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

Takumi Inoue, Atsuo Sueoka

Research output: Contribution to journalArticle

Abstract

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 points of discontinuity 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.

Original languageEnglish
Pages (from-to)1074-1081
Number of pages8
JournalNihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C
Volume66
Issue number644
DOIs
Publication statusPublished - Jan 1 2000

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering

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