Skip to main content

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 241))

  • 301 Accesses

Abstract

The purpose of this course is to present, in condensed form, the methods of the theory of plasticity and especially of Limit Analysis and Design, with emphasis on problems pertaining to civil engineering.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. ADES C.S. “Experimental Mechanics”. 1962, p. 345–349.

    Google Scholar 

  2. BLEICH H. “Uber die Bemessung statisch unbestimmter Stahltragwerke unter Berücksichtigung des elastich — plastichen Verhaltens des Baustoffes Bauingenieur, vol. 19–20, 1932, p. 261.

    Google Scholar 

  3. BRZEZINSKI R., KÖNIG J.A. “Evaluation of shakedown deflections of framed structures by linear programming”. Proceedings of the Symposium on Plastic Analysis of Structures, vol. II, Jassy, 6–8 September 1972, p. 101–116.

    Google Scholar 

  4. BRZEZINSKI R., KÖNIG J.A. “Deflection Analysis of elastic-plastic frames at shakedown”. Journal Struct. Mech., vol. II, 1973, p. 211–228.

    Google Scholar 

  5. CHARNES A., GREENBERG H.J. “Plastic collapse and linear programming”. Amer. Math. Soc. Abs No. 506, 1951.

    Google Scholar 

  6. COHN M.Z., GHOSH S.K., PARIMI S.R. “A Unified approach to the theory of plastic structures”. Proc. ASCE, Journ. E.M. Div., Oct. 1972.

    Google Scholar 

  7. COHN M.Z. “Analysis and Design of Inelastic Structures”. Vol. 2: Problems. University of Waterloo Press, 1972, 521 pp.

    Google Scholar 

  8. COHN M.Z., RAFAY T. “Collapse load analysis of frames considering axial forces”. Proc. ASCE, Journ. Engng. Mech. Div., No. EM4, 1974, p. 773–794.

    Google Scholar 

  9. CASCIARO R., DI CARLO A. “Formulazione’ dell’analisi limite delle piastre come problema di minimax mediante una rappresentazione agli elementi finiti del campo delle tension”. Giorn. Genio Civile, 1970.

    Google Scholar 

  10. DRUCKER D.H., PRAGER W., GREENBERG H.J. “Extended limit design theorems for continuous media”. Quart. Appl. Math., vol. IX, 1952, p. 381.

    Google Scholar 

  11. DEMONSABLON P. “Le calcul à la rupture des fondations sur groupes de pieux”. Construction, vol. XX, 1965, p. 279–289.

    Google Scholar 

  12. EMKIN L.Z., LITTLE W.A. “Plastic design of multistory steel frames by computer”. Proc. ASCE, Jour. Str. Div., Nov. 1970 and Jan. 1972.

    Google Scholar 

  13. FOULKES J. “The minimum weight design of structural frames”. Proc. Royal Soc., London, Series A, vol. 223, 1954, p. 82.

    Article  MathSciNet  Google Scholar 

  14. FREY F. “Effet du dressage à froid des profilés laminés en double té sur leur force portante”. Mémoires AIPC, vol. 29 II, 1969, p.

    Google Scholar 

  15. FREY F., RONDAL J., FOURNEAUX N. “Application de la méthode des éléments finis à la résolution des problèmes de structure de l’ingénieur civil”. Mémoires CERES, Univ. de Liège, No. 48, Juillet 1974.

    Google Scholar 

  16. FRAEIJS DE VEUBEKE J.B. “Upper and lower bounds in Structural Analysis”. Agardograph No. 72, July 1969. Pergamon Press, 1964.

    Google Scholar 

  17. FRAEIJS DE VEUBEKE J.B. “Displacement and equilibrium models in the finite element method”. Chapter 9 in “Stress Analysis”, editor O.C. Zienkiewicz, John Wiley ed., 1965.

    Google Scholar 

  18. FACCIOLI E., VITIELLO E. “Finite element, linear programming method for the limit analysis of thin plates”. Int. Journ. for Numer. Method in Engng., vol. V, 1973, p. 311–325.

