• Title/Summary/Keyword: axial equilibrium

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Strength and buckling of a sandwich beam with thin binding layers between faces and a metal foam core

  • Magnucki, Krzysztof;Jasion, Pawel;Szyc, Waclaw;Smyczynski, Mikolaj Jan
    • Steel and Composite Structures
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    • v.16 no.3
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    • pp.325-337
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    • 2014
  • The strength and buckling problem of a five layer sandwich beam under axial compression or bending is presented. Two faces of the beam are thin aluminium sheets and the core is made of aluminium foam. Between the faces and the core there are two thin binding glue layers. In the paper a mathematical model of the field of displacements, which includes a share effect and a bending moment, is presented. The system of partial differential equations of equilibrium for the five layer sandwich beam is derived on the basis of the principle of stationary total potential energy. The equations are analytically solved and the critical load is obtained. For comparison reasons a finite element model of the beam is formulated. For the case of bended beam the static analysis has been performed to obtain the stress distribution across the height of the beam. For the axially compressed beam the buckling analysis was carried out to determine the buckling load and buckling shape. Moreover, experimental investigations are carried out for two beams. The comparison of the results obtained in the analytical and numerical (FEM) analysis is shown in graphs and figures. The main aim of the paper is to present an analytical model of the five layer beam and to compare the results of the theoretical, numerical and experimental analyses.

Micro-Mechanical Approach for Spanwise Periodically and Heterogeneously Beam-like Structures

  • Lee, Chang-Yong
    • Journal of the Korean Solar Energy Society
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    • v.36 no.3
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    • pp.9-16
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    • 2016
  • This paper discusses a refined model for investigating the micro-mechanical behavior of beam-like structures, which are composed of various elastic moduli and complex geometries varying through the cross-section directions and are also periodically-repeated and heterogeneous along the axial direction. Following the previous work (Lee and Yu, 2011), the original three-dimensional static problem is first formulated in a unified and compact form using the concept of decomposition of the rotation tensor. Taking advantage of the smallness of the cross-sectional dimension-to-length parameter and the micro-to-macro heterogeneity, while also performing homogenization along the dimensional reduction simultaneously, the variational asymptotic method is rigorously used to construct a total energy function, which is asymptotically correct up to the second order. Furthermore, through the transformation procedure based on the pure kinematic relations and the linearized equilibrium equations, a generalized Timoshenko model is systematically established. For the purpose of dealing with realistic and complex geometries and constituent materials at the microscopic level, this present approach is incorporated into a commercial analysis package. A few examples available in literature are used to demonstrate the consistency and efficiency of this proposed model, especially for the structures, in which the effects of transverse shear deformations are significant.

Plastic Limit Load Solutions for Circumferential Surface Cracked Cylinders Under Combined Loading (복합하중이 작용하는 원주방향 표면균열배관에 대한 소성한계하중식)

  • Shim, Do-Jun;Kim, Yun-Jae;Kim, Young-Jin;Hwang, Seong-Sik;Kim, Joung-Soo
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.27 no.9
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    • pp.1469-1476
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    • 2003
  • This paper provides plastic limit load solutions of cylinders with circumferential part-through surface cracks under combined axial tension, internal pressure and global bending. Such solutions are developed based on detailed three-dimensional (3-D) finite element (FE) limit analyses using elastic-perfectly-plastic material behaviour, together with analytical solutions based on equilibrium stress fields. For the crack location, both external and internal cracks are considered. Furthermore, in terms of the crack shape, both semi-elliptical and constant-depth surface cracks are considered. The resulting limit load solutions are given in a closed form, and thus can be easily used in practical situations. Being based on detailed 3-D FE limit analysis, the present solutions are believed to most reliable, and thus to be valuable information for integrity assessment of piping.

