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CONTENTS
Volume 53, Number 3, February10 2015
 

Abstract
Two dimensional numerical models and physical models have been developed to study the highly nonlinear interactions between waves and breakwaters, but several of these models consider the effects of the structural dynamic responses and the shape of the breakwater axis on the wave pressures. In this study, a multi-material Arbitrary Lagrangian Eulerian (ALE) method is developed to simulate the nonlinear interactions between nonlinear waves and elastic seawalls on a coastal rubble mound breakwater, and is validated experimentally. In the experiment, a solitary wave is generated and used with a physical breakwater model. The wave impact is validated computationally using a breakwater - flume coupling model that replicates the physical model. The computational results, including those for the wave pressure and the water-on-deck, are in good agreement with the experimental results. A local breakwater model is used to discuss the effects of the structural dynamic response and different design parameters of the breakwater on wave loads, together with pressure distribution up the seawall. A large-scale breakwater model is used to numerically study the large-scale wave impact problem and the horizontal distribution of the wave pressures on the seawalls.

Key Words
wave impact; dynamic response; multi-material ALE; elastic seawalls; breakwater

Address
Yun-Feng Lou, Chuan Luo and Xian-Long Jin: State Key Laboratory of Mechanical System and Vibration, Shanghai Jiaotong University, 800 Dongchuan RD, Shanghai 200240, People\'s Republic of China

Abstract
Based on linear elastic theory of quasicrystals, various equations and solutions for quasicrystal beams are deduced systematically and directly from plane problem of two-dimensional quasicrystals. Without employing ad hoc stress or deformation assumptions, the refined theory of beams is explicitly established from the general solution of quasicrystals and the Lur\'e symbolic method. In the case of homogeneous boundary conditions, the exact equations and exact solutions for beams are derived, which consist of the fourth-order part and transcendental part. In the case of non-homogeneous boundary conditions, the exact governing differential equations and solutions under normal loadings only and shear loadings only are derived directly from the refined beam theory, respectively. In two illustrative examples of quasicrystal beams, it is shown that the exact or accurate analytical solutions can be obtained in use of the refined theory.

Key Words
deep beams; two-dimensional quasicrystals; the refined theory; general solution

Address
Yang Gao, Lian-Ying Yu: College of Science, China Agricultural University, Beijing 100083, P.R. China
Lian-Zhi Yang, Liang-Liang Zhang: College of Science, China Agricultural University, Beijing 100083, P.R. China; College of Engineering, China Agricultural University, Beijing 100083, P.R. China

Abstract
The measurement from the indentation process depends on the amount of pile-up or sink-in around the contact impressions. In this paper, finite element concept is utilized to study the pile-up and sinkin behaviour for the wide range of materials with different young\'s modulus, yield stresses, strain-hardening exponents and co-efficient of friction values. The exact indentation model is created by using the two dimensional axisymmetrical model for simulating the spherical indentation process on the lines of Taljat and Pharr (2004) work. The result shows that during spherical indentation process the amount of pile-up is greatly influenced by the strain hardening exponents in addition to other material properties and depth of penetration. The numerical results from the finite element analysis are also validated using the exact multilinear material properties obtained from the tensile testing for the materials like mild steel, brass and aluminium.

Key Words
pile-up; sink-in; indentation; finite element analysis; strain hardening

Address
S. Shankar, A. Johnney Mertens: Department of Mechatronics Engineering, Kongu Engineering College, Perundurai, Erode-638052, India
P. Loganathan: Department of Mechanical Engineering, EBET Group of Institutions, Kangayam-638108, India

Abstract
Cable-beam structures characterized by variable stiffness nonlinearities are widely found in various structural engineering applications, for example in space deployable structures. Space deployable structures in orbit experience both high temperature caused by sun\'s radiation and low temperature by Earth\'s umbral shadow. The space temperature difference is above 300K at the moment of exiting or entering Earth\'s umbral shadow, which results in structural thermally induced vibration. To understand the thermally induced oscillations, the analytical expression of Boley parameter of cable-beam structures is firstly deduced. Then, the thermally induced vibration of cable-beam structures is analyzed using finite element method to verify the effectiveness of Boley parameter. Finally, by analyzing the obtained numerical results and the corresponding Boley parameters, it can be concluded that the derived expression of Boley parameter is valid to evaluate the occurrence conditions of thermally induced vibration of cable-beam structures and the key parameters influencing structural thermal flutter are the cable stiffness and thickness of beams.

Key Words
thermally induced vibration; cable-beam structure; thermal flutter; Boley parameter; finite element method; vibration analysis

Address
Han-Qing Deng, Tuan-Jie Li , Bi-Jie Xue and Zuo-Wei Wang: School of Electromechanical Engineering, Xidian University, Xi\'an, China

Abstract
This paper presents a numerical analysis of reinforced concrete slabs under missile impact loading. The specimen used for the numerical simulation was tested by the Technical Research Center of Finland. LS-DYNA, commercial available software, is used to analyze the model. The structural components of the reinforced concrete slab, missile, and their contacts are fully modeled. Included in the analysis is material nonlinearity considering damage and failure. The results of analysis are then verified with other research results. Parametric studies with different longitudinal rebar ratios, shear bar ratios, and concrete strengths are conducted to investigate their influences on the punching behavior of slabs under the impact of a missile. Finally, efficient designs are recommended.

