Zusammenfassung
Eine vom Verfasser kürzlich entwickelte allgemeine Theorie der elastischen Stabilität wird in einheitlicher und moderner Form dargestellt. Die Theorie behandelt Gleichgewicht und Stabilität diskreter kontinuierlicher Systeme und ist somit ein Beitrag zur klassischen Mechanik, mit Anwendungen in der numerischen Untersuchung von in der Praxis auftretenden Körpern und Tragwerken.
Normales und kritisches Verhalten eines allgemeinen Systems werden durch einen natürlichen Störungsansatz klassifiziert und berechnet; beides mit oder ohne Diagonalisierungsschema. Das anfängliche überkritische Verhalten eines Systems bei einem diskreten kritischen Punkt wird ausführlich untersucht; besondere Aufmerksamkeit wird der wichtigen Frage der Imperfektionenanfälligkeit gewidmet.
Einige neue Theoreme werden aufgestellt.
References
W. T. Koiter,On the Stability of Elastic Equilibrium, Dissertation, Delft, Holland (1945), English translation, NASA, TT, F10, 833 (1967).
W. T. Koiter,Buckling and Post-buckling Behaviour of a Cylindrical Panel under Axial Compression, Trans. Nat. Aero Res. Inst. Amsterdam20, Report S 476 (1956).
W. T. Koiter,Theory of Elastic Stability and Post-buckling Behaviour: Chapter I, Basic concepts, Delft Report, September 1962; Chapter II, Simple examples, Delft Report, November 1962; Chapter III, Stability of equilibrium of continuous bodies, Brown University, TR No. 79, April 1962; Appendix, Notes on tensor analysis in three-dimensional Euclidean space, Brown University, TR No. 80, October 1962.
W. T. Koiter,On the Concept of Stability of Equilibrium for Continuous Bodies, Proc. R. Neth. Acad. Sci., Ser. [B]66, 173–177 (1963).
W. T. Koiter,The Effect of Axisymmetric Imperfections on the Buckling of Cylindrical Shells under Axial Compression, Proc. R. Neth. Acad. Sci., Ser. [B]66, 265 (1963).
W. T. Koiter,Elastic Stability and Post-buckling Behaviour, Proc. Symp. Nonlinear Problems, edited by R. E. Langer, p. 257 (University of Wisconsin Press, 1963).
W. T. Koiter,On the Instability of Equilibrium in the Absence of a Minimum of the Potential Energy, Proc. R. Neth. Acad. Sci., Ser. [B]68, 107–113 (1965).
W. T. Koiter,The Energy Criterion of Stability for Continuous Elastic Bodies, Proc. R. Neth. Acad. Sci., Ser. [B]68, 178–202 (1965).
W. T. Koiter,General Equations of Elastic Stability for Thin Shells, Proc. Symp. in honour of Lloyd H. Donnell, edited by D. Muster (University of Houston, April 1966).
W. T. Koiter,Post-buckling Analysis of a Simple Two-bar Frame, Recent Progress in Applied Mechanics (Almqvist & Wiksell, Stockholm 1966).
W. T. Koiter,Purpose and Achievements of Research in Elastic Stability, Proc. Fourth Technical Conference, Soc. for Engng. Sci. (North Carolina State University, Raleigh, N.C., November 1966).
W. T. Koiter,A Sufficient Condition for the Stability of Shallow Shells, Report No. 362 (Delft, Holland, 1967).
W. T. Koiter,The Nonlinear Buckling Problem of a Complete Spherical Shell under Uniform External Pressure, Report No. 412 (Delft, Holland, 1968).
B. Budiansky andJ. W. Hutchinson,Dynamic Buckling of Imperfection-Sensitive Structures, Proc. XI. Internat. Congr. Appl. Mech., Munich, pp. 636–651 (Julius Springer-Verlag, Berlin 1964).
B. Budiansky,Dynamic Buckling of Elastic Structures: Criteria and Estimates. Dynamic Stability of Structures, Proc. of an International Conference held at Northwestern University, Evanston, Illinois, October 1965 (Pergamon Press).
J. W. Hutchinson,Axial Buckling of Pressurized Imperfect Cylindrical Shells, AIAA Journal3, 1461–1466 (1965) [See also:Buckling of Imperfect Cylindrical Shells under Axial Compression and External Pressure, Un-dated Harvard Report].