    Google Scholar 

  19. GVOZDEV A.A. “The determination of the value of the collapse load for statically indeterminate systems undergoing plastic deformation”. Proc. of the Conf. on Plastic Deformations, Akademia Nauk U.S.S.R., Moscow, Dec. 1936.

    Google Scholar 

  20. GRIERSON D.E. “Computer based methods for the plastic analysis and design of building frames”, Report to Technical Committee 15 of the IABSE-ASCE Committee on planning and design of tall buildings, August 1974. ( Unpublished).

    Google Scholar 

  21. HILL R. “The Mathematical Theory of Plasticity”. Clarendon Press, Oxford, 1950.

    MATH  Google Scholar 

  22. HILL R. “On the state of stress in a plastic-rigid body at the yield point”. Phil. Mag., vol. 42, 1951, p. 868.

    MATH  Google Scholar 

  23. HELLAN K. “Journal of Engineering Materials and Technology”. vol. 96, 1974, p. 78–80.

    Google Scholar 

  24. HEYMAN J. “The Stone Skeleton”. Int. Journ. of Solids and Structures, vol. II, 1966, p. 249–279.

    Google Scholar 

  25. HENCKY H. “Zeitschrift für Angewandte Mathematik und Mech.”, vol. IV, 1924, p. 323.

    Google Scholar 

  26. HODGE P.G. Jr.. BELYTSCHKO T. “Numerical methods for the limit analysis of plates”. Jour. App’. Mech., vol. 35, 1968, p. 797–802.

    Google Scholar 

  27. HOCHFELD D.A. “Carrying capacity of Structures in conditions of temperature variations.’ (in russian. Maskinosrr., Mo,çow 1970.

    Google Scholar 

  28. HORNE M.R. “The effect of variable repeated loads in building structures designed by the plastic theory”. IABSE Publications, vol. 14, 1954, p. 53.

    Google Scholar 

  29. HORNE M.R., MORRIS L.J. “Optimum design of multistorey rigid frames”. Chapter 14 of the book by Gallagher and Zienkiewicz: Optimum Structural Design, John Wiley ed., 1973.

    Google Scholar 

  30. ILYUSHIN A.A. “Plasticité”. Eyrolles ed., Paris, 1956.

    Google Scholar 

  31. KOITER W.T. “General Theorems for Elastic-plastic Bodies. Chapter IV, p. 167–224 of Progress in Solid Mechanics”, vol. I, edited by I.N. Sneddon and R. Hill-NorthHolland Publishing Company, Amsterdam, 1960.

    Google Scholar 

  32. KÔNIG J.A. “On shakedown design of structures with temperature depending elastic modules”. Proc. 1st International Conference on Structural Mechanics in Reactor Technology, vol. VI, part L, Berlin, Sept. 1972, p. 503–517.

    Google Scholar 

  33. KONIG J.A. “Deflection bounding at shakedown under thermal and mechanical loadings”. Proc. 2nd International Conference on Structural Mechanics in Reactor Technology, vol. 5, part L, Berlin, Sept. 1973, p. 1–13.

    Google Scholar 

  34. KACHANOV L.M. “Foundations of the theory of plasticity”. North-Holland Publ. Co., 1971.

    Google Scholar 

  35. LEBLOIS C., MASSONNET C. “Influence of the upper yield stress on the behaviour of mild steel in bending and torsion”. Inter. Journ. of Mech. Sciences, vol. 14, 1972, p. 95–115.

    Article  Google Scholar 

  36. VON MISES R. “Göttinger Nachrichten”. Math.-Phys. Klasse, 1913, p. 582.

    Google Scholar 

  37. MAIER—LEIBNITZ H. “Bautechnik”, vol. 6, 1928, p. 11.

    Google Scholar 

  38. MELAN E. “Zur Plastizität des räumlichen Kontinuums”. Ing. Archiv., vol. 9, 1938, p. 116.

    Article  MATH  Google Scholar 

  39. MASSONNET C., MAUS H. “Force portante plastique des systèmes de pieux”. Symposium on the Use of Computers in Civil Engineering, vol. I, No. 12, Lisbonne, 1962.

