• Steel and Composite Structures
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• v.28 no.5
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• pp.541-557
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• 2018

This paper presents the influence of carbon nanotubes (CNTs) waviness and aspect ratio on the vibrational behavior of functionally graded nanocomposite sandwich annular sector plates resting on two-parameter elastic foundations. The carbon nanotube-reinforced (CNTR) sandwich plate has smooth variation of CNT fraction along the thickness direction. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness and their mechanical properties are estimated by an extended rule of mixture. In this study, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. Effects of CNT distribution, volume fraction, aspect ratio and waviness, and also effects of Pasternak's elastic foundation coefficients, sandwich plate thickness, face sheets thickness and plate aspect ratio are investigated on the free vibration of the sandwich plates with wavy CNT-reinforced face sheets. The study is carried out based on three-dimensional theory of elasticity and in contrary to two-dimensional theories, such as classical, the first- and the higher-order shear deformation plate theories, this approach does not neglect transverse normal deformations. The sandwich annular sector plate is assumed to be simply supported in the radial edges while any arbitrary boundary conditions are applied to the other two circular edges including simply supported, clamped and free.

• Tunnel and Underground Space
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• v.20 no.3
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• pp.225-232
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• 2010

In this study, a newly modified 3-dimensional strain-dependent hydraulic conductivity modification relation which incorporates the influences of normal deformation and shear dilation is suggested. Since rock mass is simulated as a orthogonally jointed medium, an anisotropic hydraulic conductivity field can be evaluated using that relation. The empirical relationship on the basis of GSI and disturbance factor has been used to estimate the value of a modulus reduction ratio (ratio of rock mass deformation modulus to rock matrix elastic modulus). Principal hydraulic conductivity directions is not generally coincident with the global coordinate due to the inclining of joint and the influence of joint inclination is evaluated under strain rotation. Result shows that change of hydraulic conductivity does decreases with the increase of GSI and disturbance factor has much effects on the hydraulic conductivity of rock mass getting GSI value above 50. It is found that the inclination of joint impacts on the variation of hydraulic conductivity.

• Structural Engineering and Mechanics
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• v.44 no.4
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• pp.431-448
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• 2012

In this paper, the first-order shear deformation theory (FSDT) (Mindlin) for continuum incorporating surface energy is exploited to study the static behavior of ultra-thin functionally graded (FG) plates. The size-dependent mechanical response is very important while the plate thickness reduces to micro/nano scales. Bulk stresses on the surfaces are required to satisfy the surface balance conditions involving surface stresses. Unlike the classical continuum plate models, the bulk transverse normal stress is preserved here. By incorporating the surface energies into the principle of minimum potential energy, a series of continuum governing differential equations which include intrinsic length scales are derived. The modifications over the classical continuum stiffness are also obtained. To illustrate the application of the theory, simply supported micro/nano scaled rectangular films subjected to a transverse mechanical load are investigated. Numerical examples are presented to present the effects of surface energies on the behavior of functionally graded (FG) film, whose effective elastic moduli of its bulk material are represented by the simple power law. The proposed model is then used for a comparison between the continuum analysis of FG ultra-thin plates with and without incorporating surface effects. Also, the transverse shear strain effect is studied by a comparison between the FG plate behavior based on Kirchhoff and Mindlin assumptions. In our analysis the residual surface tension under unstrained conditions and the surface Lame constants are expected to be the same for the upper and lower surfaces of the FG plate. The proposed model is verified by previous work.

• Steel and Composite Structures
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• v.25 no.6
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• pp.649-661
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• 2017

This paper is motivated by the lack of studies in the technical literature concerning to the influence of carbon nanotubes (CNTs) waviness and aspect ratio on the vibrational behavior of functionally graded nanocomposite annular sector plates resting on two-parameter elastic foundations. The carbon nanotube-reinforced (CNTR) plate has smooth variation of CNT fraction based on the power-law distribution in the thickness direction, and the material properties are also estimated by the extended rule of mixture. In this study, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. Parametric studies are carried out to highlight the influence of CNTs volume fraction, waviness and aspect ratio, boundary conditions and elastic foundation on vibrational behavior of FG-CNT thick sectorial plates. The study is carried out based on three-dimensional theory of elasticity and in contrary to two-dimensional theories, such as classical, the first- and the higher-order shear deformation plate theories, this approach does not neglect transverse normal deformations. The annular sector plate is assumed to be simply supported in the radial edges while any arbitrary boundary conditions are applied to the other two circular edges including simply supported, clamped and free. For an overall comprehension on 3-D vibration of annular sector plates, some mode shape contour plots are reported in this research work.

• Steel and Composite Structures
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• v.48 no.2
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• pp.191-206
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• 2023

The present research investigates how micromechanical models affect the behavior of Functionally Graded (FG) plates under different boundary conditions. The study employs diverse micromechanical models to assess the effective material properties of a two-phase particle composite featuring a volume fraction of particles that continuously varies throughout the thickness of the plate. Specifically, the research examines the vibrational response of the plate on a Winkler-Pasternak elastic foundation, considering different boundary conditions. To achieve this, the governing differential equations and boundary conditions are derived using Hamilton's principle, which is based on a four-variable shear deformation refined plate theory. Additionally, the Galerkin method is utilized to compute the plate's natural frequencies. The study explores how the plate's natural frequencies are influenced by various micromechanical models, such as Voigt, Reuss, Hashin-Shtrikman bounds, and Tamura, as well as factors such as boundary conditions, elastic foundation parameters, length-to-thickness ratio, and aspect ratio. The research results can provide valuable insights for future analyses of FG plates with different boundaries, utilizing different micromechanical models.