B. Budiansky andJ. W. Hutchinson,A Survey of Some Buckling Problems, AIAA Journal4, 1505–1510 (1966).
J. W. Hutchinson andB. Budiansky,Dynamic Buckling Estimates, AIAA Journal4, 525–530 (1966).
B. Budiansky,Post-buckling Behaviour of Cylinders in Torsion, Proc. Second IUTAM Symp. on the Theory of Thin Shells, Copenhagen, September 1967.
J. W. Hutchinson,Imperfection-sensitivity of Externally Pressurized Spherical Shells, J. appl. Mech., March 1967, pp. 49–55 (1967).
J. W. Hutchinson,Initial Post-buckling Behaviour of Toroidal Shell Segments, Int. J. Solids Struct.3, 97–115 (1967).
J. W. Hutchinson andJ. C. Amazigo,Imperfection-sensitivity of Eccentrically Stiffened Cylindrical Shells, AIAA Journal5, 392–401 (1967).
B. Budiansky andJ. C. Amazigo,Initial Post-buckling Behaviour of Cylindrical Shells under External Pressure, J. Math. Phys.47, No. 3 (1968).
D. A. Danielson,Buckling and Initial Post-buckling Behaviour of Spheroidal Shells under Pressure, Report SM-22, Harvard, March 1968.
J. R. Fitch,The Buckling and Post-buckling Behaviour of Spherical Caps under Concentrated Load, Int. J. Solids Struct.4, 421–446 (1968).
J. R. Fitch andB. Budiansky,The Buckling and Post-buckling of Spherical Caps under Axisymmetric Load, Report SM-29, Harvard, December 1968.
J. W. Hutchinson,Buckling and Initial Post-buckling Behaviour of Oval Cylindrical Shells under Axial Compression, J. appl. Mech., March 1968, pp. 66–72.
J. W. Hutchinson andJ. C. Frauenthal,Elastic Post-buckling Behaviour of Stiffened and Barreled Cylindrical Shells, Report SM-27, Harvard, August 1968.
J. C. Amazigo,Buckling under Axial Compression of Long Cylindrical Shells with Random Axisymmetric Imperfections, Quart. appl. Math.26, No. 4, January 1969.
J. M. T. Thompson,Basic Principles in the General Theory of Elastic Stability, J. Mech. Phys. Solids11, 13–20 (1963).
H. Ziegler,On the Concept of Elastic Stability, Adv. in Appl. Mech. IV (Academic Press, 1956), p. 351.
H. Ziegler,Principles of Structural Stability (Blaisdell, Waltham Mass., 1968).
S. J. Britvec andA. H. Chilver,Elastic Buckling of Rigidly-jointed Braced Frames, J. Eng. Mech. Div. ASCE89, No. EM 6, p. 217 (1963).
J. M. T. Thompson,Basic Concepts of Elastic Stability, Report No. 146, Department of Aeronautics and Astronautics, Stanford University, February 1963.
J. M. T. Thompson,The Rotationally-symmetric Branching Behaviour of a Complete Spherical Shell, Proc. R. Neth. Acad. Sci., [B]67, 295–311 (1964).
J. M. T. Thompson,Eigenvalue Branching Configurations and the Rayleigh-Ritz Procedure, Quart. appl. Math.22, 244–251 (1964).
J. Roorda,The Instability of Imperfect Elastic Structures, Ph. D. Dissertation (University College, London 1965).
J. Roorda,Stability of Structures with Small Imperfections, J. Eng. Mech. Div. ASCE91, No. EM 1, pp. 87–106 (1965).
J. Roodra,The Buckling Behaviour of Imperfect Structural Systems, J. Mech. Phys. Solids13, 267–280 (1965).
J. M. T. Thompson,Discrete Branching Points in the General Theory of Elastic Stability, J. Mech. Phys. Solids13, 295–310 (1965).
J. M. T. Thompson,Dynamic Buckling under Step Loading. Dynamic Stability o Structures, Proc. of an International Conference held at Northwestern University, Evanston, Illinois, October 1965 (Pergamon Press).
