• Title/Summary/Keyword: spring element

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An energy-based vibration model for beam bridges with multiple constraints

  • Huang, Shiping;Zhang, Huijian;Chen, Piaohua;Zhu, Yazhi;Zuazua, Enrique
    • Structural Engineering and Mechanics
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    • v.82 no.1
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    • pp.41-53
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    • 2022
  • We developed an accurate and simple vibration model to calculate the natural frequencies and their corresponding vibration modes for multi-span beam bridges with non-uniform cross-sections. A closed set of characteristic functions of a single-span beam was used to construct the vibration modes of the multi-span bridges, which were considered single-span beams with multiple constraints. To simplify the boundary conditions, the restraints were converted into spring constraints. Then the functional of the total energy has the same form as the penalty method. Compared to the conventional penalty method, the penalty coefficients in the proposed approach can be calculated directly, which can avoid the iteration process and convergence problem. The natural frequencies and corresponding vibration modes were obtained via the minimum total potential energy principle. By using the symmetry of the eigenfunctions or structure, the matrix size can be further reduced, which increases the computational efficiency of the proposed model. The accuracy and efficiency of the proposed approach were validated by the finite element method.

An Iterative Scheme for Resolving Unbalanced Forces Between Nonlinear Flexural Bending and Shear Springs in Lumped Plasticity Model (비선형 휨 및 전단 힌지 사이의 불평형력 해소를 위한 수렴계산 기법)

  • Kim, Yousok
    • Journal of the Earthquake Engineering Society of Korea
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    • v.26 no.6
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    • pp.227-235
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    • 2022
  • For a member model in nonlinear structural analysis, a lumped plastic model that idealizes its flexural bending, shear, and axial behaviors by springs with the nonlinear hysteretic model is widely adopted because of its simplicity and transparency compared to the other rigorous finite element methods. On the other hand, a challenging task in its numerical solution is to satisfy the equilibrium condition between nonlinear flexural bending and shear springs connected in series. Since the local forces between flexural and shear springs are not balanced when one or both springs experience stiffness changes (e.g., cracking, yielding, and unloading), the additional unbalanced force due to overshooting or undershooting each spring force is also generated. This paper introduces an iterative scheme for numerical solutions satisfying the equilibrium conditions between flexural bending and shear springs. The effect of equilibrium iteration on analysis results is shown by comparing the results obtained from the proposed method to those from the conventional scheme, where the equilibrium condition is not perfectly satisfied.

Efficiency of CFT column plastic design approach for frame structures subjected to horizontal forces

  • SeongHun Kim;Hyo-Gyoung Kwak
    • Computers and Concrete
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    • v.32 no.5
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    • pp.527-541
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    • 2023
  • This paper emphasizes the use of CFT columns in frame structures subjected to strong horizontal forces and shows that the efficiency of using CFT columns is increased when the plastic design approach is adopted. Because the plastic design approach is based on redistribution of the force of the internal member, a double node for the rotational degrees of freedom, where the adjacent two rotational degrees of freedom can be connected by a non-dimensional spring element, is designed and implemented into the formulation. In addition, an accompanying criterion is considered in order to make it possible to describe the continuous moment redistribution in members connected to a nodal point up to a complete plastic state. The efficiency of CFT columns is reviewed in comparison with RC columns in terms of the cost and the resistance capacity, as defined by a P-M interaction diagram. Three representative frame structures are considered and the obtained results show that the most efficient and economical design can be expected when the use of CFT columns is considered on the basis of the plastic design, especially when a frame structure is subjected to significant horizontal forces, as in a high-rise building.

