Skip to main content
Article thumbnail
Location of Repository

Bounding Techniques in Shakedown and Ratchetting

By Jose Ricardo Queiroz Franco

Abstract

A review of Shakedown and Ratchetting concepts and their extensions is presented in an attempt to recount all the aspects of the problems considered in this research programme. The concept of Stress Concentration Factor was the first to be further investigated, by analysing two representative types of structures operating under severe stress concentration, namely; two-bar structures and cylindrical vessels with variable thickness subjected to cyclic mechanical loads. The material behaviour considered are: elastic-perfectly plastic and isotropic hardening. Such an analytical investigation allowed the assessment of the influence of the Stress Concentration Factor below and above the limit of reversed plasticity.\ud The primary aim of this research was to develop simplified techniques capable of solving thermal loading problems in the presence of steady mechanical loads. A simplified technique was then developed to analyse a tube subjected to a complex thermal loading simulating the fluctuation of level of sodium in Liquid Metal Fast Breeder Reactors (LMFBR). The technique was also able to include a second important aspect of shakedown problems which is cases of multiple mechanical loads. The construction of bi-dimensional Bree type diagrams, from tri-dimensional ones obtained for such cases, allowed an easy assessment of the modes of deformation of the structure. The effects of the temperature on the yield stress were explored.\ud A third aspect of thermal cyclic problems investigated was the experimental verification of the reliability of the extended Upper Bound Theorem proposed in Chapter 2. This was achieved by experimental tests on portal frames at 400°C. Contours representing states of constant of deformation were obtained from the experimental measurements. A fourth aspect of the problem was the development of theoretical technique to estimate the transient plastic deformation in excess of the shakedown limit which allowed the construction of theoretical contours directly comparable with the experimental ones.\ud The fifth and major contribution of this thesis was the development of a general technique for the analysis of axi-symmetric shells based in a displacement formulation for the Finite Element Method. Limit analysis and shakedown problems were reduced to minimization problems by developing a technique to obtain consistent relationship between the displacement field and the plastic strain field. Such a technique, based upon a Galerkin type of approach, consist of minimizing the difference between the two representations of the strain within the element; in terms of nodal displacement and in terms of plastic multipliers. The problem was then solved by Linear Programming. Finally, the conclusions and proposal for future work are presented

Publisher: University of Leicester
Year: 1987
OAI identifier: oai:lra.le.ac.uk:2381/8237

