• Computers and Concrete
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• v.25 no.2
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• pp.133-144
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• 2020

This paper aims to study vibration characteristics of chiral and zigzag double-walled carbon nanotubes entrenched on Donnell shell model. The Eringen's nonlocal elastic equations are being combined with Donnell shell theory to observe small scale response. Wave propagation is proposed technique to establish field equations of model subjected to four distinct end supports. A nonlocal model has been formulated to explore the frequency spectrum of both chiral and zigzag double-walled CNTs along with diversity of indices and nonlocal parameter. The significance of scale effect in relevance of length-to-diameter and thickness- to- radius ratios are discussed and displayed in detail. The numerical solution based on this nonlocal Donnell shell model can be further used to predict other frequency phenomena of double-walled and multi-walled CNTs.

• Steel and Composite Structures
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• v.36 no.6
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• pp.643-656
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• 2020

This article presents a comprehensive static analysis of simply supported cross-ply carbon nanotubes reinforced composite (CNTRC) laminated nanobeams under various loading profiles. The nonlocal strain gradient constitutive relation is exploited to present the size-dependence of nano-scale. New higher shear deformation beam theory with hyperbolic function is proposed to satisfy the zero-shear effect at boundaries and parabolic variation through the thickness. Carbon nanotubes (CNTs), as the reinforced elements, are distributed through the beam thickness with different distribution functions, which are, uniform distribution (UD-CNTRC), V- distribution (FG-V CNTRC), O- distribution (FG-O CNTRC) and X- distribution (FG-X CNTRC). The equilibrium equations are derived, and Fourier series function are used to solve the obtained differential equation and get the response of nanobeam under uniform, linear or sinusoidal mechanical loadings. Numerical results are obtained to present influences of CNTs reinforcement patterns, composite laminate structure, nonlocal parameter, length scale parameter, geometric parameters on center deflection ad stresses of CNTRC laminated nanobeams. The proposed model is effective in analysis and design of composite structure ranging from macro-scale to nano-scale.

• Structural Engineering and Mechanics
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• v.71 no.3
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• pp.257-269
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• 2019

This paper develops a nonlocal strain gradient plate model for damping vibration analysis of smart magneto-electro-viscoelastic nanoplates resting on visco-Pasternak medium. For more accurate analysis of nanoplate, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. Viscoelastic effect which is neglected in all previous papers on magneto-electro-viscoelastic nanoplates is considered based on Kelvin-Voigt model. Governing equations of a nonlocal strain gradient smart nanoplate on viscoelastic substrate are derived via Hamilton's principle. Galerkin's method is implemented to solve the governing equations. Effects of different factors such as viscoelasticity, nonlocal parameter, length scale parameter, applied voltage and magnetic potential on damping vibration characteristics of a nanoplate are studied.

• Transactions of Materials Processing
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• v.13 no.3
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• pp.248-252
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• 2004

The mechanical properties of polycrystalline thin-films, critical for Micro-Electro-Mechanical Systems (MEMS) components, are known to have the size effect and the scatter in the length scale of microns by the numbers of intensive investigation by experiments and simulations. So, the consideration of the microstructure is essential to cover these length scale effects. The lattice based stochastic model for the microstructure evolution is used to simulate the actual microstructure, and the fast and reliable algorithm is described in this paper. The kinetics parameters, which are the key parameters for the microstructure evolution based on the nucleation and growth mechanism, are extracted from the given micrograph of a polycrystalline material by an inverse method. And the method is verified by the comparison of the quantitative measures, the number of grains and the grain size distribution, for the actual and simulated microstructures. Finite element mesh is then generated on this lattice based microstructure by the developed code. And the statistical finite element analysis is accomplished for selected microstructure.

• Computers and Concrete
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• v.29 no.6
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• pp.393-405
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• 2022

Lightweight concrete is a superior material due to its light weight and high strength. There however remain significant lacunae in engineering knowledge with regards to shear failure of lightweight fiber reinforced concrete beams. The main aim of the present study is to investigate the optimum usage of steel fibers in lightweight fiber reinforced concrete (LWFRC). Multi-scale finite element model calibrated with experimental results is developed to study the effect of steel fibers on the mechanical properties of LWFRC beams. To decrease the amount of steel fibers, it is preferred to reinforce only the middle section of the LWFRC beams, where the flexural stresses are higher. For numerical simulation, a multi-scale finite element model was developed. The cement matrix was modeled as homogeneous and uniform material and both steel fibers and lightweight coarse aggregates were randomly distributed within the matrix. Considering more realistic assumptions, the bonding between fibers and cement matrix was considered with the Cohesive Zone Model (CZM) and its parameters were determined using the model update method. Furthermore, conformity of Load-Crack Mouth Opening Displacement (CMOD) curves obtained from numerical modeling and experimental test results of notched beams under center-point loading tests were investigated. Validating the finite element model results with experimental tests, the effects of fibers' volume fraction, and the length of the reinforced middle section, on flexural and residual strengths of LWFRC, were studied. Results indicate that using steel fibers in a specified length of the concrete beam with high flexural stresses, and considerable savings can be achieved in using steel fibers. Reducing the length of the reinforced middle section from 50 to 30 cm in specimens containing 10 kg/m3 of steel fibers, resulting in a considerable decrease of the used steel fibers by four times, whereas only a 7% reduction in bearing capacity was observed. Therefore, determining an appropriate length of the reinforced middle section is an essential parameter in reducing fibers, usage leading to more affordable construction costs.

