Skip to main content
SpringerLink
Log in

Nichtlineare Stabilitätsuntersuchungen mit der Methode der Finiten Elemente

Nonlinear stability analysis in finite element formulation

  • Published:
Ingenieur-Archiv Aims and scope Submit manuscript

Übersicht

Ziel der Arbeit ist die exakte und genäherte Bestimmung der kritischen Last von elastischen Systemen mit nichtlinearem Vorbeulverhalten. Grundlage ist die Verschiebungsformulierung der Methode der finiten Elemente in inkrementell/iterativer Darstellung. Im ersten Hauptteil werden begleitende Stabilitätsuntersuchungen bei der exakten Auswertung der nichtlinearen Gleichungen behandelt. Hierzu gehören die Determinantenbeobachtung sowie Eigenwertuntersuchungen für den Lastparameter und die Eigenfrequenz. Im zweiten Hauptteil werden zwei verbesserte Anfangsstabilitätsanalysen zur genäherten Bestimmung der kritischen Last vorgestellt, die auf Reihenlösungen der Gleichgewichts- und Stabilitätsgleichungen basieren. In beiden Teilen bestätigen zahlreiche Beispiele die Brauchbarkeit der behandelten Verfahren.

Summary

Exact and approximate solutions for the critical load of elastic structures exhibiting a nonlinear prebuckling response are described. The incremental iterative displacement finite element formulation is used. Two main aspects are covered. First different supplementary procedures evaluating the stability citerion parallel to the nonlinear analysis are investigated. Among these are the function of the determinant, and eigenvalue formulations for the load parameter and the frequency. In the second part two improved initial stability analyses are proposed to determine an approximate solution of the final critical load. They are based on the perturbation method in which the equilibrium and stability equations are expanded in series solutions. In both parts several numerical examples are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literatur

  1. Almroth, B. O.; Brogan, F. A.: Bifurcation Analysis as an Approximation for the Collapse Load for General Shells. AIAA J. 10 (1972) 463–467

    Google Scholar 

  2. Bathe, K.-J.; Wilson, E. L.: Numerical Methods in Finite Element Anal. Prentice-Hall 1976

  3. Bergan, P. G.; Horrigmoe, G.; Krakeland, B.; Søreide, T.: Solution Techniques for Nonlinear Finite Element Problems. Int. J. Num. Meth. Eng. 12 (1978) 1677–1696

    Google Scholar 

  4. Brendel, B.; Häfner, L.; Ramm, E.; Sättele, J. M.: Programmdokumentation und Eingabebeschreibung zum Programmsystem NISA. Dokumentation Inst. für Baustatik Univ. Stuttgart 1977

    Google Scholar 

  5. Brendel, B.: Zur geometrisch nichtlinearen Elastostabilität. Diss. Univ. Stuttgart 1978

  6. Brendel, B.; Ramm, E.: Linear and Nonlinear Stability Analysis of Cylindrical Shells. Comput. Struct. 5 (1980) 549–558

    Google Scholar 

  7. Brendel, B.; Ramm, E.; Bornscheuer, F. W.: Stabilitätsuntersuchungen weitgespannter Flächentragwerke. Mitt. Sonderforschungsbereichs 64 „Weitgespannte Flächentragwerke” Univ. Stuttgart, H. 57 (1980)

  8. Bushnell, D.: Analysis of Buckling and Vibration of Ring-Stiffened, Segmented Shells of Revolution. Int. J. Solids Struct. 6 (1970) 157–181

    Google Scholar 

  9. Bushnell, D.: Stress, Stability and Vibration of Complex Branched Shells of Revolution: Analysis and User's Manual for BOSOR 4. NASA CR-2116 (1972)

  10. Cohen, G. A.: Computer Analysis of Asymmetric Buckling of Ring-Stiffened Orthotropic Shells of Revolution. AIAA — J. 6 (1968) 141–149

    Google Scholar 

  11. Connor, J.; Morin, N.: Perturbation Techniques in the Analysis of Geometrically Nonlinear Shells. Proc. IUTAM — Symposium on “High Speed Computing of Elastic Structures”, Liège 1970

