• Title/Summary/Keyword: Elastic Contact Theory

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Determination of the Vlasov foundation parameters -quadratic variation of elasticity modulus- using FE analysis

  • Celik, Mecit;Omurtag, Mehmet H.
    • Structural Engineering and Mechanics
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    • v.19 no.6
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    • pp.619-637
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    • 2005
  • The objective of this research was to determine the Vlasov soil parameters for quadratically varying elasticity modulus $E_s$(z) of the compressible soil continuum and discuss the interaction affect between two close plates. Interaction problem carried on for uniformly distributed load carrying plates. Plate region was simulated by Kirchhoff plate theory based (mixed or displacement type) 2D elements and the foundation continuum was simulated by displacement type 2D elements. At the contact region, plate and foundation elements were geometrically coupled with each other. In this study the necessary formulas for the Vlasov parameters were derived when Young's modulus of the soil continuum was varying as a quadratic function of z-coordinate through the depth of the foundation. In the examples, first the elements and the iterative FE algorithm was verified and later the results of quadratic variation of $E_s$(z) were compared with the previous examples in order to discuss the general behavior. As a final example two plates close to each other resting on elastic foundation were handled to see their interaction influences on the Vlasov foundation parameters. Original examples were solved using both mixed and displacement type plate elements in order to confirm the results.

Dynamic Fracture Analysis of High-speed Impact on Granite with Peridynamic Plasticity (페리다이나믹 소성 모델을 통한 화강암의 고속 충돌 파괴 해석)

  • Ha, Youn Doh
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.32 no.1
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    • pp.37-44
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    • 2019
  • A bond-based peridynamic model has been reported dynamic fracture characteristic of brittle materials through a simple constitutive model. In the model, each bond is assumed to be a simple spring operating independently. As a result, this simple bond interaction modeling restricts the material behavior having a fixed Poisson's ratio of 1/4 and not being capable of expressing shear deformation. We consider a state-based peridynamics as a generalized peridynamic model. Constitutive models in the state-based peridynamics are corresponding to those in continuum theory. In state-based peridynamics, thus, the response of a material particle depends collectively on deformation of all bonds connected to other particles. So, a state-based peridynamic theory can represent the volume and shear changes of the material. In this paper, the perfect plasticity is considered to express plastic deformation of material by the state-based peridynamic constitutive model with perfect plastic flow rule. The elastic-plastic behavior of the material is verified through the stress-strain curves of the flat plate example. Furthermore, we simulate the high-speed impact on 3D granite model with a nonlocal contact modeling. It is observed that the damage patterns obtained by peridynamics are similar to experimental observations.

Particle-based Numerical Simulation of Continuous Ice Breaking Process around Wedge-type Model Ship (쐐기형 모형선 주위 연속 쇄빙과정에 관한 입자 기반 수치 시뮬레이션)

  • Ren, Di;Sin, Woo-Jin;Kim, Dong-Hyun;Park, Jong-Chun;Jeong, Seong-Yeob
    • Journal of the Society of Naval Architects of Korea
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    • v.57 no.1
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    • pp.23-34
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    • 2020
  • This paper covers the development of prediction techniques for ice load on ice-breakers operating in continuous ice-breaking under level ice conditions using particle-based continuum mechanics. Ice is assumed to be a linear elastic material until the fracture occurs. The maximum normal stress theory is used for the criterion of fracture. The location of the crack can be expressed using a local scalar function consisting of the gradient of the first principal stress and the corresponding eigen-vector. This expression is used to determine the relative position of particle pair to the new crack. The Hertz contact model is introduced to consider the collisions between ice fragments and the collisions between hull and ice fragments. In order to verify the developed technique, the simulation results for the three-point bending problems of ice-specimen and the continuous ice-breaking problem around a wedge-type model ship with bow angle of 20° are compared with the experimental results carrying out at Korea Research Institute of Ships and Ocean Engineering (KRISO).

Rotordynamic Model Development with Consideration of Rotor Core Laminations for 2.2 kW-Class Squirrel-Cage Type Induction Motors and Influence Investigation of Bearing Clearance (2.2 kW급 유도전동기의 회전자 적층구조를 고려한 회전체 동역학 해석모델 개발 및 베어링 간극의 영향 분석)

  • Park, Jisu;Sim, Kyuho;Lee, Sung-Ho
    • Tribology and Lubricants
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    • v.35 no.3
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    • pp.158-168
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    • 2019
  • This paper presents the investigation of two types of rotordynamic modeling issues for 2.2 kW-class, rated speed of 1,800 rpm, squirrel-cage type induction motors. These issues include the lamination structure of rotor cores, and the radial clearance of ball bearings that support the shaft of the motor. Firstly, we focus on identifying the effects of rotor core lamination on the rotordynamic analysis via a 2D prediction model. The influence of lamination is considered as the change in the elastic modulus of the rotor core, which is determined by a modification factor ranging from 0 to 1.0. The analysis results show that the unbalanced response of the rotor-bearing system significantly varies depending on the value of the modification factor. Through modal testing of the system, the modification factor of 0.079 is proven to be appropriate to consider the effects of lamination. Next, we investigate the influence of ball bearing clearance on the rotordynamic analysis by establishing a bearing analysis model based on Hertz's contact theory. The analysis results indicate that negative clearance greatly changes the bearing static behavior. Rotordynamic analysis using predicted bearing stiffness with various clearances from -0.005 mm to 0.010 mm reveals that variations in clearance result in a slight difference in the displacement of the system up to 18.18. Thus, considering lamination in rotordynamic analysis is necessary as it can cause serious analysis errors in unbalanced response. However, considering the effect of the bearing clearance is optional because of its relatively weak impact.

