• 제목/요약/키워드: Equation of plane

검색결과 749건 처리시간 0.028초

On the tensile strength of brittle materials with a consideration of Poisson's ratios

  • Hu Guoming;Cho Heechan;Wan Hui;Ohtaki Hideyuki
    • 한국지구물리탐사학회:학술대회논문집
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    • 한국지구물리탐사학회 2003년도 Proceedings of the international symposium on the fusion technology
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    • pp.603-610
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    • 2003
  • The influence of Poisson's ratio on the tensile strength of brittle materials is neglected in many studies. When brittle materials are loaded in compression or impact, substantial tensile stresses are induced within the materials. These tensile stresses are responsible for splitting failure of the materials. In this paper, the state of stress in a spherical particle due to two diametrically opposed forces is analyzed theoretically. A simple equation for the state of stress at the center of the particle is obtained. An analysis of the distribution of stresses along the z-axis due to distributed pressures and concentrated forces, and on diametrically horizontal plane due to concentrated forces, shows that it is reasonable to propose the tensile stress at the center of the particle at the point of failure as a tensile strength of the particle. Moreover, the tensile strength is a function of the Poisson's ratio of the material. As the state of stress along the z-axis in an irregular specimen tends to be similar to that in a spherical particle compressed diametrically with the same force, this tensile strength has some validity for irregular particles as well. Therefore, it can be proposed as the tensile strength for brittle materials generally. The effect of Poisson's ratio on the tensile strength is discussed.

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규칙파(規則波)에 놓인 구(球)의 수평운동(水平運動)에 대(對)한 해석(解析) (On the Surge Motion of a Freely-Floating Sphere in a Plane Progressive Wave)

  • 박찬욱;최항순
    • 대한조선학회지
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    • 제18권1호
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    • pp.19-27
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    • 1981
  • The surge motion of a freely-floating sphere in a regular wave is studied within the framework of a linear potential theory. The fluid is assumed to be perfect and only the steady-state harmonic motion in a water of infinite depth is considered. A velocity potential describing the fluid motion is decomposed into three parts; the incident wave potential, the diffraction potential and the radiation potential. In this paper the diffraction potential and the radiation potential are analysed by using multipole expansion method. Upon calculating pressures over the immersed surface of the sphere, the hydrodynamic forces are evaluated in terms of Froude-Krylov, diffraction, added mass and damping forces as functions of the frequency of the incident wave. Finally the frequency dependence of two pertinent parameters, the amplitude ratio and the phase lag between the motion of the sphere and that of the incident wave is derived from the equation of motion. As for numerical results the general tendency of the present calculation shows good agreement with Kim's work who also treated this problem utilizing the Green's function method.

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Free vibration analysis of pores functionally graded plates using new element based on Hellinger-Reissner functional

  • Majid Yaghoobi;Mohsen Sedaghatjo;Mohammad Karkon;Lazreg Hadji
    • Steel and Composite Structures
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    • 제49권6호
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    • pp.713-728
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    • 2023
  • This paper aims to investigate the free vibration analysis of FG plates, taking into account the effects of even and uneven porosity. The study employs the Hellinger-Reisner functional and obtains the element's bending stress and membrane stress fields from the analytical solution of the governing equations of the thick plate and plane problem, respectively. The displacement field serves as the second independent field. While few articles on free vibration analysis of circular plates exist, this paper investigates the free vibration of both rectangular and circular plates. After validating the proposed element, the paper investigates the effects of porosity distributions on the natural frequency of the FG porous plate. The study calculates the natural frequency of thin and thick bending plates with different aspect ratios and support conditions for various porosity and volume fraction index values. The study uses three types of porosity distributions, X, V, and O, for the uneven porosity distribution case. For O and V porosity distribution modes, porosity has a minor effect on the natural frequency for both circular and rectangular plates. However, in the case of even porosity distribution or X porosity distribution, the effect of porosity on the natural frequency of circular and rectangular plates increases with an increase in the volume fraction index.

Design and Performance Evaluation of Mini-Lightweight Piezo-Composite Actuators

  • Tran, Anh Kim;Yoon, Kwang-Joon
    • Advanced Composite Materials
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    • 제18권4호
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    • pp.327-338
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    • 2009
  • In this paper, through an evaluation process conducted on several designs of mini-LIPCA (Lightweight Piezo-Composite curved Actuator), an optimal design of a mini-LIPCA has been proposed. Comparing with the LIPCA-C2, the design of the mini-LIPCA comes with reduced overall size and a thinner active layer. Since a variation in the number and lay-up of fiber composite layers may strongly affect the performance of the device, one is able to configure several designs of mini-LIPCA. The evaluation process is then followed in order to determine a configuration which characterizes the possibly optimal performance. That is, a design of a mini-LIPCA is said to be optimal if it is capable of producing a maximum out-of-plane displacement. The size of the LIPCA to be investigated was selected to be $10\;mm\;{\times}\;20\;mm$ in which the thickness of PZT plate is about 0.1 mm. The thickness of glass/epoxy and carbon/epoxy are about 0.09 mm and 0.1 mm, respectively. The evaluation process has been conducted thoroughly, i.e., analytical estimation, numerical approximation and the experimental measurement are all involved. Firstly, the design equation was used to calculate essential parameters of proposed lay-up configurations. Secondly, ANSYS, a commercial FEA package, was utilized to estimate displacement outputs of the actuators upon being excited. Finally, experimental measurements were able to verify the predicted results.

Numerical investigation of buckling strength of longitudinally stiffened web of plate girders subjected to bending

  • Kim, Hee Soon;Park, Yong Myung;Kim, Byung Jun;Kim, Kyungsik
    • Structural Engineering and Mechanics
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    • 제65권2호
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    • pp.141-154
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    • 2018
  • In this study, the bend-buckling strength of the web in longitudinally stiffened plate girder was numerically investigated. The buckling strength of the reinforced web was evaluated through an eigenvalue analysis of the hypothetical model, in which the top and bottom junctions of the web to the flanges were assumed as simple support conditions. Major parameters in the analysis include asymmetrical cross-sectional property, aspect ratio of the web, stiffener locations, and bending rigidity of the stiffeners. The numerical results showed that current AASHTO LRFD specifications (2014) provides the buckling strength from considerably safe side to slightly unsafe side depending on the location of the stiffeners. A modified equation for buckling coefficients was proposed to solve the shortcomings. The bending rigidity requirements of longitudinal stiffeners stipulated in AASHTO were also investigated. It is desirable to increase the rigidity of the stiffeners when the aspect ratio is less than 1.0.

임의 형태의 해양구조물에 의한 해수파의 산란 (The Water Wave Scattering by the Marine Structure of Arbitrary Shape)

  • 신승호;이중우
    • 한국항해학회지
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    • 제17권1호
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    • pp.61-78
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    • 1993
  • Large offshore structure are to be considered for oil storage facilities , marine terminals, power plants, offshore airports, industrial complexes and recreational facilities. Some of them have already been constructed. Some of the envisioned structures will be of the artificial-island type, in which the bulk of structures may act as significant barriers to normal waves and the prediction of the wave intensity will be of importance for design of structure. The present study deals wave scattering problem combining reflection and diffraction of waves due to the shape of the impermeable rigid upright structure, subject to the excitation of a plane simple harmonic wave coming from infinity. In this study, a finite difference technique for the numerical solution is applied to the boundary integral equation obtained for wave potential. The numerical solution is verified with the analytic solution. The model is applied to various structures, such as the detached breakwater (3L${\times}$0.1L), bird-type breakwater(318L${\times}$0.17L), cylinder-type and crescent -type structure (2.89L${\times}$0.6L, 0.8L${\times}$0.26L).The result are presented in wave height amplification factors and wave height diagram. Also, the amplification factors across the structure or 1 or 2 wavelengths away from the structure are compared with each given case. From the numerical simulation for the various boundary types of structure, we could figure out the transformation pattern of waves and predict the waves and predict the wave intensity in the vicinity of large artificial structures.

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전기절연유의 절연파괴에 미치는 전극간격 및 곡률반경의 영향 (The Influence of Gap Length and Tip Radius on Breakdown of Electrical Insulating Oil)

  • 강성화;채홍인;이종필;임기조
    • 한국안전학회지
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    • 제19권1호
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    • pp.56-59
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    • 2004
  • In this paper, we investigated the influence of gap length and tip radius on breakdown of mineral based insulation oil. Applied voltages were DC and AC voltage. Electrode system was needle-plane structure. The tip radius of needle electrode was 5, 10, 20 and 25${\mu}m$, respectively. We measured breakdown voltage for each of tip radius with increasing electrode gap, 2mm to 12mm. Electric breakdown strength at tip was calculated using Mason's equation contained geometric figure. As gap length increased, breakdown strength increased linearly. But, as tip radius of needle increased, breakdown strength decreased exponentially. It can be explained by the phenomenon that electron is easily injected, as tip radius increases, and effective work function decreases. When appling DC voltage, breakdown strength was higher when polarity of needle was negative than positive. It is because of the space charge effect in accordance with the influence of liquid motion.

