• Title/Summary/Keyword: system of discrete equations

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Total Dynamic Analysis of Deep-Seabed Integrated Mining System (심해저 광물자원 채광시스템의 통합거동 해석)

  • Kim, Hyung-Woo;Hong, Sup;Lee, Chang-Ho;Choi, Jong-Su;Yeu, Tae-Kyeong
    • Journal of Navigation and Port Research
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    • v.34 no.3
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    • pp.195-203
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    • 2010
  • This paper concerns about total dynamic analysis of integrated mining system. This system consists of vertical steel pipe, intermediate buffer station, flexible pipe and self-propelled miner. The self-propelled miner and buffer are assumed as rigid-body of 6-dof. Discrete models of vertical steel pipe and flexible pipe are adopted, which are obtained by means of lumped-parameter method. The motion of mining vessel is not considered. Instead, the motion of mining vessel is taken into account in form of various boundary conditions (e.g. forced excitation in slow motion and/or fast oscillation and so on). A terramechanics model of extremely cohesive soft soil is applied to the self-propelled miner. Hinged and ball constraints are used to define the connections between sub-systems (vertical steel pipe, buffer, flexible pipe, self-propelled miner). Equations of motion of the coupled model are derived with respect to the each local coordinates system. Four Euler parameters are used to express the orientations of the sub-systems. To solve the equations of motion of the total dynamic model, an incremental-iterative formulation is employed. Newmark-${\beta}$ method is used for time-domain integration. The total dynamic responses of integrated mining system are investigated.

Modeling and analysis of dynamic heat transfer in the cable penetration fire stop system by using a new hybrid algorithm (새로운 혼합알고리즘을 이용한 CPFS 내에서의 일어나는 동적 열전달의 수식화 및 해석)

  • Yoon En Sup;Yun Jongpil;Kwon Seong-Pil
    • Journal of the Korean Institute of Gas
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    • v.7 no.4 s.21
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    • pp.44-52
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    • 2003
  • In this work dynamic heat transfer in a CPFS (cable penetration fire stop) system built in the firewall of nuclear power plants is three-dimensionally investigated to develop a test-simulator that can be used to verify effectiveness of the sealant. Dynamic heat transfer in the fire stop system is formulated in a parabolic PDE (partial differential equation) subjected to a set of initial and boundary conditions. First, the PDE model is divided into two parts; one corresponding to heat transfer in the axial direction and the other corresponding to heat transfer on the vertical planes. The first PDE is converted to a series of ODEs (ordinary differential equations) at finite discrete axial points for applying the numerical method of SOR (successive over-relaxation) to the problem. The ODEs are solved by using an ODE solver In such manner, the axial heat flux can be calculated at least at the finite discrete points. After that, all the planes are separated into finite elements, where the time and spatial functions are assumed to be of orthogonal collocation state at each element. The initial condition of each finite element can be obtained from the above solution. The heat fluxes on the vertical planes are calculated by the Galerkin FEM (finite element method). The CPFS system was modeled, simulated, and analyzed here. The simulation results were illustrated in three-dimensional graphics. Through simulation, it was shown clearly that the temperature distribution was influenced very much by the number, position, and temperature of the cable stream, and that dynamic heat transfer through the cable stream was one of the most dominant factors, and that the feature of heat conduction could be understood as an unsteady-state process.

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Tourists' Excursion Behavior Analysis Considering Their Information Usage (관광객의 정보이용이 관광주유행동에 미치는 영향분석)

  • Kim, Hyun
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.30 no.4D
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    • pp.339-349
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    • 2010
  • The objective of this paper is to develop a structural equations model system for the purpose of tourists' excursion behaviour analysis with their information usage. A tourist' excursion behavior defined as activities in the sightseeing region between arriving and leaving time includes indexes with respect to activity' time use and the number of spots. Additionally, such indexes can be modeled as endogenous variables in the structural equation model system on the assumption that they are influenced by the degree of familarity on the sightseeing region, the degree of information usage, and individual attributes. The case study application involves excursion behaviour data such as one-day excursion activity and information usage diary that are observed in the Fuji Five Lakes, Japan. Since the models presented in the paper are available to statistically analyze the covariance among the endogenous variables, they have the advantage of effectiveness analysis on information usage in the excursion area, compared to the prior approaches such as discrete choice models.