Suggested articles

Citations

  1. A Displacement Formulation for the Finite Element Elastic-Plastic Problem", doi
  2. A Linear Programming Approach to Shakedown Analysis of Structures", doi
  3. A Linear Programming Upper Bound Approach to the Shakedown Limit of Thin Shells Subjected to Variable Thermal Loading", doi
  4. (1952). A More Fundamental Approch to Plastic Stress-Strain Relations",
  5. A New General Theorem on Shakedown of Elastic Plastic Structures",
  6. (1974). A Review of Bounding Techniques in Shakedown and Ratche&ing at Elevated Temperature",
  7. An Assement of Kinematic Hardening Thermal Ratchetting",
  8. An Experimantal Study on Thermal-Stress Ratchetting of Austenic Stainless Steel by a Three Bars Specimen", doi
  9. An Extended Shakedown Theory for Structures That Suffer Cyclic Thermal Loading", Part 1: Theory, doi
  10. An Extended Shakedown Theory for Structures That Suffer Cyclic Thermal Loading", Part 2: Applications, doi
  11. (1965). Analysis of Plastic Spherical Shells",
  12. (1968). Applying the Shakedown Concept to Pressure vessel Design", The Engineer,
  13. (1974). Beams and Framed Structures", 2nd edition, doi
  14. (1980). Behaviour of Structures Subjected to Cyclic Plastic Deformation",
  15. Beruecksichtigung der elastischen Formaenderungen in der Plastizitaetstheorie",
  16. (1978). Bornes Quasi-Inferieures et Bornes Superieures de la Pression de Ruine des Coques de Revolution par la Methode des Elements Finis et par la Programmation Non Lineaire", doi
  17. (1984). Colloquium on Matematical Programming Methods for the Plastic Analysis of Structure"
  18. Cyclic plastic Strain Energy and Fatigue of Metals", doi
  19. (1977). Defining a Proper Material Characteristic for the Shakedown Analysis",
  20. Der Spannungszustand Eines Mises-Henckey'schen Kontinuums bei veranderlicher Belastung",
  21. Determination of the Cyclic Stress-Strain Curves",
  22. (1926). Die Tragfahigkeit statisch unbestimmter Tragwerke aus Stahl bei beliebig haufig wiederholter Belastung",
  23. Elastic-Plastic Behaviour of Thin Tubes Subjected to Internal Pressure and Intermittent High-Heat Fluxes with Applications to Fast-Nuclear-Reactor Fuel Elements", doi
  24. Etude Numerique de L"adaptation Plastique des Plaques et des Coques de Revolution par les Elements Finis D'equilibre",
  25. Experimental Investigation into Elastic/Plastic Behavioar of Isolated Nozzles in Spherical Shells", Part II, "Shakedown and Plastic Analysis",
  26. (1983). Experimental investigations into the Influence of Cyclic Phenomena of Metals on Structural Ratchetting Behaviour" doi
  27. Extended Limit Design Theorems for Continuous Media",
  28. (1960). Extension of the Stability Postulate with Emphasis on Temperature Changes", doi
  29. General Theorems for Elastic-Plastic Solids",
  30. (1959). In Introduction to Plasticity",
  31. Incremental Growth Due to Creep and Plastic Yielding of Thin Tubes Subjected to internal Pressure and Cyclic Thermal Stresses", doi
  32. (1978). Incremental Plastic Deformation of a Cylinder Subjected to Cyclic Thermal Loading", "Non-Linear Problems in Stress Analysis",
  33. Influence of Hardening Rules on the Elasto-Plastic Behaviour of a Simple Structure Under Cyclic Loading", doi
  34. (1980). International Benchmark Project on Simplified Methods for Elevated Temperature Design and Analysis; Problem 11 - The Saclay Fluctuating sodium Level Experiment",
  35. Limit analysis of Axisymmetric Pressure Vessel Intersections of Arbitrary Shape", doi
  36. (1953). Limit Analysis of Cylindrical Shells Under Axially-symmetric Loading",
  37. Limit Analysis of Shells of Revolution"
  38. (1958). Limit Anlysis of Symmetrically Loaded Thin Shells of Revolution",
  39. (1958). Limit Strength of Thin walled Pressure Vessels with an ASME Standard Torispherical Head", #rd Congr.
  40. (1979). Mathematical Programming Methods in Engineering Plasticity",
  41. Mechanik der Festen Koerper in Plastisch Deformablem Zustand",
  42. Memoire sur 1'Etablissement des Equations Differentielles des Mouvements Interieurs Operes dans les Corps Solides ductiles au dela des Limites ou l'Elasticite Pourrait les Ramener a leur Premier Etat",
  43. Memoire sur les Equations Generales des Mouvements Interieurs des Corps Solides Ductile au dela Limites ou l'Elasticite Pourrait les Ramener a leur Premier Etat",
  44. Modifications to an Intron-Testing Machine for Cyclic Loading in the Plastic Range",
  45. (1962). New Design Method for Pressure Vessel Nozzle", The Engineer,
  46. Note on the Approximate Method for Computing Consistent Conjugate Stresses in Elastic Finite Elements", doi
  47. Notes on Incremental Collapse in Pressure vessels".
  48. (1970). Numerical Method for Limit Analysis of Rotationally Symmetric Shells", doi
  49. Numerical Shakedown Analysis of Axisymmetric Sandwich Shells", doi
  50. (1958). On Pragers Hardening Rule", Contract No. 562(10) to the Office of Naval Research,
  51. (1965). On Shakedown Analysis of Non-Uniformily Heated Elastic-Plastic Solids",