Implementation of Markerless Augmented Reality with Deformable Object Simulation (변형물체 시뮬레이션을 활용한 비 마커기반 증강현실 시스템 구현)

  • Sung, Nak-Jun;Choi, Yoo-Joo;Hong, Min
    • Journal of Internet Computing and Services
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    • v.17 no.4
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    • pp.35-42
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    • 2016
  • Recently many researches have been focused on the use of the markerless augmented reality system using face, foot, and hand of user's body to alleviate many disadvantages of the marker based augmented reality system. In addition, most existing augmented reality systems have been utilized rigid objects since they just desire to insert and to basic interaction with virtual object in the augmented reality system. In this paper, unlike restricted marker based augmented reality system with rigid objects that is based in display, we designed and implemented the markerless augmented reality system using deformable objects to apply various fields for interactive situations with a user. Generally, deformable objects can be implemented with mass-spring modeling and the finite element modeling. Mass-spring model can provide a real time simulation and finite element model can achieve more accurate simulation result in physical and mathematical view. In this paper, the proposed markerless augmented reality system utilize the mass-spring model using tetraheadron structure to provide real-time simulation result. To provide plausible simulated interaction result with deformable objects, the proposed method detects and tracks users hand with Kinect SDK and calculates the external force which is applied to the object on hand based on the position change of hand. Based on these force, 4th order Runge-Kutta Integration is applied to compute the next position of the deformable object. In addition, to prevent the generation of excessive external force by hand movement that can provide the natural behavior of deformable object, we set up the threshold value and applied this value when the hand movement is over this threshold. Each experimental test has been repeated 5 times and we analyzed the experimental result based on the computational cost of simulation. We believe that the proposed markerless augmented reality system with deformable objects can overcome the weakness of traditional marker based augmented reality system with rigid object that are not suitable to apply to other various fields including healthcare and education area.

The PM2.5 Concentration and Components Characteristics in Miryang (밀양지역의 PM2.5 농도 및 성분특성)

  • Suh, Jeong-Min;Kim, Young-Sik;Jeon, Bo-Kyung;Choi, Kum-Chan;Ryu, Jae-Yong;Park, Jeong-Ho
    • Journal of Environmental Science International
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    • v.16 no.12
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    • pp.1355-1367
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    • 2007
  • This study summarizes the relations among $PM_{2.5}$ concentration, water-soluble ions concentration, metallic element Components characteristics and SPSS in negative ion and metallic element of $PM_{2.5}$ particle in Miryang.(By the urban area, the industrial complex area and the suburban area according to the season) $PM_{2.5}$ concentration of total 72 samples collected from 3 sites turned out to range from 3.47 to 34.7 ${\mu}g/m^3$, and the average concentration was the suburban area-the kin nup(16.00 ${\mu}g/m^3$) > the urban area-the roof of the old Miryang university(10.32 ${\mu}g/m^3$) > the industrial complex-Sapo industrial complex(10.29 ${\mu}g/m^3$). In particular, the suburban area had $PM_{2.5}$ concentration 1.5 times those of urban area, industrial complex. It was thought although the site was suburban and farm-side without pollutants around, it had a higher concentration value influenced by external factors including the brickyard, small-scale incinerator, driving range construction, construction on the Daegu-Busan express and the widening of the four-lane road between Miryang-Anyang nearby. As for water-soluble ions among $PM_{2.5}$ particle collected in Miryang area, $SO4_{2^-}$ accounted for 60% and $NO_{3^-}$, was 30% in spring and summer. And $NO_{3^-}$ accounted for 50% and $SO4_{2^-}$ was 35% in fall and winter. The AI value of metallic Components among $PM_{2.5}$ particle collected in Miryang area had a high value influenced by the apartment complex construction and the extension work of road. The industrial complex area had Zn concentration 3 times, and Fe concentration 2 times those of urban area and suburb area. When it comes to the relation with metallic elements in urban area, the highest coefficient of correlation was between Cr-Fe with 0.85, and Pb-Cd turned out in the reverse correlation. Among metallic elements, the coefficients of correlation between Zn and Cr, Mn, Fe, NI were high in industrial complex area. The highest coefficient of correlation was between Mn-Zn with 0.88, meanwhile Ni and Cu, Cd turned out in the reverse correlation in the suburb area. These coefficients of correlation are attributed to the difference in pollutant sources, rather than difference in pollutant and non-pollutant.

