Some experiences in the equilibrium path determination

  • Tomasz Sokół Warsaw University of Technology
  • Marek Witkowski Warsaw University of Technology

Abstract

The paper presents numerical techniques useful in nonlinear analysis of structures. The main attention is focused on procedures for the determination of equilibrium paths and examination of critical points. Most of them are connected with the arc length method and can be treated as additional tools, that improve the effectiveness and reliability of computations. It was confirmed in a number of test examples, presented in authors' earlier papers [1-4]. In this paper only one, but the most representative example including different types of critical points has been chosen. The conclusions are that even highly nonlinear problems can effectively be solved using relatively simple algorithms.

Keywords

References

[1] T. Sokół, M. Witkowski. Numerical problems of controlling the incremental process in geometrically nonlinear analysis. (in Polish), In: Proc. IX Polish Conf. on "Computer Methods in Mechanics". Vol. 3,1009- 1016, CracowRytro, 1989.
[2] T. Sokół, M. Witkowski. The equilibrium path determination in nonlinear analysis of structures, Advances in nonlinear finite element methods. B.H.P. Topping, M. Papadrakakis, eds., 35--45, Civil-Comp Press, Edinburgh 1994.
[3] T. Sokół, M. Witkowski. Critical states of imperfect sensitive structures. In: J. Obrębski, ed., Int. Conf. On "Lightweight Structures in Civil Engineering", 228-235, Warsaw 1995.
[4] T. Sokół. Non-linear analysis of space bar structures with regard to the imperfections. (in Polish), Ph.D. Thesis, Warsaw University of Technology, 1995.
[5] E. Riks. The application of Newton's method to the problem of elastic stability. J. Appl. Mech., 39: 1060-1066, 1972.
Published
Jun 22, 2023
How to Cite
SOKÓŁ, Tomasz; WITKOWSKI, Marek. Some experiences in the equilibrium path determination. Computer Assisted Methods in Engineering and Science, [S.l.], v. 4, n. 2, p. 189-208, june 2023. ISSN 2956-5839. Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/1402>. Date accessed: 13 nov. 2024.
Section
Articles

Most read articles by the same author(s)