  12. Gallagher, R. H.; Mau, S. T.: A Method of Limit Point Calculation in Finite Element Structural Analysis. NASA CR — 2115 (1972)

  13. Gjelsvik, A.; Bodner, S. R.: The Energy Criterion and Snap Buckling of Arches. J. Eng. Mech. Div. Proc. ASCE 88 (1962) 87–134

    Google Scholar 

  14. Glaum, L. W.; Belytschko, T.; Masur, E. F.: Buckling of Structures with Finite Prebuckling Deformations — a Perturbation, Finite Element Analysis. Int. J. Solids Struct. 11 (1975) 1023–1033

    Google Scholar 

  15. Kerr, A. D.; Soifer, M. T.: The Linearization of the Prebuckling State and its Effect on the Determined Instability Loads. J. Appl. Mech. Trans. ASME 91 (1969) 775–783

    Google Scholar 

  16. Kiciman, Ö. K.: Postbuckling Analysis of Shells with Applications to Cylindrical Segments. Ph. D. Diss., Univ. California, Berkeley 1975

    Google Scholar 

  17. Mallet, R. H.; Marcal, P. V.: Finite Element Analysis of Nonlinear Structures. J. Struct. Div. Proc. ASCE 94 (1968) 2081–2105

    Google Scholar 

  18. Masur, E. F.; Schreyer, H. L.: A Second Approximation to the Problem of Elastic Instability. Proc. Symp. Theory of Shells, Donnel Anniversary Volume, University of Texas, Houston (1967) 231–249

    Google Scholar 

  19. Otto, F.: Gitterschalen. Eigenvlg. Inst, f. leichte Flächentragwerke, Univ. Stuttgart, erschienen als IL 10, 1975

    Google Scholar 

  20. Prabhu, S. K.; Gopalacharyulu, S.; Johns, D. J.: Stability of Cantilever Shells under Wind Loads. J. Eng. Mech. Div. Proc. ASCE 101 (1975) 517–530

    Google Scholar 

  21. Pflüger, A.: Stabilitätsprobleme der Elastostatik. 3. Aufl. Berlin, Heidelberg, New York: Springer 1975

    Google Scholar 

  22. Ramm, E.: Geometrisch nichtlineare Elastostatik und finite Elemente. Habilitationsschrift, Univ. Stuttgart 1976

    Google Scholar 

  23. Stricklin, J. A.; V. Riesemann, W. A.; Tillerson, J. R.; Haisler, W. E.: Static Geometric and Material Nonlinear Analysis. Advances in Computational Methods in Structural Mechanics and Design. 2nd US-Japan Seminar on Matrix Meth. of Struct. Anal. Des. Univ. Alabama Press (1972) 301–324

  24. Svalbanos, V.; Balderes, T.: Buckling and Vibration Analysis for Stiffened Orthotropic Shells of Revolution. AIAA J. 10 (1972) 944–946

    Google Scholar 

  25. Uemura, M.: Axisymmetrical Buckling of an Initially Deformed Shallow Spherical Shell under External Pressure. Int. J. Non-Linear Mech. 6 (1971) 177–192

    Google Scholar 

  26. Walker, A. C.: A Non-Linear Finite Element Analysis of Shallow Circular Arches. Int. J. Solids Struct. 5 (1969) 97–107

    Google Scholar 

  27. Zarghamee, M. S.; Shah, J. M.: Stability of Spaceframes. J. Eng. Mech. Div. Proc. ASCE 94 (1968) 371–384

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Nachtigallenweg 4, D-4152, Kempen 1

    B. Brendel

  2. Institut für Baustatik, Universität Stuttgart, Pfaffenwaldring 7, D-7000, Stuttgart 80, Bundesrepublik Deutschland

    E. Ramm

Authors
  1. B. Brendel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Ramm
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brendel, B., Ramm, E. Nichtlineare Stabilitätsuntersuchungen mit der Methode der Finiten Elemente. Ing. arch 51, 337–362 (1982). https://doi.org/10.1007/BF00536659

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00536659

Search

Navigation