Key Words
missile impact; reinforced concrete slabs; LS-DYNA; dynamic analysis; punching behavior

Address
Duc-Kien Thai and Seung-Eock Kim: Department of Civil and Environmental Engineering, Sejong University, 98 Kunja-dong, Kwangjin-ku, Seoul, 143-747, South Korea

Abstract
Many hydropower stations in southwest China are located in regions of brittle rock mass with high geo-stresses. Under these conditions deep fractured zones often occur in the sidewalls of the underground caverns of a power station. The theory and methods of fracture and damage mechanics are therefore adopted to study the phenomena. First a flexibility matrix is developed to describe initial geometric imperfections of a jointed rock mass. This model takes into account the area and orientation of the fractured surfaces of multiple joint sets, as well as spacing and density of joints. Using the assumption of the equivalent strain principle, a damage constitutive model is established based on the brittle fracture criterion. In addition the theory of fracture mechanics is applied to analyze the occurrence of secondary cracks during a cavern excavation. The failure criterion, for rock bridge coalescence and the damage evolution equation, has been derived and a new sub-program integrated into the FLAC-3D software. The model has then been applied to the stability analysis of an underground cavern group of a hydropower station in Sichuan province, China. The results of this method are compared with those obtained by using a conventional elasto-plastic model and splitting depth calculated by the splitting failure criterion proposed in a previous study. The results are also compared with the depth of the relaxation and fracture zone in the surrounding rock measured by field monitoring. The distribution of the splitting zone obtained both by the proposed model and by the field monitoring measurements are consistent to the validity of the theory developed herein.

Key Words
underground cavern group; splitting failure; damage evolution equation; numerical analysis; field monitoring

Address
Song Yu: State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071, China; School of Civil Engineering, Shandong University, Ji\'nan, 250061, China
Wei-shen Zhu: State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071, China; Geotechnical and Structural Engineering Research Center, Shandong University, Ji\'nan, 250061, China
Wei-min Yang, Qing-song Ma: Geotechnical and Structural Engineering Research Center, Shandong University, Ji\'nan, 250061, China
Dun-fu Zhang: School of Civil Engineering, Shandong University, Ji\'nan, 250061, China

Abstract
In this study, nonlocal nonlinear buckling analysis of embedded polymeric temperaturedependent microplates resting on an elastic matrix as orthotropic temperature-dependent elastomeric medium is investigated. The microplate is reinforced by single-walled carbon nanotubes (SWCNTs) in which the equivalent material properties nanocomposite are estimated based on the rule of mixture. For the carbon-nanotube reinforced composite (CNTRC) plate, both cases of uniform distribution (UD) and functionally graded (FG) distribution patterns of SWCNT reinforcements are considered. The small size effects of microplate are considered based on Eringen\'s nonlocal theory. Based on orthotropic Mindlin plate theory along with von Karman geometric nonlinearity and Hamilton\'s principle, the governing equations are derived. Generalized differential quadrature method (GDQM) is applied for obtaining the buckling load of system. The effects of different parameters such as nonlocal parameters, volume fractions of SWCNTs, distribution type of SWCNTs in polymer, elastomeric medium, aspect ratio, boundary condition, orientation of foundation orthtotropy direction and temperature are considered on the nonlinear buckling of the microplate. Results indicate that CNT distribution close to top and bottom are more efficient than those distributed nearby the mid-plane for increasing the buckling load.

Key Words
nonlinear buckling; temperature-dependent; nanocomposite microplates; orthotropic elastomeric medium; FG materials

Address
Ali Akbar Mosallaie Barzoki , Abbas Loghman and Ali Ghorbanpour Arani: Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran

Abstract
On-line electric vehicle (OLEV) is a new eco-friendly transportation system that collects electricity from a power cable buried beneath the road surface, allowing the system to resolve various problems associated with batteries in electric vehicles. This paper presents a finite element (FE) based thermo-mechanical analysis of precast concrete structures that are utilized in the OLEV system. An experimental study is also conducted to identify materials used for a joint filler, and the observed experimental results are applied to the FE analysis. Traffic loading and boundary conditions are modeled in accordance with the related standards and environmental characteristics of a road system. A series of structural analyses concerning various test scenarios are conducted to investigate the sensitivity of design parameters and to evaluate the structural performance of the road system.

