Advertisement

Comparison of Time Discretization Schemes to Simulate the Motion of an Inextensible Beam

  • Steffen Basting
  • Annalisa Quaini
  • Roland Glowinski
  • Suncica Canic
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 103)

Abstract

We compare three different time discretization schemes in combination with an augmented Lagrangian method to simulate the motion of an inextensible beam. The resulting saddle-point problem is solved with an Uzawa-Douglas-Rachford algorithm. The three schemes are tested on a benchmark with an analytical solution and on a more challenging application. We found that in order to obtain optimal convergence behavior in time, the stopping tolerance for the Uzawa-type algorithm should be balanced against the time step size.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J.-F. Bourgat, M. Dumay, R. Glowinski, Large displacement calculations of inexstensible pipelines by finite element and nonlinear programming methods. SIAM J. Sci. Stat. Comput. 1, 34–81 (1980)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    M. Fortin, R. Glowinski, Augmented Lagrangian Methods: Application to the Numerical Solution of Boundary Value Problem (North-Holland, Amsterdam, 1983)Google Scholar
  3. 3.
    R. Glowinski, M. Holmstrom, Constrained motion problems with applications by nonlinear programming methods. Surv. Math. Ind. 5, 75–108 (1995)zbMATHMathSciNetGoogle Scholar
  4. 4.
    R. Glowinski, P.L. Tallec, Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics (SIAM, Philadelphia, 1988)Google Scholar
  5. 5.
    J.C. Houbolt, A recurrence matrix solution for the dynamic response of elastic aircraft. J. Aeronaut. Sci. 17(9), 540–550 (1950)CrossRefMathSciNetGoogle Scholar
  6. 6.
    N.M. Newmark, A method of computation for structural dynamics. J. Eng. Mech. Div. 85(3), 67–94 (1959)Google Scholar
  7. 7.
    K. Subbaraj, M. Dokainish, A survey of direct time-integration methods in computational structural dynamics II. Implicit methods. Comput. Struct. 32(6), 1387–1401 (1989)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Steffen Basting
    • 1
  • Annalisa Quaini
    • 2
  • Roland Glowinski
    • 2
  • Suncica Canic
    • 2
  1. 1.Friedrich-Alexander-University Erlangen-NurembergErlangenGermany
  2. 2.University of HoustonHoustonUSA

Personalised recommendations