High precision integration for dynamic structural systems with holonomic constraints

Xiaojian Liu*, D. W. Begg, M. A. Devane, Wanxie Zhong

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper presents a high precision integration method for the dynamic response analysis of structures with holonomic constraints. A detail recursive scheme suitable for algebraic and differential equations (ADEs) which incorporates generalized forces is established. The matrix exponential involved in the scheme is calculated precisely using 2N algorithm. The Taylor expansions of the nonlinear term concerned with state variables of the structure and the generalized constraint forces of the ADEs are derived and consequently, their particular integrals are obtained. The accuracy and effectiveness of the present method is demonstrated by two numerical examples, a plane truss with circular slot at its tip point and a slewing flexible cantilever beam which is currently interesting in optimal control of robot manipulators.

Original languageEnglish
Pages (from-to)283-295
Number of pages13
JournalStructural Engineering and Mechanics: An International Journal
Issue number3
Publication statusPublished - 25 May 1997


  • Algebraic and differential equations
  • Dynamic structures
  • Holonomic constraints
  • Matrix exponential
  • Numerical integration


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