• Title/Summary/Keyword: 4차 Runge-Kutta

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Effect of Compressibility on Flow Field and Fiber Orientation in the Filling Stage of Injection Molding (사출성형의 충전시 고분자용융액의 압축성이 유동장과 단섬유 배향에 미치는 영향)

  • Lee, S.C.;Ko, J;Youn, J.R.
    • The Korean Journal of Rheology
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    • v.10 no.4
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    • pp.217-226
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    • 1998
  • The anisotropy caused by the fiber orientation, which is inevitably generated by the flow during injection molding of short fiber reinforced polymers, greatly influences dimensional accuracy, mechanical properties, and other quality of the final product. Since the filling stage of the injection molding process plays a vital role in determining fiber orientation, an accurate analysis of flow field for the filling stage is needed. Unbalanced filling occurs when a complex or a multi-cavity mold is used leading to development of regions where the fiber suspension is under compression. It is impossible to make an accurate calculation of the flow field during filling with the analysis assuming incompressible fluid. A mold with four cavities with different filling times was produced to compare the numerical analysis results with the experimental data. There was a good agreement between the experimental and theoretical results when the compressibility of the polymer melt was considered for the numerical simulation. The fiber orientation states for compressible and incompressible fluids were also compared qualitatively as well as quantitatively in this study.

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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.