    Google Scholar 

  40. MASSONNET C., SAVE M. “Résistance limite d’une poutre courbe en double té à parois minces soumise à flexion pure”. Publications AIBSE, vol. 23, 1964, p. 245.

    Google Scholar 

  41. MASSONNET C., SAVE M. “Plastic Analysis and Design”. Vol. I: Beams and Frames. Blaisdell Publ. Co., New York, 1965.

    Google Scholar 

  42. MASSONNET C., SAVE M. “Calcul Plastique des Constructions”. Vol. I: Structures dependant d’un paramètre. 2è édition, CBLIA éditeur, Bruxelles, 1967.

    Google Scholar 

  43. MASSONNET C. “Développement d’un programme automatique de dimensionnement plastique des structures planes en acier à l’aide de la programmation linéaire”. Proc. pf the Symposium on Plastic Analysis of Structures, vol. 2, Jassy, 6–8 Sept. 1972, p. 238–259.

    Google Scholar 

  44. MASSONNET C. “Résistance des Maériaux”. Tome II, 2è édition, G. Thone éditeur, 1973.

    Google Scholar 

  45. MASSONNET C., RONDAL J. “Structural Mechanics and Optimization”. General Lecture at the 16 th Polish Solid Mechanics Conference, Krynica 26 August - 3 September 1974. ( To be published).

    Google Scholar 

  46. MASSONNET C., SAVE M. “Résistance limite d’une poutre courbe en caisson soumis à flexion pure”. Amici e Alumini, (The Campus Anniversary Volume), Liège, 1964.

    Google Scholar 

  47. MURRAY D.W., WILSON E.L. “Finite element large deflection analysis of plates”. Proc. ASCE, J. Engng. Mech. Div., vol. 95, 1969, p. 143.

    Google Scholar 

  48. MARKOV A.A. “On variational Principles in Theory of Plasticity”. Prikladnaia Matematika i Mekhanika, vol. II, 1947, p. 339–350.

    Google Scholar 

  49. MARCAL P.V., KING I.P. “Elastic-plastic analysis of two-dimensional stress systems by the Finite Element method”, Int. J. Mech. Sci. 9, 1967, 143.

    Article  Google Scholar 

  50. NADAI A. “Plasticity”. Mac GrawHill, New York, 1931.

    Google Scholar 

  51. NEAL B.G., SYMONDS P.S. “The rapid calculation of the plastic collapse load of a framed structure”. Proc. Inst. Civil Engineers, vol. 1, London, 1952, p. 58–71.

    Google Scholar 

  52. NEAL B.G. “The plastic methods of structural analysis”. Second edition, Chapman and Hall, 1963.

    Google Scholar 

  53. NAYAK G.C., ZIENKIECWICZ O.C. “Elasto-plastic stress analysis; a generalization for various constitutive relations including strain softening”. Int. Journ. for Num. Methods in Engn., vol. 5, 1972, p. 113.

    Article  MATH  Google Scholar 

  54. NGUYEN DANG HUNG “Displacement and equilibrium methods in matrix analysis of trapezoidal Structures”. Collection des Publications de la Fac. des Sciences Appl. de l’Université de Liège, No. 21, 1970.

    Google Scholar 

  55. NUYEN DANG HUNG “Analyse limite rigide plastique par une méthode quasi-directe”. Sciences et Techn. de l’Armement, 2è fasc., 1970.

    Google Scholar 

  56. PRAGER W. “A new method of analysing stress and strain in work-hardening solids”. Journ. Appl. Mech., vol. 23, 1956, p. 493.