Key Words
on-line electronic vehicle (OLEV) system; precast concrete structure; thermo-mechanical analysis; experimental study; model sensitivity

Address
B.J. Yang, J.G. Jang, H.K. Lee: Department of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Republic of Korea
S. Na: Korea Institute of Civil Engineering and Building Technology, 283 Goyangdae-ro, Ilsanseo-gu, Goyang-si, Gyeonggi-do 411-712, Republic of Korea
H.K. Kim: School of Architecture, Chosun University, 309 Pilmun-daero, Dong-gu, Gwangju 501-759, Republic of Korea

Abstract
Multiple-step beams carrying intermediate lumped masses with/without rotary inertias are widely used in engineering applications, but in the literature for free vibration analysis of such structural systems; Bernoulli-Euler Beam Theory (BEBT) without axial force effect is used. The literature regarding the free vibration analysis of Bernoulli-Euler single-span beams carrying a number of spring-mass systems, Bernoulli-Euler multiple-step and multi-span beams carrying multiple spring-mass systems and multiple point masses are plenty, but that of Timoshenko multiple-step beams carrying intermediate lumped masses and/or rotary inertias with axial force effect is fewer. The purpose of this paper is to utilize Numerical Assembly Technique (NAT) and Differential Transform Method (DTM) to determine the exact natural frequencies and mode shapes of the axial-loaded Timoshenko multiple-step beam carrying a number of intermediate lumped masses and/or rotary inertias. The model allows analyzing the influence of the shear and axial force effects, intermediate lumped masses and rotary inertias on the free vibration analysis of the multiple-step beams by using Timoshenko Beam Theory (TBT). At first, the coefficient matrices for the intermediate lumped mass with rotary inertia, the step change in cross-section, left-end support and right-end support of the multiple-step Timoshenko beam are derived from the analytical solution. After the derivation of the coefficient matrices, NAT is used to establish the overall coefficient matrix for the whole vibrating system. Finally, equating the overall coefficient matrix to zero one determines the natural frequencies of the vibrating system and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the differential equations of the motion. The calculated natural frequencies of Timoshenko multiple-step beam carrying intermediate lumped masses and/or rotary inertias for the different values of axial force are given in tables. The first five mode shapes are presented in graphs. The effects of axial force, intermediate lumped masses and rotary inertias on the free vibration analysis of Timoshenko multiple-step beam are investigated.

Key Words
differential transform method; free vibration; intermediate lumped mass with/without rotary inertia; natural frequency; numerical assembly technique; Timoshenko multiple-step beam

Address
Yusuf Yesilce: Department of Civil Engineering, Dokuz Eylul University, 35160, Buca, Izmir, Turkey

Abstract
This paper focuses on vibration analysis of functionally graded cylindrical shell submerged in an incompressible fluid. The equation is established considering axial and lateral hydrostatic pressure based on first order shear deformation theory of shell motion using the wave propagation approach and classic Flügge shell equations. To study accuracy of the present analysis, a comparison carried out with a known data and the finite element package ABAQUS. With this method the effects of shell parameters, m, n, h/R, L/R, different boundary conditions and different power-law exponent of material of functionally graded cylindrical shells, on the frequencies are investigated. The results obtained from the present approach show good agreement with published results.

Key Words
vibration; submerged cylindrical shell; functionally graded material; first order shear deformation theory; wave propagation approach; Flügge shell equations

Address
Hossein Farahani: Department of Mechanics, College of Engineering, Hamedan Science and Research Branch, Islamic Azad University, Hamedan, Iran
Farzan Barati: Department of Mechanical Engineering, Islamic Azad University, Hamedan Brunch, Hamedan, Iran

Abstract
The use of the rigid polyurethane foam (RPF) to strengthen buried structures against blast terror has great interests from engineering experts in structural retrofitting. The aim of this study is to use the RPF to strengthen the buried structures under blast load. The buried structure is considered to study the RPF as structural retrofitting. The Guowei model (Guowei et al. 2010) is considered as a case study. The finite element analysis (FEA) is also used to model the buried structure under shock wave. The buried structure performance is studied based on detonating different TNT explosive charges. There is a good agreement between the results obtained by both the Guowei model and the proposed numerical model. The RPF improves the buried structure performance under the blast wave propagation.

Key Words
displacements; finite element analysis; blast wave; buried structure; TNT explosive charges

Address
Sherif A. Mazek and Mostafa M.A. Wahab: Civil Engineering Department, Military Technical College, Cairo, Egypt

Abstract
The wind-induced dynamic response of large-span flexible structures includes two important components-background response and resonant response. However, it is difficult to separate the two components in time-domain. To solve the problem, a relational expression of wavelet packet coefficients and power spectrum is derived based on the principles of digital signal processing and the theories of wavelet packet analysis. Further, a new approach is proposed for separation of the background response from the resonant response. Then a numerical example of frequency detection is provided to test the accuracy and the spectral resolution of the proposed approach. In the engineering example, the approach is applied to compute the power spectra of the wind-induced response of a large-span roof structure, and the accuracy of spectral estimation for stochastic signals is verified. The numerical results indicate that the proposed approach is efficient and accurate with high spectral resolution, so it is applicable for power spectral computation of various response signals of structures induced by the wind. Moreover, the background and the resonant response time histories are separated successfully using the proposed approach, which is sufficiently proved by detailed verifications. Therefore, the proposed approach is a powerful tool for the verification of the existing frequency-domain formulations.

Key Words
background response; large-span flexible structure; power spectral analysis; resonant response; wavelet packet transform; wind-induced response

Address
Jing Li, Lijuan Li and Xin Wang: Faculty of Civil and Transportation Engineering, Guangdong University of Technology, Guangzhou 510006, China


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