Skip to main content
SpringerLink
Log in

Similarity consideration of structural bifurcation buckling

Ähnlichkeitsbetrachtung bei Knickproblemen mit strukturellen Verzweigungen

  • Published:
Forschung im Ingenieurwesen Aims and scope Submit manuscript

Abstract

Many structural bifurcation buckling problems exhibit a scaling or power law property. Dimensional analysis is used to analyze the general scaling property. The concept of a new dimensionless number, the response number-Rn, suggested by the present author for the dynamic plastic response and failure of beams, plates and so on, subjected to large dynamic loading, is generalized in this paper to study the elastic, plastic, dynamic elastic as well as dynamic plastic buckling problems of columns, plates as well as shells. Structural bifurcation buckling can be considered when Rn(n) reaches a critical value.

Zusammenfassung

Viele Knickprobleme mit strukturellen Verzweigungen weisen eine Skalierungseigenschaft oder Potenzgesetz-Abhängigkeit auf. Mittels einer Dimensionsanalyse wird die allgemeine Skalierungseigenschaft untersucht. Das Konzept einer neuen dimensionslosen Kennzahl, der Antwort-Zahl (response number), die der Autor für die dynamische Plastizierung und das Versagen von Balken, Platten, usw. unter großen dynamischen Lasten vorgeschlagen hat, wird in der vorliegenden Arbeit verallgemeinert und zur Untersuchung von statischen und dynamischen Problemen des elastischen und plastischen Knickens von Stäben, Platten und Schalen angewendet. Strukturelle Verzweigungen bei allgemeinen Knickproblemen treten auf, wenn die Antwort-Zahl einen kritischen Wert erreicht hat.

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

Similar content being viewed by others

Abbreviations

B :

dimension in Fig. 2(a)

c :

√E/ϱ elastic stress wave speed in a rod; √E/[ϱ(1−v)], elastic stress wave speed in spherical shell

Ca:

ϱV 20 , Cauchy number

De:

τ/T, Deborah number

ϱV 20 /σ0 :

Johnson’s damage number

E :

Young’s elastic modulus

G :

shear elastic modulus

\(\bar G\) :

reduced effective shear modulus

H :

thickness

Ir:

σ0√l/K IC, Irwin number

k :

radius of gyration

K IC :

material fracture toughness

l, L :

two characteristic dimensions of a structures

m, M :

mass

n :

positive real number

R :

radius

Rn:

response number for n=2

Rn(n):

response number for a given n

T :

period of harmonic external force

V 0 :

initial impact velocity

α :

semi-angle of circular arc

ɛ :

strain

λ :

E/E t

ν :

Poisson’s ratio

ρ :

density

σ 0 :

yield stress

τ :

twisting stress, relaxation time

c, cr:

critical

e :

effective

s :

secant

t :

tangent

References

  1. Zhao YP (1998) Suggestion of a new dimensionless number for dynamic plastic response of beams and plates. Arch. Appl. Mech., 68, 524–538

    Article  MATH  Google Scholar 

  2. Chilver AH (1974) Design philosophy in structural stability, in Buckling of Structures (Ed. Budiansky, B.), Springer-Verlag, 331–345

  3. Hutchinson JW (1974) Plastic buckling, in Advances in Applied Mechanics, 67–144

  4. Hutchinson JW, Budiansky B (1976) Analytical and numerical study of the effects of initial imperfections on the inelastic buckling of a cruciform column, in Buckling of Structures (Ed. Budiansky, B.), Springer-Verlag, 98–105

  5. Gerard G, Becker H (1957) Handbook of Structural Stability: Part I — Buckling of Flat Plates. Nat. Adv. Comm. Aeronaut. Tech. Note 3781

  6. Johnson W (1972) Impact Strength of Materials. Edward Arnold

  7. Jones N, Ahn CS (1974) Dynamic elastic and plastic buckling of complete spherical shells. Int. J. Solid Structures, 10, 1357–1374

    Article  MATH  Google Scholar 

  8. Jones N (1989) Structural Impact. Cambridge University Press

  9. Barenblatt GI (1996) Scaling, self-similarity, and intermediate asymptotics. Cambridge University Press

  10. Barenblatt GI (1993) Micromechanics of fracture. Theoretical and Applied Mechanics 1992, Bodner SR et al. (Eds.), Elsevier Science Publishers B. V

  11. Zhao YP (1998) On the similarity methods in fracture mechanics. Forsch. Ingenieurwes., 64, 257–268

    Article  Google Scholar 

  12. Zhao YP (1998) Prediction of structural dynamic plastic shear failure by Johnson’s damage number. Forsch. Ingenieurwes., 63, 349–352

    Article  Google Scholar 

  13. Zhao YP (1997) On some dimensionless numbers in fracture mechanics. Int. J. Fracture, 83, L7 - L13

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory for Nonlinear Mechanics of Continuous Media (LNM), Institute of Mechanics Chinese Academy of Sciences, 100080, Beijing, People’s Republic of China

    Y. P. Zhao

Authors
  1. Y. P. Zhao
    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

Zhao, Y.P. Similarity consideration of structural bifurcation buckling. Forsch Ing-Wes 65, 107–112 (1999). https://doi.org/10.1007/PL00010868

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/PL00010868

Keywords

Search

Navigation