A Step-by-Step Integration Scheme Utilizing the Cardinal B-splines

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  • INOUE Takumi
    Department of Intelligent Machinery and Systems, Faculty of Engineering, Kyushu University
  • SUEOKA Atsuo
    Department of Intelligent Machinery and Systems, Faculty of Engineering, Kyushu University

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  • カーディナルＢスプラインを利用した逐次積分法
  • カーディナル Bスプライン オ リヨウ シタ チクジ セキブンホウ
  • Step by Step Integration Scheme Utilizing the Cardinal B splines

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The authors present a new step-by-step integration scheme by utilizing the cardinal B-splines. The new method organizes conventional implicit methods such as Newmark-β method and Wilson-θ method and so on, and provides a simple computation procedure so that the step-by-step integration can be carried out efficiently. In addition, when we analyze a nonlinear system with discontinuity the computational accuracy can be improved by the approximate detection of the discontinuous points by making good use of the two-scale relation. In this paper, we formulate an algorithm of a time historical response analysis of a straight-line beam structure as an elementary example of multi-degree of freedom system besides a simple single degree of freedom system. The cardinal B-splines used here are only the ones of orders 3 and 4 but the other cardinal B-splines are also available for the step-by-step integration in the same way.

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