 2, July25 2015
 

Abstract
A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of eccentric hemi-spherical shells of revolution with variable thickness. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components ur, uo, and uz in the radial, circumferential, and axial directions, respectively, are taken to be periodic in o and in time, and algebraic polynomials in the r and z directions. Potential and kinetic energies of eccentric hemi-spherical shells with variable thickness are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to three or four-digit exactitude is demonstrated for the first five frequencies of the shells. Numerical results are presented for a variety of eccentric hemi-spherical shells with variable thickness.

Key Words
vibration; eccentric hemi-spherical shell; variable thickness; shell of revolution

Address
Jae-Hoon Kang: Department of Architectural Engineering, Chung-Ang University, Seoul, 156-756 South Korea

Abstract
This paper describes a study of the collision of hard steel spheres against aluminium thin circular plates at speeds up to 140 m/s. The tests were monitored by a high speed camera and a chronoscope, which allowed the determination of the ballistic limit and the plate deformation pattern. Quasi-static material parameters were obtained from tests on a universal testing machine and dynamic mechanical characterization of two aluminium alloys were conducted in a split Hopkinson pressure bar. Using a damage model, the perforation of the plates was simulated by finite element analysis. Axisymmetric, shell and solid elements were employed with various parameters of the numerical analysis being thoroughly discussed, in special, the dynamic model parameters. A good agreement between experiments and the numerical analysis was obtained.

Key Words
impact tests; ballistic limit; dynamic material properties; numerical analysis

Address
Giancarlo B. Micheli: Group of Solid Mechanics and Structural Impact–GMSIE, Department of Mechatronics and Mechanical Systems Engineering, University of Sao Paulo, Av. Prof. Mello Moraes, 2231, 05508-900 São Paulo, SP, Brazil; National Institute of Metrology, Quality and Technology–Inmetro, Av. N. Sa. das Graças, 50, 25250-020,
Duque de Caxias, RJ, Brazil
Larissa Driemeier: National Institute of Metrology, Quality and Technology–Inmetro, Av. N. Sa. das Graças, 50, 25250-020, Duque de Caxias, RJ, Brazil
Marcílio Alves: Group of Solid Mechanics and Structural Impact–GMSIE, Department of Mechatronics and Mechanical Systems Engineering, University of Sao Paulo, Av. Prof. Mello Moraes, 2231, 05508-900 São Paulo, SP, Brazil

Abstract
In this study, nonlinear transverse vibrations of tensioned Euler-Bernoulli nanobeams are studied. The nonlinear equations of motion including stretching of the neutral axis and axial tension are derived using nonlocal beam theory. Forcing and damping effects are included in the equations. Equation of motion is made dimensionless via dimensionless parameters. A perturbation technique, the multiple scale methods is employed for solving the nonlinear problem. Approximate solutions are applied for the equations of motion. Natural frequencies of the nanobeams for the linear problem are found from the first equation of the perturbation series. From nonlinear term of the perturbation series appear as corrections to the linear problem. The effects of the various axial tension parameters and different nonlocal parameters as well as effects of different boundary conditions on the vibrations are determined. Nonlinear frequencies are estimated; amplitude-phase modulation figures are presented for simple-simple and clamped-clamped cases.

Key Words
nanobeam; transverse vibration; axial tension; perturbation method; nonlocal elasticity

Address
Suleyman M. Bagdatli: Faculty of Engineering, Department of Mechanical Engineering, Celal Bayar University, 45140, Yunusemre, Manisa, Turkey

Abstract
In this paper, an optimization process using Genetic Algorithm (GA) that mimics biological processes is presented for optimum design of planar frames with semi-rigid connections by selecting suitable standard sections from a specified list taken from American Institute of Steel Construction (AISC). The stress constraints as indicated in AISC-LRFD (American Institute of Steel Construction - Load and Resistance Factor Design), maximum lateral displacement constraints and geometric constraints are considered for optimum design. Two different planar frames with semi-rigid connections taken from the literature are carried out first without considering concrete slab effects in finite element analyses and the results are compared with the ones available in literature. The same optimization procedures are then repeated for full and semi rigid planar frames with composite (steel and concrete) beams. A program is developed in MATLAB for all optimization procedures. Results obtained from this study proved that consideration of the contribution of the concrete on the behavior of the floor beams provides lighter planar frames.

Key Words
genetic algorithm, weight optimization, planar frame, composite beams, semi-rigid connection

Address
Musa Artar: Department of Civil Engineering, Bayburt University, Bayburt 69000, Turkey
Ayse T. Daloglu: Department of Civil Engineering, Karadeniz Technical University, Trabzon 61000, Turkey

Abstract
This study\'s primary aim is to check the existence of a representative volume element for granular materials and determine the link between the properties (responses) of macro structures and the size of the discrete particle assembly used to represent a constitutive relation in a two-scale model. In our two-scale method the boundary value problem on the macro level was solved using finite element method, based on the Cosserat continuum; the macro stresses and modulus were obtained using a solution of discrete particle assemblies at certain element integration points. Meanwhile, discrete particle assemblies were solved using discrete element method under boundary conditions provided by the macro deformation. Our investigations focused largely on the size effects of the discrete particle assembly and the radius of the particle on macro properties, such as deformation stiffness, bearing capacity and the residual strength of the granular structure. According to the numerical results, we suggest fitting formulas linking the values of different macro properties (responses) and size of discrete particle assemblies. In addition, this study also concerns the configuration and displacement fluctuation of discrete particle assemblies on the micro level, accompanied with the evolution of bearing capacity and deformation on the macro level.