Exhaust Plasma Characteristics of Direct-Current Arcjet Thrusters

  • Tahara, Hirokazu
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • 2004.03a
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    • pp.327-334
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    • 2004
  • Spectroscopic and electrostatic probe measurements were made to examine plasma characteristics with or without a metal plate for a 10-㎾-class direct-current arcjet Heat fluxes into the plate from the plasma were also evaluated with a Nickel slug and thermocouple arrangement. Ammonia and mixtures of nitrogen and hydrogen were used. The NH$_3$ and $N_2$+3H$_2$ plasmas in the nozzle and in the downstream plume without a plate were in thermodynamical nonequilibrium states. As a result, the H-atom electronic excitation temperature and the $N_2$ molecule-rotational excitation temperature intensively decreased downstream in the nozzle although the NH molecule-rotational excitation temperature did not show an axial decrease. Each temperature was kept in a small range in the plume without a plate except for the NH rotational temperature for NH$_3$ gas. On the other hand, as approaching the plate, the thermodynamical nonequilibrium plasma came to be a temperature-equilibrium one because the plasma flow tended to stagnate in front of the plate. The electron temperature had a small radial variation near the plate. Both the electron number density and the heat flux decreased radially outward, and an increase in H$_2$ mole fraction raised them at a constant radial position. In cases with NH$_3$ and $N_2$+3H$_2$ a large number of NH radical with a radially wide distribution was considered to cause a large amount of energy loss, i.e., frozen flow loss, for arcjet thrusters.

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Development of a High Flow CHF Correlation for the KMRR Fuel (KMRR 핵연료에 대한 고유량 임계열속 상관식 개발)

  • Park, Cheol;Hwang, Dae-Hyun;Yoo, Yeon-Jong;Park, Jong-Ryul
    • Nuclear Engineering and Technology
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    • v.26 no.2
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    • pp.237-246
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    • 1994
  • A high flow critical heat flux (CHF) correlation, based on the single-pin CHF experimental data for finned and unfinned heated rods, was developed for the thermal-hydraulic design and safety analysis of the Korea Multi-purpose Research Reactor (KMRR) core. The correlation consists of dimensionless parameters such as Reynolds number, thermodynamic equilibrium quality, liquid-to-vapor density ratio, and hydraulic equivalent diameter ratio. The fin effect was taken into account in the correlation by a finned-to-unfinned heated perimeter ratio. The effects of a cold wall and non-uniform axial power distribution ore discussed to verify the applicability of the single-pin based correlation to the KMRR fuel bundle. The correlation limit departure from nucleate boiling ratio (DNBR) was determined as 1.44 from the statistical analysis of the CHF data.

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Epitaxy of Si and Si1-xGex(001) by ultrahigh vacuum ion-beam sputter deposition

  • Lee, N. E.;Greene, J. E.
    • Journal of Korean Vacuum Science & Technology
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    • v.2 no.2
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    • pp.107-117
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    • 1998
  • Epitaxial undoped and Sb-doped si films have been grown on Si(001) substrates at temperatures T between 80 and 750$^{\circ}C$ using energetic Si in ultra-high-vacuum Kr+-ion-beam sputter deposition(IBSD). Critical epitaxial thicknesses te, The average thickness of epitaxial layers, in undoped films were found to range from 8nm at Ts=80$^{\circ}C$ to > 1.2 ${\mu}$m at Ts=300$^{\circ}C$ while Sb incorporation probabilities $\sigma$sb varied from unity at Ts 550$^{\circ}C$ to 0.1 at 750$^{\circ}C$. These te and $\sigma$Sb values are approximately one and one-to-three orders of magnitude, respectively, higher than reported results achieved with molecular-beam epitaxy. Plan-view and cross-sectional transmission electron microscopy, high-resolution x-ray diffraction, channeling and axial angular-yield profiles by Rutherford back scattering spectroscopy for epitaxial Si1-x Gex(001) alloy films (0.15$\leq$x$\leq$0.30) demonstrated that the films are of extremely high crystalline quality. critical layer thicknesses hc the film thickness where strain relaxation starts, I these alloys wre found to increase rapidly with decreasing growth temperature. For Si0.70 Ge0.30, hc ranged from 35nm at Ts=550$^{\circ}C$ to 650nm at 350$^{\circ}C$ compared to an equilibrium value of 8nm.

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Structural ordering, electronic and magnetic properties of bundled $Mo_6S_9-_xI_x$ nanowires