• Advances in nano research
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• v.10 no.3
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• pp.281-293
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• 2021

This paper presents a new nonlocal Hyperbolic Shear Deformation Beam Theory (HSDBT) for the free vibration of porous Functionally Graded (FG) nanobeams. A new displacement field containing integrals is proposed which involves only three variables. The present model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect and its account for shear deformation by a hyperbolic variation of all displacements through the thickness without using the shear correction factor. It has been observed that during the manufacture of Functionally Graded Materials (FGMs), micro-voids and porosities can occur inside the material. Thus, in this work, the investigation of the free vibration analysis of FG beams taking into account the influence of these imperfections is established. Four different porosity types are considered for FG nanobeam. Material characteristics of the FG beam are supposed to vary continuously within thickness direction according to a power-law scheme which is modified to approximate material characteristics for considering the influence of porosities. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the nanobeam are derived using Hamilton's principle. The effects of nonlocal parameter, aspect ratio, and the porosity types on the dynamic responses of the nanobeam are discussed.

• Smart Structures and Systems
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• v.22 no.1
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• pp.105-120
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• 2018

In this paper, the nonlinear free and forced vibration responses of sandwich nano-beams with three various functionally graded (FG) patterns of reinforced carbon nanotubes (CNTs) face-sheets are investigated. The sandwich nano-beam is resting on nonlinear Visco-elastic foundation and is subjected to thermal and electrical loads. The nonlinear governing equations of motion are derived for an Euler-Bernoulli beam based on Hamilton principle and von Karman nonlinear relation. To analyze nonlinear vibration, Galerkin's decomposition technique is employed to convert the governing partial differential equation (PDE) to a nonlinear ordinary differential equation (ODE). Furthermore, the Multiple Times Scale (MTS) method is employed to find approximate solution for the nonlinear time, frequency and forced responses of the sandwich nano-beam. Comparison between results of this paper and previous published paper shows that our numerical results are in good agreement with literature. In addition, the nonlinear frequency, force response and nonlinear damping time response is carefully studied. The influences of important parameters such as nonlocal parameter, volume fraction of the CNTs, different patterns of CNTs, length scale parameter, Visco-Pasternak foundation parameter, applied voltage, longitudinal magnetic field and temperature change are investigated on the various responses. One can conclude that frequency of FG-AV pattern is greater than other used patterns.

• Journal of the Korea Safety Management & Science
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• v.13 no.1
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• pp.195-202
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• 2011

The study interprets each of three classification models based on Bath-Tub Failure Rate (BTFR), Extreme Value Distribution (EVD) and Conjugate Bayesian Distribution (CBD). The classification model based on BTFR is analyzed by three failure patterns of decreasing, constant, or increasing which utilize systematic management strategies for reliability of time. Distribution model based on BTFR is identified using individual factors for each of three corresponding cases. First, in case of using shape parameter, the distribution based on BTFR is analyzed with a factor of component or part number. In case of using scale parameter, the distribution model based on BTFR is analyzed with a factor of time precision. Meanwhile, in case of using location parameter, the distribution model based on BTFR is analyzed with a factor of guarantee time. The classification model based on EVD is assorted into long-tailed distribution, medium-tailed distribution, and short-tailed distribution by the length of right-tail in distribution, and depended on asymptotic reliability property which signifies skewness and kurtosis of distribution curve. Furthermore, the classification model based on CBD is relied upon conjugate distribution relations between prior function, likelihood function and posterior function for dimension reduction and easy tractability under the occasion of Bayesian posterior updating.

• Steel and Composite Structures
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• v.25 no.2
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• pp.141-155
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• 2017

This paper presents an investigation into the magneto-thermo-mechanical vibration and damping of a viscoelastic functionally graded-carbon nanotubes (FG-CNTs)-reinforced curved microbeam based on Timoshenko beam and strain gradient theories. The structure is surrounded by a viscoelastic medium which is simulated with spring, damper and shear elements. The effective temperature-dependent material properties of the CNTs-reinforced composite beam are obtained using the extended rule of mixture. The structure is assumed to be subjected to a longitudinal magnetic field. The governing equations of motion are derived using Hamilton's principle and solved by employing differential quadrature method (DQM). The effect of various parameter like volume percent and distribution type of CNTs, temperature change, magnetic field, boundary conditions, material length scale parameter, central angle, viscoelastic medium and structural damping on the vibration and damping behaviors of the nanocomposite curved microbeam is examined. The results show that with increasing volume percent of CNTs and considering magnetic field, material length scale parameter and viscoelastic medium, the frequency of the system increases and critically damped situation occurs at higher values of damper constant. In addition, the structure with FGX distribution type of CNTs has the highest stiffness. It is also observed that increasing temperature, structural damping and central angle of curved microbeam decreases the frequency of the system.

• Journal of the Korean Geotechnical Society
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• v.18 no.4
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• pp.229-238
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• 2002

This paper introduces the surface roughness parameter, Rs to the characterization of joint roughness and quantitatively illustrates the influence of joint roughness on the joint shear strength. A new peak shear strength criterion for rock joints using Rs is suggested. The results show that the surface roughness parameter, Rs can appropriately reflect the degree of roughness for the rock joint surfaces tested in this study A measuring interval of 2mm and profile length of 5cm can be used to characterize the joint roughness of the rock core size surfaces; however, the scale of fluctuation, $\delta_\alpha$ should be considered to extend the surface roughness parameter, Rs to the large-scale field rock joint surfaces. For the smooth joint roughness, sliding of the rock cores is the principal shear mechanism; however, the breakage of roughness from the rock cores is inferred for rougher joint roughness.