• Journal of the Korean Society for Precision Engineering
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• v.25 no.4
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• pp.61-68
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• 2008

Of the seven base units of the international system of units, only the kilogram is still defined in terms of a material artifact. One of the experimental approaches opening the way to a new definition of the kilogram is the watt balance To improve the performance of the NPL watt balance, we need to quantify and reduce hysteresis effects in the balance knives. In this paper, we discuss the mechanical characteristics of the knife edges used in the NPL watt balance. The hysteresis mechanism is analyzed using the finite element method. It is found that the cause of hysteresis is not normal stress but shear, and the deformation of the flat, rather than the knife, is an important factor in the hysteresis mechanism. The study presented here, using finite element analysis, suggests that parameters such as material property, tip radius and knife straightness can be more important than others, such as friction coefficient, tip angle, etc.

• Smart Structures and Systems
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• v.26 no.3
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• pp.331-343
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• 2020

In this paper, based on the CPT, motion equations for a sandwich plate containing a core and two integrated face-sheets have derived. The structure rests on the Visco-Pasternak foundation, which includes normal and shear modules. The piezo-magnetic core is made of CoFe₂O₄ and also is subjected to 3D magnetic potential. Two face sheets at top and bottom of the core are under electrical fields. Also, in order to obtain more accuracy, the effect of flexoelectricity has took into account at face sheets' relations in this work. Flexoelectricity is a property of all insulators whereby they polarize when subject to an inhomogeneous deformation. This property plays a crucial role in small-scale rather than macro scale. Employing CPT, Hamilton's principle, flexoelectricity considerations, the governing equations are derived and then solved analytically. By present work a detailed numerical study is obtained based on Piezoelectricity, Flexoelectricity and modified couple stress theories to indicate the significant effect of length scale parameter, shear correction factor, aspect and thickness ratios and boundary conditions on natural frequency of sandwich plates. Also, the figures show that there is an excellent agreement between present study and previous researches. These finding can be used for automotive industries, aircrafts, marine vessels and building industries.

• Journal of Korean Society of Steel Construction
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• v.12 no.6
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• pp.639-648
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• 2000

A model analysis is used to predict the impact response of a simply supported elastic circular cylindrical shell composed of two bonded isotropic layers. The governing equations for a two-layered cylindrical shell are derived on the basis of an improved theory for the single-layer shell which includes the effects of transverse shear deformation and rotary inertia. Calculations are made for the specific case of the steel-concrete cylindrical shell subjected to a suddenly applied load. The solutions show that the method yields very good results. Therefore the proposed method is useful not only for a better investigating of the response characteristics of the shell but also available for a check on other numerical methods such a FEM.

• Korean Journal of Metals and Materials
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• v.50 no.12
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• pp.913-920
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• 2012

In spite of some problems in processability and bondability, Au wires in the microelectronics industry are gradually being replaced by copper wires to reduce the cost of raw material. In this article, the effects of surface roughness enhanced capillaries on thermosonic Cu wire bonding were evaluated. The roughness-enhanced zirconia toughened alumina (ZTA) capillaries were fabricated via a thermal grooving technique. As a result, the shear bond strength of first bonds (ball bonds) bonded using the roughness-enhanced capillary was enhanced by 15% as compared with that of normal bonds due to more effective plastic deformation and flow of a Cu ball. In the pull-out test of second bonds (stitch bonds), processed at two limit conditions on combinations of process parameters, the bond strength of bonds formed using the roughness-enhanced capillary also resulted in values higher by 55.5% than that of normal bonds because of the increase in the bonding area, indicating the expansion of a processing window for Cu wire bonding. These results suggest that the adoption of roughness-enhanced capillaries is a promising approach for enhancing processability and bondability in Cu wire bonding.

• Steel and Composite Structures
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• v.26 no.6
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• pp.771-791
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• 2018

This paper deals with the low velocity impact response and dynamic stresses of composite sandwich truncated conical shells (STCS) with compressible or incompressible core. Impacts are assumed to occur normally over the top face-sheet and the interaction between the impactor and the structure is simulated using a new equivalent three-degree-of-freedom (TDOF) spring-mass-damper (SMD) model. The displacement fields of core and face sheets are considered by higher order and first order shear deformation theory (FSDT), respectively. Considering continuity boundary conditions between the layers, the motion equations are derived based on Hamilton's principal incorporating the curvature, in-plane stress of the core and the structural damping effects based on Kelvin-Voigt model. In order to obtain the contact force, the displacement histories and the dynamic stresses, the differential quadrature method (DQM) is used. The effects of different parameters such as number of the layers of the face sheets, boundary conditions, semi vertex angle of the cone, impact velocity of impactor, trapezoidal shape and in-plane stresses of the core are examined on the low velocity impact response of STCS. Comparison of the present results with those reported by other researchers, confirms the accuracy of the present method. Numerical results show that increasing the impact velocity of the impactor yields to increases in the maximum contact force and deflection, while the contact duration is decreased. In addition, the normal stresses induced in top layer are higher than bottom layer since the top layer is subjected to impact load. Furthermore, with considering structural damping, the contact force and dynamic deflection decrees.