  • Kang, Seoung-Hun;Tomanek, David;Kwon, Young-Kyun
    • Proceedings of the Korean Vacuum Society Conference
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    • 2010.02a
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    • pp.55-55
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    • 2010
  • We use ab initio density functional theory to determine the effect of bundling on the equilibrium structure, electronic and magnetic properties of $Mo_6S_{9-x}I_x$nanowires with x = 0, 3, 4.5, 6. Each unit cell of these systems contains two $Mo_6S_{6-x}I_x$ clusters connected by S3 linkages to form an ordered linear array. Due to the bi-stability of the sulfur linkages, the total energy of the nanowires exhibits typically many minima as a function of the wire length. We find that nanowires can switch over from metallic to semiconducting by applying axial stress. Structural order is expected in bundles with x=0 and x=6, since there is no disorder in the decoration of the Mo clusters. In bundles with other stoichiometries, we expect structural disorder to occur. We find the optimum inter-wire distance to depend sensitively on the orientation of the wires, but only weakly on x. It is also found that the electronic properties of nanowires are affected strongly due to bundling of nanowires exhibiting very unusual Fermi surfaces. Furthermore, ferromagnetic behaviors are observed in selected stable and many more unstable atomic arrangements in nanowire bundles.

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Compensation of Inclined Rotating Axis Using Unsymmetric Groove Patterns (비대칭 Groove를 이용한 FDB 회전축의 기울기 보상)

  • Lee, Nam-Hun;Han, Jae-Hyuk;Oh, Dong-Ho;Kim, Chul-Soon;Byun, Yong-Kyu;Koo, J.C.
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2004.11a
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    • pp.582-585
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    • 2004
  • Most of hard disk drives currently employ fluid dynamic bearing (FDB) for their rotor support. Stiffness of the FDB is affected by many design factors such as bearing clearance, fluid viscosity, and rotational speed. For the high rotating speed HDDs stiffness of the rotor is normally high enough to accomodate load disturbances. However small form factor HDDs that are to be operated in low power consumption are often designed with low stiffness rotors. Although the low stiffness rotor clearly benefits low power operation, it could damage the entire motor structure or head disk interface even by a light mechanical load disturbance such as shock or vibration. In addition, since a single channel HDD does not provide gram load equilibrium in axial direction the rotor could be tilted and make a hard contact to stator. A non-symmetric groove pattern could successfully compensate the tilted rotor angle during operation.

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Mathematical modelling of the stability of carbon nanotube-reinforced panels

  • Sobhani Aragh, B.
    • Steel and Composite Structures
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    • v.24 no.6
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    • pp.727-740
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    • 2017
  • The present paper studies the stability analysis of the continuously graded CNT-Reinforced Composite (CNTRC) panel stiffened by rings and stringers. The Stiffened Panel (SP) subjected to axial and lateral loads is reinforced by agglomerated CNTs smoothly graded through the thickness. A two-parameter Eshelby-Mori-Tanaka (EMT) model is adopted to derive the effective material moduli of the CNTRC. The stability equations of the CNRTC SP are obtained by means of the adjacent equilibrium criterion. Notwithstanding most available literature in which the stiffener effects were smeared out over the respective stiffener spacing, in the present work, the stiffeners are modeled as Euler-Bernoulli beams. The Generalized Differential Quadrature Method (GDQM) is employed to discretize the stability equations. A numerical study is performed to investigate the influences of different types of parameters involved on the critical buckling of the SP reinforced by agglomerated CNTs. The results achieved reveal that continuously distributing of CNTs adjacent to the inner and outer panel's surface results in improving the stiffness of the SP and, as a consequence, inclining the critical buckling load. Furthermore, it has been concluded that the decline rate of buckling load intensity factor owing to the increase of the panel angle is significantly more sensible for the smaller values of panel angle.

Shear strength evaluation of RC solid piers of high-speed railway bridges in China

  • Guo, Wei;Fan, Chao;Cui, Yao;Zeng, Chen;Jiang, Lizhong;Yu, Zhiwu
    • Structural Engineering and Mechanics
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    • v.78 no.4
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    • pp.413-423
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    • 2021
  • Piers are the main lateral force-resisting members of high-speed railway (HSR) bridges used in China and are characterized by low axial load ratios, low longitudinal reinforcement ratios, low stirrup ratios, and high shear span ratios. It is well known that flexural, flexural-shear, and shear failures of piers may occur during an earthquake. In this study, a new shear strength model was developed to simulate the seismic failure of HSR solid piers accurately. First, low cyclic-loading test data of solid piers obtained in recent years were collected to set up a database for model verification. Second, based on the test database, the applicability of existing shear strength models was evaluated. Finally, a new shear strength model for HSR solid piers with round-ended cross-sections was derived based on the truss model and ultimate equilibrium theory. In comparison with existing models, it was demonstrated that the proposed model could be used to predict the shear strength of HSR piers more accurately.