Analysis of Dynamic Deformation of 4-Bar Linkage Mechanism (1) Finite Element Analysis and Numerical Solution (4절 링크 기구의 동적 변형 해석 (I) 유한 요소 해석 및 수치해)

  • Cho, Sun-Whi;Park, Jong-Keun;Lee, Jin
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.16 no.4
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    • pp.737-752
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    • 1992
  • Analysis of elasto-dynamic deformation of flexible linkage mechanism is conducted using the finite element method. The equations of motion of the system are derived from the static structural problem in which dynamic inertia, gravitational and driving forces are treated as external loads. Linear spring model is included in the formulation of equation of motions to represent the effects of deformation of elastic bearings of revolute joints on the system behavior. A computer program is constructed and applied to analyze a specific crank-lever 4-bar mechanism. The algorithm of the program is as follows. First, the natural frequencies and the mode shapes of the system are calculated by solving the eigenproblem of the mechanism system which can be considered as a static structure by assuming the input shaft (crank shaft) to be fixed at any given configuration of mechanism. And finally, the elasto-dynamic deformation of the whole system is obtained using mode superposition method for the case of constant input speed. The effect of geometric stiffness on the mechamism is included in the program with the axial forces of links obtained through the quasi-static displacement analysis. It is found that the geometric stiffness exerts an important effect upon the elasto-dynamic behavior of the flexible linkage mechanism. Elastic deformation of bearing lowers the natural frequencies of the system, resulting smaller elastic displacement at the mid-point of the links and bigger elestic displacement at the ends of the links than rigid bearing. The above investigation of flexible linkage mechanism shows that the effects of the elastic deformation of bearing on the mechanism should be considered to design the mechanism which satisfies more preciously the purpose and the condition of design.

Rare Earth Element, Sm-Nd and Rb-Sr Age and its Geochemical Implication of Leucogranite in the Deokgu Hot Spring Area, Yeongnam Massif, Korea (영남육괴 북동부 덕구온천지구 우백질 화강암의 희토류원소 분포도, Sm-Nd, Rb-Sr 연대 및 지구화학적 의의)

  • Lee, Seung-Gu;Kim, Tong-Kwon;Lee, Tae-Jong
    • The Journal of the Petrological Society of Korea
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    • v.20 no.4
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    • pp.207-217
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    • 2011
  • Here we report major element composition, trace and rare earth element abundance, Sm-Nd and Rb-Sr isotopic composition from Deokgu leucogranite. Chondrite-normalized REE pattern and its Eu anomaly are divided into 3 types systematically, and have close relationship with $SiO_2$ contents. Such geochemical characteristic indicates that the leucogranite was derived by feldspar fractionation from a common source magma. Sm-Nd and Rb-Sr whole rock ages are $1,785{\pm}180Ma$ (initial $^{143}Nd/^{144}Nd\;ratio=0.51003{\pm}0.00016,\;2{\sigma}$; ${\varepsilon}_{Nd}(T)=-5.9$) and $1,735{\pm}260Ma$ (initial $^{87}Sr/^{86}Sr\;ratio=0.702{\pm}0.046,\;2{\sigma}$), respectively. Initial ${\varepsilon}_{Nd}$ value indicates that the magma should be derived from the crustal material. This initial ${\varepsilon}_{Nd}$ value also corresponds well with those from the Precambrian granitoids from North-China Craton rather than those of South-China Craton.

Development of Three-Dimensional Finite Element Model for Structural Analysis of Airport Concrete Pavements (공항 콘크리트 포장 구조해석을 위한 3차원 유한요소 모형 개발)