Formulation and evaluation a finite element model for free vibration and buckling behaviours of functionally graded porous (FGP) beams

  • Abdelhak Mesbah;Zakaria Belabed;Khaled Amara;Abdelouahed Tounsi;Abdelmoumen A. Bousahla;Fouad Bourada
    • Structural Engineering and Mechanics
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    • v.86 no.3
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    • pp.291-309
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    • 2023
  • This paper addresses the finite element modeling of functionally graded porous (FGP) beams for free vibration and buckling behaviour cases. The formulated finite element is based on simple and efficient higher order shear deformation theory. The key feature of this formulation is that it deals with Euler-Bernoulli beam theory with only three unknowns without requiring any shear correction factor. In fact, the presented two-noded beam element has three degrees of freedom per node, and the discrete model guarantees the interelement continuity by using both C0 and C1 continuities for the displacement field and its first derivative shape functions, respectively. The weak form of the governing equations is obtained from the Hamilton principle of FGP beams to generate the elementary stiffness, geometric, and mass matrices. By deploying the isoparametric coordinate system, the derived elementary matrices are computed using the Gauss quadrature rule. To overcome the shear-locking phenomenon, the reduced integration technique is used for the shear strain energy. Furthermore, the effect of porosity distribution patterns on the free vibration and buckling behaviours of porous functionally graded beams in various parameters is investigated. The obtained results extend and improve those predicted previously by alternative existing theories, in which significant parameters such as material distribution, geometrical configuration, boundary conditions, and porosity distributions are considered and discussed in detailed numerical comparisons. Determining the impacts of these parameters on natural frequencies and critical buckling loads play an essential role in the manufacturing process of such materials and their related mechanical modeling in aerospace, nuclear, civil, and other structures.

A Study of Rayleigh Damping Effect on Dynamic Crack Propagation Analysis using MLS Difference Method (MLS 차분법을 활용한 동적 균열전파해석의 Rayleigh 감쇠영향 분석)

  • Kim, Kyeong-Hwan;Lee, Sang-Ho;Yoon, Young-Cheol
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.29 no.6
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    • pp.583-590
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    • 2016
  • This paper presents a dynamic crack propagation algorithm with Rayleigh damping effect based on the MLS(Moving Least Squares) Difference Method. Dynamic equilibrium equation and constitutive equation are derived by considering Rayliegh damping and governing equations are discretized by the MLS derivative approximation; the proportional damping, which has not been properly treated in the conventional strong formulations, was implemented in both the equilibrium equation and constitutive equation. Dynamic equilibrium equation including time relevant terms is integrated by the Central Difference Method and the discrete equations are simplified by lagging the velocity one step behind. A geometrical feature of crack is modeled by imposing the traction-free condition onto the nodes placed at crack surfaces and the effect of movement and addition of the nodes at every time step due to crack growth is appropriately reflected on the construction of total system. The robustness of the proposed numerical algorithm was proved by simulating single and multiple crack growth problems and the effect of proportional damping on the dynamic crack propagation analysis was effectively demonstrated.

Dynamic Instability and Multi-step Taylor Series Analysis for Space Truss System under Step Excitation (스텝 하중을 받는 공간 트러스 시스템의 멀티스텝 테일러 급수 해석과 동적 불안정)

  • Lee, Seung-Jae;Shon, Su-Deok
    • Journal of Korean Society of Steel Construction
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    • v.24 no.3
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    • pp.289-299
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    • 2012
  • The goal of this paper is to apply the multi-step Taylor method to a space truss, a non-linear discrete dynamic system, and analyze the non-linear dynamic response and unstable behavior of the structures. The accurate solution based on an analytical approach is needed to deal with the inverse problem, or the dynamic instability of a space truss, because the governing equation has geometrical non-linearity. Therefore, the governing motion equations of the space truss were formulated by considering non-linearity, where an accurate analytical solution could be obtained using the Taylor method. To verify the accuracy of the applied method, an SDOF model was adopted, and the analysis using the Taylor method was compared with the result of the 4th order Runge-Kutta method. Moreover, the dynamic instability and buckling characteristics of the adopted model under step excitation was investigated. The result of the comparison between the two methods of analysis was well matched, and the investigation shows that the dynamic response and the attractors in the phase space can also delineate dynamic snapping under step excitation, and damping affects the displacement of the truss. The analysis shows that dynamic buckling occurs at approximately 77% and 83% of the static buckling in the undamped and damped systems, respectively.

A Meshless Method Using the Local Partition of Unity for Modeling of Cohesive Cracks (점성균열 모델을 위한 국부단위분할이 적용된 무요소법)

  • Zi, Goangseup;Jung, Jin-kyu;Kim, Byeong Min
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.26 no.5A
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    • pp.861-872
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    • 2006
  • The element free Galerkin method is extended by the local partition of unity method to model the cohesive cracks in two dimensional continuum. The shape function of a particle whose domain of influence is completely cut by a crack is enriched by the step enrichment function. If the domain of influence contains a crack tip inside, it is enriched by a branch enrichment function which does not have the LEFM stress singularity. The discrete equations are obtained directly from the standard Galerkin method since the enrichment is only for the displacement field, which satisfies the local partition of unity. Because only particles whose domains of influence are influenced by a crack are enriched, the system matrix is still sparse so that the increase of the computational cost is minimized. The condition for crack growth in dynamic problems is obtained from the material instability; when the acoustic tensor loses the positive definiteness, a cohesive crack is inserted to the point so as to change the continuum to a discontiuum. The crack speed is naturally obtained from the criterion. It is found that this method is more accurate and converges faster than the classical meshless methods which are based on the visibility concept. In this paper, several well-known static and dynamic problems were solved to verify the method.