Key Words
granular materials; two-scale modeling; representative volume element; strain localization; displacement fluctuation

Address
Xihua Chu, Cun Yu, Chenxi Xiu and Yuanjie Xu: Department of Engineering Mechanics, Wuhan University, Wuhan 430072, China

Abstract
The influence of the interface imperfect bonding on the flexural wave dispersion in the bilayered hollow circular cylinder is studied with utilizing three-dimensional linear theory of elastodynamics. The shear-spring type model is used for describing the imperfect bonding on the interface between the layers and the degree of the imperfectness is estimated through the dimensionless shear-spring parameters which enter the mentioned model. The method for finding the analytical expressions for the sought values and dispersion equation are discussed and detailed. Numerical results on the lowest first and second modes are presented and analyzed. These results are obtained for various values of the shear-spring parameters. According to these results, in particular, it is established that as a results of the imperfection of the bonding between the layers the new branches of the dispersion related the first fundamental mode arise and the character of the dispersion curve related to the second mode becomes more complicated.

Key Words
layered structures; debonding; analytical modelling; flexural waves; dispersion

Address
Cengiz Ipek: Member of 2nd Committee of Kocaeli Chamber of Commerce, Kocaeli, Turkey

Abstract
Analytical solutions for modeling geotextile tubes during the filling process and approximation method to determine the densified tube shape are reviewed. The geotextile tube filling analysis is based on Plaut & Suherman\'s two-dimensional solution for geotextile tubes having a weightless and frictionless inextensible membrane resting on a rigid horizontal foundation subjected to internal and external hydrostatic pressures. The approximation for the densified tube shape developed by Leshchinsky et al. was adopted. A modified method for approximating the densified tube shape based on an areal-strain deformation analysis is introduced. Design diagrams useful for approximating geotextile tube measurements in the design process are provided.

Key Words
geotextile tube; membrane structure; analytic solution; structural analysis; design charts

Address
Hyeong-Joo Kim and Myoung-Soo Won: Department of Civil Engineering, Kunsan National University, Gunsan 573-701, Republic of Korea
Tae-Woong Park, Min-Jun Choi and Jay C. Jamin: School of Civil and Environmental Engineering, Kunsan National University, Gunsan 573-701, Republic of Korea

Abstract
Large-amplitude vibration of overhead sign structures can cause unfavorable psychological responses in motorists, interfere with readability of the signs, and lead to fatigue cracking in the sign structures. Field experience in Texas suggests that an overhead sign structure can vibrate excessively when supported within the span of a highway bridge instead of at a bent. This study used finite element modeling to analyze the dynamic displacement response of three hypothetical sign structures subjected to truckpassage-induced vertical oscillations recorded for the girders from four actual bridges. The modeled sign bridge structures included several span lengths based on standard design practices in Texas and were mounted on precast concrete I-girder bridges. Results revealed that resonance with bridge girder vertical vibrations can amplify the dynamic displacement of sign structures, and a specific range of frequency ratios subject to undesirable amplification was identified. Based on these findings, it is suggested that this type of sign structure be located at a bridge bent if its vertical motion frequency is within the identified range of bridge structure excitation frequencies. Several alternatives are investigated for cases where this is not possible, including increasing sign structure stiffness, reducing sign mass, and installing mechanical dampers.

Key Words
overhead sign structure; sign structure vibration; bridge vibration; dynamic displacement

Address
Janghwan Kim: Samsung Heavy Industries Ltd., Gyeongsangnam-Do 656-710, Republic of Korea
Jun Won Kang: Department of Civil Engineering, Hongik University, Seoul 121-791, Republic of Korea
Hieyoung Jung: Department of Civil Engineering, University of Seoul, Seoul 130-743, Republic of Korea
Seung-woo Pack: Samsung Heavy Industries Ltd., Gyeongsangnam-Do 656-710, Republic of Korea

Abstract
Confinement is known to have important influence on ductility of high-strength concrete (HSC) members and it may therefore be anticipated that this parameter would also affect notably the moment redistribution in these members. The correctness of this \"common-sense knowledge\" is examined in the present study. A numerical test is performed on two-span continuous reinforced HSC beams with and without confinement using an experimentally validated nonlinear model. The results show that the effect of confinement on moment redistribution is totally different from that on flexural ductility. The moment redistribution at ultimate limit state is found to be almost independent of the confinement, provided that both the negative and positive plastic hinges have formed at failure. The numerical findings are consistent with tests performed on prototype HSC beams. Several design codes are evaluated. It is demonstrated that the code equations by Eurocode 2 (EC2), British Standards Institution (BSI) and Canadian Standards Association (CSA) can well reflect the effect of confinement on moment redistribution in reinforced HSC beams but the American Concrete Institute (ACI) code cannot.