Vertical Vibration of Rigid Circular Footings on Sand (사질토(砂質土) 위에 놓인 강성(剛性) 원형기초(圓形基礎)의 수직진동(垂直振動))

  • Kim, Soo Il;Min, Tuk Ki
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.5 no.3
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    • pp.127-136
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    • 1985
  • A simplified single degree of freedom analog with mass-spring-dashpot is proposed in this study. The simplified analog can describe the dynamic behavior of a rigid circular footings whose contact pressures are parabolic. The analog proposed in this study shows remarkable agreement when compared with the elastic half-space theory the analog is also compared with vertical vibration test results of model concrete footings. For the vibration experiments, 11 circular footings with different mass ratio are constructed. The elastic half-space is represented by compacted sand layer. A constant force excitation vibrator is used for the dynamic loading. The frequency range for vibration tests is 30 to 100 Hz. From the dynamic experiments, it is found that the measured resonant frequencies agree very well with the analog results, however, the ratio of theoretical and measured resonant amplitudes vary between 0.5 and 1.7. It is also found that, when the dynamic force is increased, the resonant frequency is decreased slightly and the resonant amplitude is increased slightly.

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Analysis of Reinforcement Effect of TSL (Thin Spray-on Liner) as Supports of Tunnel by Numerical Analysis (수치해석에 의한 터널 지보재로서 TSL(Thin Spray-on Liner)의 보강 효과 분석)

  • Lee, Kicheol;Kim, Dongwook;Chang, Soo-Ho;Choi, Soon-Wook;Lee, Chulho
    • Journal of the Korean Geosynthetics Society
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    • v.16 no.4
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    • pp.151-161
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    • 2017
  • A TSL (Thin Spray-on Liner) has a higher initial strength and faster construction time than conventional cementitious shotcrete. Because of its high adhesion and tensile strength, the TSL reinforced concrete show a characteristic like composite materials. In this study, to consider an application to the conventional design method, ASD (allowable stress design), numerical study was used. In the numerical analysis, material and contact properties were adopt from previous studies. Then a thickness of concrete in the tunnel was evaluated with the TSL reinforced case by the ASD concept. In other words, bending compressive stress, bending tensile stress and shearing force of the concrete were considered to determine a thickness of concrete lining by the given boundary conditions. From the numerical analysis, there was no tendency to show by the ASD because the ASD is based on the elastic theory while the TSL typically contributes to reinforcement after yielding.

Reliability of mortar filling layer void length in in-service ballastless track-bridge system of HSR

  • Binbin He;Sheng Wen;Yulin Feng;Lizhong Jiang;Wangbao Zhou
    • Steel and Composite Structures
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    • v.47 no.1
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    • pp.91-102
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    • 2023
  • To study the evaluation standard and control limit of mortar filling layer void length, in this paper, the train sub-model was developed by MATLAB and the track-bridge sub-model considering the mortar filling layer void was established by ANSYS. The two sub-models were assembled into a train-track-bridge coupling dynamic model through the wheel-rail contact relationship, and the validity was corroborated by the coupling dynamic model with the literature model. Considering the randomness of fastening stiffness, mortar elastic modulus, length of mortar filling layer void, and pier settlement, the test points were designed by the Box-Behnken method based on Design-Expert software. The coupled dynamic model was calculated, and the support vector regression (SVR) nonlinear mapping model of the wheel-rail system was established. The learning, prediction, and verification were carried out. Finally, the reliable probability of the amplification coefficient distribution of the response index of the train and structure in different ranges was obtained based on the SVR nonlinear mapping model and Latin hypercube sampling method. The limit of the length of the mortar filling layer void was, thus, obtained. The results show that the SVR nonlinear mapping model developed in this paper has a high fitting accuracy of 0.993, and the computational efficiency is significantly improved by 99.86%. It can be used to calculate the dynamic response of the wheel-rail system. The length of the mortar filling layer void significantly affects the wheel-rail vertical force, wheel weight load reduction ratio, rail vertical displacement, and track plate vertical displacement. The dynamic response of the track structure has a more significant effect on the limit value of the length of the mortar filling layer void than the dynamic response of the vehicle, and the rail vertical displacement is the most obvious. At 250 km/h - 350 km/h train running speed, the limit values of grade I, II, and III of the lengths of the mortar filling layer void are 3.932 m, 4.337 m, and 4.766 m, respectively. The results can provide some reference for the long-term service performance reliability of the ballastless track-bridge system of HRS.