  • Park, Hae Won;Shim, Cha Sang;Lim, Jin Seon;Joe, Nam Hyun;Jeong, Jin Hoon
    • International Journal of Highway Engineering
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    • v.19 no.6
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    • pp.67-74
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    • 2017
  • PURPOSES : In this study, a three-dimensional nonlinear finite element analysis (FEA) model for airport concrete pavement was developed using the commercial program ABAQUS. Users can select an analysis method and set the range of input parameters to reflect actual conditions such as environmental loading. METHODS : The geometrical shape of the FEA model was chosen by considering the concrete pavement located in the third-stage construction site of Incheon International Airport. Incompatible eight-node elements were used for the FEA model. Laboratory test results for the concrete specimens fabricated at the construction site were used as material properties of the concrete slab. The material properties of the cement-treated base suggested by the Federal Aviation Administration(FAA) manual were used as those of the lean concrete subbase. In addition, preceding studies and pavement evaluation reports of Incheon International Airport were referred for the material properties of asphalt base and subgrade. The kinetic friction coefficient between the concrete slab and asphalt base acquired from a preceding study was used for the friction coefficient between the layers. A nonlinear temperature gradient according to slab depth was used as an input parameter of environmental loading, and a quasistatic method was used to analyze traffic loading. The average load transfer efficiency obtained from an Heavy falling Weight Deflectomete(HWD) test was converted to a spring constant between adjacent slabs to be used as an input parameter. The reliability of the FEA model developed in this study was verified by comparing its analysis results to those of the FEAFAA model. RESULTS : A series of analyses were performed for environmental loading, traffic loading, and combined loading by using both the model developed in this study and the FEAFAA model under the same conditions. The stresses of the concrete slab obtained by both analysis models were almost the same. An HWD test was simulated and analyzed using the FEA model developed in this study. As a result, the actual deflections at the center, mid-edge, and corner of the slab caused by the HWD loading were similar to those obtained by the analysis. CONCLUSIONS : The FEA model developed in this study was judged to be utilized sufficiently in the prediction of behavior of airport concrete pavement.

Effect of Foundation Flexibility of Offshore Wind Turbine on Force and Movement at Monopile Head (해상풍력발전기 기초구조물의 강성이 모노파일 두부의 부재력 및 변위에 미치는 영향)

  • Jung, Sungmoon;Kim, Sung-Ryul;Lee, Juhyung;Le, Chi Hung
    • Journal of the Korean Geosynthetics Society
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    • v.13 no.4
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    • pp.21-31
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    • 2014
  • Recently, the research on renewable energy against depletion of fossil fuel have been actively carried out in the world. Especially, offshore wind turbines are very economical and innovative technology. However, offshore wind turbines experience large base moments due to the wind and wave loading, so the monopile with large diameter needs to be applied. For the economical design of the large diameter pile, it is important to consider the flexibility of the foundation to estimate the maximum moment accurately, based on studies conducted so far. In this paper, the foundation was modeled using the finite element method in order to better describe the large diameter effect of a monopile and the results were compared with those of p-y method. For the examples studied in this paper, the change in maximum moment was insignificant, but the maximum tilt angle from the finite element method was over 14% larger than that of p-y method. Therefore, the finite element approach is recommended to model the flexibility effect of the pile when large tilt angles may cause serviceability issues.

Damage Evaluation of Track Components for Sleeper Floating Track System in Urban Transit (도시철도 침목플로팅궤도 궤도구성품의 손상평가)

  • Choi, Jung-Youl;Kim, Hak-Seon;Han, Kyung-Sung;Jang, Cheol-Ju;Chung, Jee-Seung
    • The Journal of the Convergence on Culture Technology
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    • v.5 no.4
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    • pp.387-394
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    • 2019
  • In this study, in order to evaluate the damage and deterioration of the track components of sleeper floating track (STEDEF), the field samples(specimens) were taken from the serviced line over 20 years old, and the track components were visually inspected, and investigated by laboratory tests and finite element analysis. As a result of visual inspection, the damage of the rail pad and fastener was slight, but the rubber boot was worn and torn at the edges of bottom. The resilience pads were clearly examined for thickness reduction and fatigue hardening layer. As a result of spring stiffness test of rail pad and resilience pad, the deterioration of rail pad was insignificant, but the deterioration of resilience pad exceeded design standard value. Therefore resilience pad was directly affected by train passing tonnage. As a result of comparing the deterioration state of the field sample and the numerical analysis result, the stress and displacement concentration position of the finite element model and the damage position of the field sample were coincident.