• Title, Summary, Keyword: quadratic form

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On the Use of Modal Derivatives for Reduced Order Modeling of a Geometrically Nonlinear Beam (모드 미분을 이용한 기하비선형 보의 축소 모델)

  • Jeong, Yong-Min;Kim, Jun-Sik
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.30 no.4
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    • pp.329-334
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    • 2017
  • The structures, which are made up with the huge number of degrees-of-freedom and the assembly of substructures, have a great complexity. In order to increase the computational efficiency, the analysis models have to be simplified. Many substructuring techniques have been developed to simplify large-scale engineering problems. The techniques are very powerful for solving nonlinear problems which require many iterative calculations. In this paper, a modal derivatives-based model order reduction method, which is able to capture the stretching-bending coupling behavior in geometrically nonlinear systems, is adopted and investigated for its performance evaluation. The quadratic terms in nonlinear beam theory, such as Green-Lagrange strains, can be explained by the modal derivatives. They can be obtained by taking the modal directional derivatives of eigenmodes and form the second order terms of modal reduction basis. The method proposed is then applied to a co-rotational finite element formulation that is well-suited for geometrically nonlinear problems. Numerical results reveal that the end-shortening effect is very important, in which a conventional modal reduction method does not work unless the full model is used. It is demonstrated that the modal derivative approach yields the best compromised result and is very promising for substructuring large-scale geometrically nonlinear problems.

Growth Model of Sowthistle (Ixeris dentata Nakai) Using Expolinear Function in a Closed-type Plant Production System (완전제어형 식물 생산 시스템에서 선형 지수 함수를 이용한 씀바귀의 생육 모델)

  • Cha, Mi-Kyung;Son, Jung-Eek;Cho, Young-Yeol
    • Horticultural Science & Technology
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    • v.32 no.2
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    • pp.165-170
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    • 2014
  • The objective of this study was to make growth and yield models of sowthistle (Ixeris dentata Nakai) by using an expolinear functional equation in a closed-type plant production system. The growth and yield of hydroponically-grown sowthistle were investigated under four different planting distances ($15{\times}10$, $15{\times}15$, $15{\times}20$, and $15{\times}25$ cm). Shoot dry weights per plant was the highest at $15{\times}25$ cm, but was the lowest at $15{\times}10$ cm. Shoot dry weights per area was the highest at $15{\times}15$ cm, but was the lowest at $15{\times}25$ cm. The optimum planting density and planting distance for yield of sowthistle were 44 plants/$m^2$ and $15{\times}15$ cm, respectively. Shoot dry weights per plant and per area were showed as an expolinear type functional equation. A linear relationship between shoot dry and fresh weights was observed to be linear regardless of the planting distance. Crop growth rate, relative growth rate and lost time in an expolinear functional equation showed quadratic function form. Radiation use efficiency of sowthistle was $4.3-6.1g{\cdot}MJ^{-1}$. The measured and estimated shoot dry weights showed a good agreement using days after transplanting as input data. It is concluded that the expolinear growth model can be a useful tool for quantifying the growth and yield of sowthistle in a closed-type plant production system.

A Study on Technological Forecasting for Promising Alternative Technologies Using Fisher-Pry Modification Model (Fisher-Pry 수정모형을 활용한 유망대체기술 예측에 관한 연구)

  • Hong, Sung-Il;Kim, Byung-Nam
    • The Journal of the Korea Contents Association
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    • v.19 no.5
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    • pp.104-114
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    • 2019
  • In the global market competition, countries and businesses are actively engaged in technology prediction activities to maximize their profits by attempting to enter and preempting the core technology of the future. In this paper, we propose a growth model based on patent application trends to predict the time to replace a product with a promising new technology to dominate the market. Although the Fisher-Pry model that Bhargava generalized to predict the emergence of promising alternative technologies was relatively satisfactory compared to the original Fisher-Pry model, it was difficult to predict the replacement rate behavior properly due to a parameter problem. The application of the Fisher-Pry Modification Model in the form of a quadratic equation through the patent trend analysis of the optical storage system for the purpose of verifying the time alternative to the light storage technology has resulted in satisfactory verification results. It is expected that small and medium-sized companies and individual researchers will apply this model and use it more easily to predict the time to replace the market for promising replacement technologies.