    MATH  MathSciNet  Google Scholar 

  57. PRAGER W. “Théorie générale des états limites d’équilibre”. Jour. Math. pures et appliquées, vol. 34, 1955, p. 4.

    MathSciNet  Google Scholar 

  58. PRAGER W. “Problèmes de plasticité théorique”. Dunod, Paris, 1958.

    Google Scholar 

  59. PRAGER W. “Shakedown in elastic-plastic media subjected to cycles of load and temperature”. Symposium on “Plasticità nella Scienza delle Costruzioni”, Bologna, 1957, p. 122–125.

    Google Scholar 

  60. PONTER A.R.S. “Journal of Applied Mechanics”, vol. 39, 1972, p. 953–958 and p. 959–963.

    Google Scholar 

  61. PIAN T.H.H. “Formulations of Imite element methods for solid continua”. US Japan Seminar on Structural Analysis, Tokyo, 1969.

    Google Scholar 

  62. RANAWEERA — LECKIE F.A. “Bound methods in limit analysis. ”Proc. Seminar on F.E. Techniques in Structural Mechanics, H. Tottenham and C. Brebbia editors, University of Southampton, 1970.

    Google Scholar 

  63. RIMAWI W.H. — DOGANE “Experiments on yielding of tension specimens with notches and holes”. Experimental mechanics, vol. 10, Oct. 1970.

    Google Scholar 

  64. SOKOLOWSKY V.V. “Theorie der Plastizität”. V.E.B. Verlag Technik, Berlin, 1955.

    Google Scholar 

  65. SAWCZUK A., RYCHLLEWSKI J. “On Yield Surfaces for Plastic Shells”. Archiwum Mechaniki Stosowanej, vol. I, 1960, p. 12.

    Google Scholar 

  66. SAVE M.A., MASSONNET C.E. “Plastic Analysis and Design of Plates, Shells and Disks”. North-Holland Publishing Co., Amsterdam, 1972.

    MATH  Google Scholar 

  67. STANG A.H., GREENSPAN M., NEWMAN S.D. Journ. Research Nat. Bur. Standards, vol. 37, No. 4, Oct. 1946.

    Google Scholar 

  68. SADOWSKY N.A. “A principle of maximum plastic resistance”. Journ. Appl. Mech., vol. X, 1943, p. 65–68.

    Google Scholar 

  69. SAYEGH A.F., RUBINSTEIN M.F. “Elastic-plastic analysis by quadratic programming”. Proc. ASCE, Journ. Engng. Mech. Div., 1972, p. 1547–1572.

    Google Scholar 

  70. THEOCARIS P.S., MARKETOS E. “Elastic-plastic analysis of perforated thin strips of strain-hardening material”. Journ. of Mech. and Phys. of Solids, vol. XII, 1964, p. 377.

    Google Scholar 

  71. WASHIZU K. “Variational methods in elasticity and plasticity”. Pergamon Press, Oxford, 1968.

    MATH  Google Scholar 

  72. YAMAHA Y., YOSHIMURA N., SAKURAI T. “Plastic stress-strain matrix and its application for the solution of elastic-plastic problems by the finite element method”. Int. Journ. Mech. Sci., 10, 1968, p. 343.

    Article  Google Scholar 

  73. ZIENKIEWICZ O.C., VALLIAPPAN S., KING I.P. “Elasto-plastic solutions of engineering problems: Initial stress, Imite element approach”. Int. Journ. for num. methods in engng., vol. I, 1969. p. 75.

    Google Scholar 

  74. ZIENKIEWICZ O.C. “The finite element in engineering science.” Mac Graw Hill, London, 1971.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1979 Springer-Verlag Wien

About this chapter

Cite this chapter

Massonnet, C. (1979). Theory of Plasticity. In: Plasticity in Structural Engineering, Fundamentals and Applications. International Centre for Mechanical Sciences, vol 241. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2902-9_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-2902-9_1

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-81350-8

  • Online ISBN: 978-3-7091-2902-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics