• Title/Summary/Keyword: Elastic Theory

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Free Vibration Characteristics of a Composite Beam with Multiple Transverse Open Cracks (다중 크랙이 있는 복합재료 보의 자유진동 특성)

  • 하태완;송오섭
    • Composites Research
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    • v.13 no.3
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    • pp.9-20
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    • 2000
  • Free vibration characteristics of a cantilevered laminated composite beam with multiple non-propagating transverse open cracks are investigated. In the present analysis a special ply-angle distribution referred to as asymmetric stiffness configuration inducing the elastic coupling between chord-wise bending and extension is considered. The multiple open cracks are modelled as equivalent rotational springs whose spring constants are calculated based on the fracture mechanics of composite material structures. Governing equations of a composite beam with open cracks are derived via Hamilton's Principle and Timoshenko beam theory encompassing transverse shear and rotary inertia effect is adopted. The effects of various parameters such as the ply angle, fiber volume fraction, crack numbers, crack positions and crack depthes on the free vibration characteristics of the beam with multiple cracks are highlighted. The numerical results show that the existence of the multiple cracks in an anisotropic composite beam affects the free vibration characteristics in a more complex fashion compared with the beam with a single crack.

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Vibration of Steel Composite Railway Bridges under High Speed Train (고속열차하중 하의 강합성형 철도교의 진동)

  • Chang, Sung Pil;Kwark, Jong Won;Ha, Sang Gil;Kim, Sung Il
    • Journal of Korean Society of Steel Construction
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    • v.10 no.4 s.37
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    • pp.577-587
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    • 1998
  • The influences of high speed train on the dynamic responses of steel composite railway bridges are investigated. The bridge system which has two I-girder and several cross beams is modeled with plate and frame elements. With assumption of concrete slabs are fully connected with steel girders, the offset between slabs and girders is modeled using constraint equation. The track system is modeled using beams on elastic foundation theory. And, the TGV train model is developed in 2-dimension considering bouncing and pitching motion. And braking action of vehicle is considered using speed dependent braking function. To investigate the behavior of bridges due to moving trains, parametric studies on the variation of natural frequency of bridge, speed parameter, vehicle modeling method, braking action of train, etc are performed.

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On the Oil Film Behaviors of Engine Bearing Considering Crankshaft Misalignment (크랭크축 경사도를 고려한 엔진 베어링의 유막거동에 관한 연구)

  • Kim, Han-Goo
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.11 no.9
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    • pp.3119-3124
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    • 2010
  • The purpose of this paper is to analyze dynamic behaviors of the oil film thickness and engine bearings in both aligned and misaligned operation conditions of a crankshaft using computer simulation techniques. A crankshaft as an elastic body is modeled for a misaligned crankshaft which is very important design parameter of the film thickness and engine bearings. In this analysis, a dynamic characteristic of a minimum oil film is analyzed based on the elastohydrodynamic lubrication theory. The boundary conditions for analyzing the film behaviors include non-linear constraint forces and bending moments in engine bearings. The more expedient model of an engine bearing is extended to consider the effect of crankshaft misalignment. The computed results indicate that the minimum oil film thickness that causes a major influence on the performance of engine bearings has showed a decrease of 16% to 24% for the misaligned crankshaft compared with an aligned crankshaft. The computed results show that the misalignment of a crankshaft inevitably brings the reduction of minimum oil film thickness and this may increase the failure of a bearing. These results as design parameters are very useful for a bearing designer as a firm reference data of an automotive engine.

Measurement of $G_{max}$ of Sands Using Bender Element in Resonant Column and Torsional Shear Equipment (공진주/비틂전단 시험 및 벤더엘리먼트 시험을 이용한 사질토 지반의 최대전단탄성계수 평가)

  • Kim Dong-Soo;Youn Jun-Ung;Lee Sei-Hyun;Choo Yun-Wook
    • Journal of the Korean Geotechnical Society
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    • v.21 no.10
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    • pp.17-25
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    • 2005
  • The bender element method is an experimental technique to determine very small strain ($<10^{-3}\%$), elastic shear modulus of a soil, $G_{max}$ by measuring the velocity of shear wave propagation through a sample. Bender elements have been applied as versatile transducers to measure small strain modulus of wet or dry soils in various laboratory apparatus. In this paper, bender element (BE), resonant column (RC) and torsional shear (TS) tests were performed on Toyoura sand at various testing conditions using the modified Stokoe type RC/TS testing equipment capable of performing BE test. Based on the results, applicabilities of the testing method using bender element were evaluated by comparing the values of $G_{max}$ obtained from RC/TS and BE testing methods. For more dependable evaluation, the loading frequency of each testing method was considered for the results obtained for samples in saturated condition by adapting Biot's theory.

Increasing Effect in Local Buckling Strength of Laminated Composite Plates Stiffened with Closed-section Ribs under Uniaxial Compression (폐단면리브로 보강된 일축압축을 받는 복합적층판의 국부좌굴강도 증가효과)

  • Hwang, Su-Hee;Kim, Yu-Sik;Choi, Byung-Ho
    • Journal of the Korean Society for Advanced Composite Structures
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    • v.4 no.2
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    • pp.39-44
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    • 2013
  • This study is aimed to examine the influence of the rotational stiffness of U-shaped ribs on the local buckling behaviors of laminated composite plates. Applying the orthotropic plates with eight layers of the layup $[(0^{\circ})4]s$ and $[(0^{\circ}/90^{\circ})2]s$, 3-dimensional finite element models for the U-rib stiffened plates were setup by using ABAQUS and then a series of eigenvalue analyses were conducted. There is a need to develope a simple design equation to establish the rotational stiffness effect, which could be easily quantified by comparing the theoretical critical stress equation for laminated composite plates with elastic restraints based on the Classical laminated plate theory. Through the parametric numerical studies, it is confirmed that there should clearly exist an increasing effect of local plate buckling strength due to the rotational stiffness by closed-section ribs. An applicable coefficient for practical design should be verified and proposed for future study. This study will contribute to the future study for establishing an increasing coefficient for the design strength and optimum design of U-rib stiffened plates.

A Conical Indentation Technique Based on FEA Solutions for Property Evaluation (유한요소해에 기초한 원뿔형 압입 물성평가법)

  • Hyun, Hong-Chul;Kim, Min-Soo;Lee, Jin-Haeng;Lee, Hyung-Yil
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.33 no.9
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    • pp.859-869
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    • 2009
  • The sharp indenters such as Berkovich and conical indenters have a geometrical self-similarity in theory, but different materials have the same load-depth curve in case of single indentation. In this study, we analyze the load-depth curves of conical indenter with angles of indenter via finite element method. From FE analyses of dual-conical indentation test, we investigate the relationships between indentation parameters and load-deflection curves. With numerical regressions of obtained data, we finally propose indentation formulae for material properties evaluation. The proposed approach provides stress-strain curve and the values of elastic modulus, yield strength and strain-hardening exponent with an average error of less than 2%. It is also discussed that the method is valid for any elastically deforming indenters made of tungsten carbide and diamond for instance. The proposed indentation approach provides a substantial enhancement in accuracy compared with the prior methods.

An experimental study on behavior of tunnel in jointed rock mass (절리암반내 터널라이닝 거동에 관한 실험적 연구)

  • Oh, Young-Seok;Park, Yong-Won;Yoon, Hyo-Seok
    • Journal of Korean Tunnelling and Underground Space Association
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    • v.6 no.4
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    • pp.315-326
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    • 2004
  • This study performed model tunnel tests in order to investigate the influence of discontinuity condition of rock mass to the stress and deformation of tunnel lining. Tests were carried out changing the direction of main joint and lateral earth pressure condition of rock mass. Test results revealed that the axial force in tunnel lining showed a tendency of decrease with the presence of joints. It decreased much with the increase of lateral earth pressure coefficient. And, it also showed that the location or maximum displacement and maximum stress in lining were changed by the direction of main joint of rock mass. The tangential stress and normal stress showed the difference above the maximum twenty times as lateral earth pressure coefficient due to effect of joints increased. Also, these tendencies of concentration of tensile stress in tunnel lining were confirmed by elastic theory.

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Nonlinear Analysis of Functionally Graded Materials Plates and Shells (점진기능재료(FGM) 판과 쉘의 비선형 해석)

  • Han, Sung-Cheon;Lee, Chang-Soo;Kim, Gi-Dong;Park, Weon-Tae
    • Journal of the Korean Society of Hazard Mitigation
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    • v.7 no.5
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    • pp.61-71
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    • 2007
  • Navier's and Finite element solutions based on the first-order shear deformation theory are presented for the analysis of through-thickness functionally graded plates and shells. The functionally graded materials are considered: a sigmoid function is utilized for the mechanical properties through the thickness of the isotropic structure which varies smoothly through the plate and shell thickness. The formulation of a nonlinear 9-node Element-based Lagrangian shell element is presented for the geometrically nonlinear analysis. Natural-coordinate-based strains are used in present shell element. Numerical results of the linear and nonlinear analysis are presented to show the effect of the different top/bottom elastic modulus, loading conditions, aspect ratios and side-to-thickness ratios on the mechanical behaviors. Besides, the result according to the variation of the power-law index of isotropic functionally graded structures is investigated.

Analytical Method for Bending Moment of Slab-on-Steel-Girder Bridge (강판형교 바닥판 모멘트의 해석기법)

  • Park, Nam Hoi;Choi, Jin Yu;Yu, Chul Soo;Kang, Young Jong
    • Journal of Korean Society of Steel Construction
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    • v.12 no.1 s.44
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    • pp.17-28
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    • 2000
  • The current specifications for bridge decks requires the same amount of upper and lower reinforcement mats. There have been many empirical activities that the partial elimination of upper reinforcing bars was not caused the structural integrity of a deck. A simplified method is derived based on thin plate theory for three and four-girder-span bridge decks. A simplified method for bridge deck considering the effect of girder deflection is proposed based on a closed-form solution that shows good agreement with the results of finite element models. In this research, a new design approach for deck slabs is proposed based on the simplified method. The negative bending moments in a deck can be evaluated with the simplified method based on the position of a wheel load, the aspect ratio and relative stiffness and the span length. This new approach can lead to a significant reduction of the quantity of the top reinforcing steel bars in a deck. Reducing the quantify of the top reinforcement not only reduces the construction costs for bridge decks, but also reduces the corrosion of reinforcement to a minimum.

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Stiffness Modeling of a Low-DOF Parallel Robot (저자유도 병렬형 로봇의 강성 모델링)

  • Kim, Han-Sung
    • Journal of Institute of Control, Robotics and Systems
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    • v.13 no.4
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    • pp.320-328
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    • 2007
  • This paper presents a stiffness modeling of a low-DOF parallel robot, which takes into account of elastic deformations of joints and links, A low-DOF parallel robot is defined as a spatial parallel robot which has less than six degrees of freedom. Differently from serial chains in a full 6-DOF parallel robot, some of those in a low-DOF parallel robot may be subject to constraint forces as well as actuation forces. The reaction forces due to actuations and constraints in each serial chain can be determined by making use of the theory of reciprocal screws. It is shown that the stiffness of an F-DOF parallel robot can be modeled such that the moving platform is supported by 6 springs related to the reciprocal screws of actuations (F) and constraints (6-F). A general $6{\times}6$ stiffness matrix is derived, which is the sum of the stiffness matrices of actuations and constraints, The compliance of each spring can be precisely determined by modeling the compliance of joints and links in a serial chain as follows; a link is modeled as an Euler beam and the compliance matrix of rotational or prismatic joint is modeled as a $6{\times}6$ diagonal matrix, where one diagonal element about the rotation axis or along the sliding direction is infinite. By summing joint and link compliance matrices with respect to a reference frame and applying unit reciprocal screw to the resulting compliance matrix of a serial chain, the compliance of a spring is determined by the resulting infinitesimal displacement. In order to illustrate this methodology, the stiffness of a Tricept parallel robot has been analyzed. Finally, a numerical example of the optimal design to maximize stiffness in a specified box-shape workspace is presented.