n-Pentane 증기의 광촉매 분해 시 Methyl Ethyl Ketone 증기와 Ethyl Acetate 증기의 영향 (Effect of Methyl Ethyl Ketone and Ethyl Acetate Vapor on Photocatalytic Decomposition of n-Pentane Vapor)

  • 감상규;전진우;이민규
    • 한국환경과학회지
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    • 제23권6호
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    • pp.1151-1156
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    • 2014
  • The photocatalytic decomposition characteristics of single n-pentane, n-pentane mixed with methyl ethyl ketone (MEK), and n-pentane mixed with ethyl acetate (EA) by cylindrical UV reactor installed with $TiO_2$-coated perforated plane were studied. The effects of the residence time, the inlet gas concentration, and the oxygen concentration were investigated. The removal efficiency of n-pentane was increased with increasing the residence time and the oxygen concentration, but decreased with increasing the inlet concentration of n-pentane. The photocatalytic decomposition rates of single n-pentane, n-pentane mixed with MEK, and n-pentane mixed with EA fitted well on Langmuir-Hinshelwood kinetics equation. The maximum elimination capacities of single n-pentane, n-pentane mixed with MEK, and n-pentane mixed with EA were obtained to be $465g/m^3{\cdot}day$, $217g/m^3{\cdot}day$, and $320g/m^3{\cdot}day$, respectively. The presence of coexisting MEK and EA vapor had a negative effect on the photocatalytic decomposition of n-pentane and the negative effect of MEK was higher than that of EA.

Mathieu stability of offshore Buoyant Leg Storage & Regasification Platform

  • Chandrasekaran, S.;Kiran, P.A.
    • Ocean Systems Engineering
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    • 제8권3호
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    • pp.345-360
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    • 2018
  • Increasing demand for large-sized Floating, Storage and Regasification Units (FSRUs) for oil and gas industries led to the development of novel geometric form of Buoyant Leg Storage and Regasification Platform (BLSRP). Six buoyant legs support the deck and are placed symmetric with respect to wave direction. Circular deck is connected to buoyant legs using hinged joints, which restrain transfer of rotation from the legs to deck and vice-versa. Buoyant legs are connected to seabed using taut-moored system with high initial pretension, enabling rigid body motion in vertical plane. Encountered environmental loads induce dynamic tether tension variations, which in turn affect stability of the platform. Postulated failure cases, created by placing eccentric loads at different locations resulted in dynamic tether tension variation; chaotic nature of tension variation is also observed in few cases. A detailed numerical analysis is carried out for BLSRP using Mathieu equation of stability. Increase in the magnitude of eccentric load and its position influences fatigue life of tethers significantly. Fatigue life decreases with the increase in the amplitude of tension variation in tethers. Very low fatigue life of tethers under Mathieu instability proves the severity of instability.

水銀滴下電極에서 一次反應에 對한 포라로그라프電流에 關한 硏究 (Studies on the Polarographic Kinetic Currents for the First Order Reactions at the Droping Mercury Electrode)

  • 김황암;태창희
    • 대한화학회지
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    • 제6권1호
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    • pp.14-18
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    • 1962
  • Solution to the diffusion layer for the first order reaction at a droping mercury electrode (D.M.E.) is presented. Equations are derived for polarographic currents for the reactions at the D.M.E. A factor which is applicable to the D.M.E. is derived, when we use the equations of the polarographic currents for the reactions at a plane electrode(P.E.), and the rate constants of the backward reactions are negligibly small. Polarographic currents from a combination of diffusions and reactions are obtained at the D.M.E. with special approximation. Rate constant for the reaction of ferrous ion with hydrogen-peroxide is determined at the D.M.E.,using the data of Kolthoff and Perry. The agreement of the equation with the data of Kolthoff and Perry for the kinetic current of ferric ion in the presence of hydrogen-peroxide is good. Ratios of diffusion layer at the D.M.E. to the diffusion layer at the P.E. are discussed and show that, when the rate constants of the backward reactions for the first order reactions are larger than 1/0.05 sec-1. and drop-time about 3 sec., these ratioes are about one.

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