M. H. R. Godley,The Elastic Buckling of Plane Frames, Ph. D. Dissertation (University College, London 1966).
S. H. Perry,Statistical Variation of Buckling Strength, Ph. D. Dissertation (University College, London 1966).
W. J. Supple,The Elastic Stability of Symmetric Systems, Ph. D. Dissertation (University College, London 1966).
A. H. Chilver,Coupled Modes of Elastic Buckling, J. Mech. Phys. Solids15, 15–28 (1967).
M. H. R. Godley andA. H. Chilver,The Elastic Post-buckling Behaviour of Unbraced Plane Frames, Int. J. Mech. Sci.9, 323–333 (1967).
J. Roorda,Some Thoughts on the Southwell Plot, J. Eng. Mech. Div. ASCE93, No. EM 6, (1967).
W. J. Supple,Coupled Branching Configurations in the Elastic Buckling of Symmetric Structural Systems, Int. J. Mech. Sci.9, 97–112 (1967).
W. J. Supple andA. H. Chilver,Elastic Post-buckling of Compressed Rectangular Plates, Contribution to Thin-walled Structures, edited by A. H. Chilver (Chatto & Windus, 1967).
J. M. T. Thompson,Localized Rayleigh Functions for Structural and Stress Analysis, Int. J. Solids Struct.3, 285–292 (1967).
J. M. T. Thompson,The Estimation of Elastic Critical Loads, J. Mech. Phys. Solids15, 311–317 (1967).
J. M. T. Thompson,Towards a General Statistical Theory of Imperfection-Sensitivity in Elastic Post-buckling, J. Mech. Phys. Solids15, 413–417 (1967).
K. Huseyin,Elastic Stability of Structures under Combined Loading, Ph. D. Dissertation (University College, London 1968).
J. Roorda,On the Buckling of Symmetric Structural Systems with First and Second Order Imperfections, Int. J. Solids Struct.4, 1137–1148 (1968).
W. J. Supple,Initial Post-buckling Behaviour of a Class of Elastic Structural Systems, Graduate Aeronautical Laboratories, California Institute of Technology, Report SM 68-1, February 1968 [To be published in the Internat. Journal of Nonlinear Mechanics].
W. J. Supple,On the Change in Buckle Pattern in Elastic Structures, Graduate Aeronautical Laboratories, California Institute of Technology, Report SM 68-3, February 1968.
J. M. T. Thompson andA. C. Walker,The Nonlinear Perturbation Analysis of Discrete Structural Systems, Int. J. Solids Struct.4, 757–768 (1968).
A. C. Walker,An Analytical Study of the Rotationally-symmetric Nonlinear Buckling of a Complete Spherical Shell under External Pressure, Int. J. Mech. Sci.10, 695–710 (1968).
A. C. Walker andD. G. Hall,An Analysis of the Large Deflections of Beams Using the Rayleigh-Ritz Finite Element Method, Aero Quart.19, 357–367 (1968).
M. H. R. Godley andA. H. Chilver,Elastic Buckling of Overbraced Frames, to be published.
M. J. Rolls,The Elastic Stability of Discontinuous Structural Systems, Ph. D. Dissertation (University College, London 1969).
J. Roorda,Some Statistical Aspects of the Buckling of Imperfection-Sensitive Structures, J. Mech. Phys. Solids17, 111–123 (1969).
J. Roorda andA. H. Chilver,Frame Buckling: an Illustration of the Perturbation Technique, Solid Mechanics Division, University of Waterloo, Report No. 2, May 1969 [To be published in the Internat. Journal of Nonlinear Mechanics].
J. M. T. Thompson,The Branching Analysis of Perfect and Imperfect Discrete Structural Systems, J. Mech. Phys. Solids17, 1–10 (1969).
J. M. T. Thompson,A New Approach to Elastic Branching Analysis, J. Mech. Phys. Solids to be published.
J. M. T. Thompson,Basic Theorems of Elastic Stability, Int. J. Engng. Sci. to be published.
J. M. T. Thompson andG. W. Hunt,Perturbation Patterns in Nonlinear Branching Theory, IUTAM Symposium on Instability of Continuous Systems, Herrenalb, September 1969 (Springer-Verlag).
J. M. T. Thompson andG. W. Hunt,Comparative Perturbation Studies of the Elastica, Int. J. Mech. Sci. to be published.
J. M. T. Thompson andA. C. Walker A General Theory for the Branching Analysis of Discrete Structural Systems, Int. J. Solids Struct.5, 281–288 (1969).