Key Words
high-strength concrete; confinement; moment redistribution; ductility; continuous beams

Address
Tiejiong Lou and Sergio M.R. Lopes: CEMUC, Department of Civil Engineering, University of Coimbra, Coimbra 3030-788, Portugal
Adelino V. Lopes: Department of Civil Engineering, University of Coimbra, Coimbra 3030-788, Portugal

Abstract
The buckling equations of filament wound composite cylindrical shell are established. The coefficients Kij and Lij of the buckling equations are determined by solving the equations. The geometric analysis and the effective stiffness calculation for the fiber crossover and undulation region are respectively accomplished. Using the effective stiffness of the undulation region, the specific formulas of the coefficients Kij and Lij of the buckling equations are determined. Numerical examples of the buckling critical loads have been performed for the different winding angles and stacking sequences cylindrical shell designs. It can be concluded that the fiber undulation results in the less effect on the buckling critical loads Pcr. Pcr increases with the thickness-radius ratio. The effect on Pcr due to the fiber undulation is more obvious with the thickness-radius ratio. Pcr decreases with the length-radius ratio. The effect on Pcr due to the fiber undulation can be neglected when the ratio is large.

Key Words
filament winding composite; cylindrical shell; buckling; fiber undulation; external pressure

Address
Zhangxin Guo: College of Mechanics, Taiyuan University of Technology, Taiyuan 030024, China; Department of Engineering Mechanics, Northwestern Polytechnical University, Xi\'an 710072, China
Xiaoping Han: Department of Engineering Mechanics, Northwestern Polytechnical University, Xi\'an 710072, China
Meiqing Guo and Zhijun Han: Taiyuan University of Technology, Taiyuan 030024, China

Abstract
The vibrations caused by metro operation propagate through surrounding soil, further induce secondary vibrations of the nearby underground structures and adjacent buildings. In order to investigate the effects of vibrations caused by metro on use performance of buildings, vibration experiment of Chengdu museum was carried out firstly. Then, the coupling tunnel-soil-structure finite element model was established with software ANSYS detailedly, providing a useful tool for investigating the vibration performances of structures. Furthermore, the dynamic responses and vibration predictions of museum building were obtained respectively by the whole process time-domain analysis and frequency-domain analysis, which were compared with the vibration reference values of museum. Quantitative analyses of the museum building performance were carried out, and the possible tendency and changing laws of vibration level with floors were proposed. Finally, the related vibration isolation measures were compared and discussed. The tests and analysis results show that: The vertical vibration responses almost increased with the increasing of building floors, while weak floors existed for the curve of horizontal vibration; The vertical vibrations were larger than the horizontal vibrations, indicating the vibration performances of building caused by metro were characterized with vertical vibrations; The frequencies of the museum corresponding to the peak vibration levels were around 6~17Hz; The damping effect of structure with 33m-span cantilever on vertical vibration was obvious, however, the damping effect of structure with foundation vibration isolators was not obvious.

Key Words
metro vibration; museum structure vibration; vibration experiment; finite element method; performance analysis

Address
Weiguo Yang, Meng Wang, Jianquan Shi and Nan Zhang: School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China
Jiaqi Ge and Botao Ma: China Aviation Planning and Construction Development Co., Ltd, Beijing 100120, China

Abstract
Parametric resonance of shear deformable composite skew plates subjected to non-uniform (parabolic) and linearly varying periodic edge loading is studied for different boundary conditions. The skew plate structural model is based on higher order shear deformation theory (HSDT), which accurately predicts the numerical results for thick skew plate. The total energy functional is derived for the skew plates from total potential energy and kinetic energy of the plate. The strain energy which is the part of total potential energy contains membrane energy, bending energy, additional bending energy due to additional change in curvature and shear energy due to shear deformation, respectively. The total energy functional is solved using Rayleigh-Ritz method in conjunction with boundary characteristics orthonormal polynomials (BCOPs) functions. The orthonormal polynomials are generated for unit square domain using Gram-Schmidt orthogonalization process. Bolotin method is followed to obtain the boundaries of parametric resonance region with higher order approximation. These boundaries are traced by the periodic solution of Mathieu-Hill equations with period T and 2T. Effect of various parameters like skew angle, span-tothickness ratio, aspect ratio, boundary conditions, static load factor on parametric resonance of skew plate have been investigated. The investigation also includes influence of different types of linearly varying loading and parabolically varying bi-axial loading.

Key Words
skew plate; BCOPs, parametric resonance; non-uniform in-plane loading; dynamic instability

Address
Rajesh Kumar: Department of Civil Engineering, Indian Institute of Technology Kharagpur, India
Abhinav Kumar and Sarat Kumar Panda: Department of Civil Engineering, Indian School of Mines Dhanbad, India


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