A. C. Walker,A Method of Solution for Nonlinear Simultaneous Algebraic Equations, Int. J. Numer. Methods Engineer.1, 177–180 (1969).
A. C. Walker,A Nonlinear Finite Element Analysis of Shallow Circular Arches, Int. J. Solids Struct.5, 97–107 (1969).
A. C. Walker,The Post-buckling Behaviour of Simply Supported Square Plates, Aero Quart.20, 203–222 (1969).
M. J. Sewell,The Static Perturbation Technique in Buckling Problems, J. Mech. Phys. Solids13, 247–265 (1965).
M. J. Sewell,On the Connexion Between Stability and the Shape of the Equilibrium Surface, J. Mech. Phys. Solids4, 203–230 (1966).
M. J. Sewell,A General Theory of Equilibrium Paths Through Critical Points, Part I, Proc. Roy. Soc. [A]306, 201–223; Part II, Proc. Roy. Soc. [A]306, 225–238 (1968).
M. J. Sewell,A Method of Post-buckling Analysis, J. Mech. Phys. Solids17, 219–233 (1969).
B. Fraeijs de Veubeke,Displacement and Equilibrium Models in the Finite Element Method. Chapter 9 of Stress Analysis, edited by O. C. Zienkiewicz and G. S. Holister (Wiley 1965).
J. M. T. Thompson,Stability of Elastic Structures and Their Loading Devices, J. Mech. Engineer. Sci.3, 153–162 (1961).
A. M. Liapounoff,Problème général de la stabilité du mouvement. Traduit du russe (imprimé en 1892 par la Société Mathématique de Kharkow) par E. Davaux. Ann. Fac. Sci. Toulouse, 2, série 9 (1907). Reprinted by Princeton University Press, Princeton, N. J., 1947.
J. M. T. Thompson,The Elastic Instability of a Complete Spherical Shell, Aero Quart.13, 189–201 (1962).
G. F. Carrier,On the Buckling of Elastic Rings, J. Math. Phys.26, 94–103 (1947).
J. G. Lekkerkerker,On the Stability of an Elastically Supported Beam Subjected to its Smallest Buckling Load, Proc. R. Neth. Acad. Sci., Ser. [B]65, No. 2 (1962).
G. E. Sliter andA. P. Boresi,Elastica Supported at Midpoint by a Spring, J. Eng. Mech. Div. ASCE90, No. EM 2, p. 1 (1964).
Y. C. Fung andA. Kaplan,Buckling of Low Arches or Curved Beams of Small Curvature, NACA Technical Note TN-2840 (1952).
S. J. Britvec,Elastic Buckling of Pin-jointed Frames, Int. J. Mech. Sci.5, 447–460 (1963).
S. J. Britvec,Overall Stability of Pin-jointed Frameworks after the Onset of Elastic Buckling, Ing. Arch.32, 443–452 (1963).
G. G. Pope,The Buckling Behaviour in Axial Compression of Slightly-curved Panels Including the Effect of Shear Deformability, Int. J. Solids Struct.4, 323–340 (1968).
B. O. Almroth, A. M. C. Holmes andD. O. Brush,An Experimental Study of the Buckling of Cylinders under Axial Compression, Exper. Mech.4, 263 (1964).
J. M. T. Thompson,Making of Thin Metal Shells for Model Stress Analysis, J. Mech. Engineer. Sci.2, 105–108 (1960).
J. L. Synge andB. A. Griffith,Principles of Mechanics (McGraw-Hill, third edition. 1959).
E. F. Masur andH. L. Schreyer,A Second Approximation to the Problem of Elastic Instability, Proc. Symp. in honour of Lloyd H. Donnell, edited by D. Muster (University of Houston, April 1966).
H. Poincaré,Sur l'équilibre d'une masse fluide animée d'un mouvement de rotation. Acta Mathematica7, 259 (1885).
E. H. Mansfield,Some Identities on Structural Flexibility after Buckling, Aero Quart.9, 300–304 (1958).
G. G. Pope,On the Bifurcational Buckling of Elastic Beams, Plates and Shallow Shells, Aero Quart.19, 20–30 (1968).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Thompson, J.M.T. A general theory for the equilibrium and stability of discrete conservative systems. Journal of Applied Mathematics and Physics (ZAMP) 20, 797–846 (1969). https://doi.org/10.1007/BF01592294
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01592294