  52. On Shakedown of Nonuniformily Heated Elastic Plastic Bodies",
  53. On the Calculation of Consistent Stress Distribution in Finite Element Approximations", doi
  54. (1977). on the Inelastic Deformation of Structures Subjected to Variable Loading",
  55. (1959). Plastic Analysis of Structures,
  56. (1979). Plastic Theory of Structures", 2nd edition, doi
  57. r al nada. ly aenatrN Sd Mrbwr of . l... n, a 30 Fl.
  58. (1973). Ratchetting Deformation as Affected by Relative Variations of the Loading Sequence", doi
  59. (1980). Ratchetting Experiments on Thin Cylinders Subjected to Axially Moving Temperature Fronts", UKAEA, Risley Nuclear Power Development Establishment, Memorandum ND-m-1325(R),
  60. (1970). Resistance of Metals to Cyclic Deformation", doi
  61. Rigid-Plastic Analysis of Symmetrically Loaded Cylindrical Shells",
  62. Second Shakedown Theorem Allowing for Cycles of Both Loads and Temperature", Istituto Lombardo(Rend.
  63. Shadedjwn Experiments on a T-Section Beam",
  64. (1981). Shakedown and Ratchetring Below the Creep Range", Part I,
  65. (1969). Shakedown as a Guide to the Design of Pressure Vessels", doi
  66. Shakedown in Continuous Media",
  67. (1957). Shakedown in Elastic, Plastic Media Subjected to Cycles of Load and Temperature",
  68. Shakedown Loads for Radial Nozzles in Spherical Pressure Vessels", doi
  69. Shakedown Pressures for Flush CylinderSphere Shell Intersections", doi
  70. Shakedown Theory in Perfect Elastoplasticity with Associated and Nonassociated Flow-Laws: A Finite Element, Linear Programming Approach", doi
  71. Some Comments on the Stress Concentration and Shakedown Factors for Spherical Pressure Vessels with Flush Radial Cylindrical Nozzles", doi
  72. Some Implications of Work Hardening and Ideal Plasticity",
  73. Some Observations on the design of spherical Pressure Vessels with Flush Cylindrical Nozzles", doi
  74. (1925). Spannungsverteilung in plastischen Koerpern",
  75. Strain ' Hardening and Softening of Metals Induced by Cycles of Plastic Deformations", doi
  76. (1963). Stress Concentration Factors for the Stresses at Nozzle Intersections in Pressure Vessels",
  77. (1960). Stresses in Shells", doi
  78. Structural Growth Induced by Thermal Cycling", doi
  79. (1985). Sur une Nouvelle Analuse ' Simple des Structures Inelastiques",
  80. (1963). Symmetric serire in M. "A comparison of Yield Surfaces for Thin Int.
  81. Tha Plastic Collapse of Cylindrical Shells Under Axially Symmetrical Loading",
  82. (1959). The Collapse Load of a Spherical Cap",
  83. (1983). The Development of Upper Bound and Associated Finite Element Techniques for the Plastic Shakedown of Thermally Loaded Structures",
  84. The Effect of 'the Circumferential Bending Moment and Change of Circumferential Curvature on the Calculation of the Limit Pressure of Symmetrically Loaded Shells of Revolution", doi
  85. (1968). The Effect of Change of Geometry on the Limit Pressure of a Flush Nozzle in a Spherical Pressure Vessel", Engiineering Plasticity,
  86. The Effect of Finite Changes of Geometry on the Rigid-Plastic Limit Pressure of Flush Nozzles in Spherical Pressure Vessels", doi
  87. (1985). The Effects of Thermal Loading on The Deformation of Shells Structures", doi
  88. (1977). The Finite Element Method", McGraw-Hill, doi
  89. The Influence of Free Ends on the Load Carrying Capacities of Cylindrical Shells", doi
  90. The Influence of Trasient Thermal Loading on the Bree Plate; A Simplified Analysis", doi
  91. (1979). The Infuence of Rapid Thermal Transients on Elastic-Plastic Ratchetting", CEGB, Berkeley Nuclear Laboratories,
  92. The Limit pressure for a. Flush Cylindrical ' Nozzle in a Spherical Pressure Vessel", doi
  93. The Load Carrying Capacities of Cylindrical Shells Subjected to a Ring of Force", doi
  94. The Load Carrying Capacities of Symmetrically Loaded Spherical Shells",
  95. (1974). The Plastic Methods of Structural Analysis", 3rd edition, Chapman and Hall,
  96. (1985). The Plastic Ratchetting of Thin Cylindrical Shells Subjected to Axisymmetric Thermal and Mechanical Loading. Report doi
  97. The Theory of Platicity; A Survey of Recent Achievements", James Clayton Lecture,
  98. (1968). The Thermal Ratchet Mechanism", doi
  99. (1936). Theorie Statich Unbestimmter Systeme aus idealplastischen Baustoff", Sitzungsberiche der Akademie der Wissenshaften,
  100. (1968). Theory of Plasticity",
  101. (1959). Theory of Plates and Shells", 2nd Ed.
  102. Thermal Ratchetting of a Beam Element Having an idealized Buaschinger Effect",
  103. (1966). Thermal Stress and Low Cyclic Fatigue", doi
  104. Thermal-Stress Ratchet Mechanism in Pressure Vessels",
  105. (1977). Thin Circular Cylinder under Axisymmetrical Thermal and Mechanical Loading", Paper 16/5,
  106. Torispherical Drumheads: A Limit Pressure and Shakedown investigation", doi
  107. Yield Conditions for Rotationally Symmetric Shells under Axisymmetric Loading", doi
  108. Yield-Point Load of a Circular Plate Sealing an Incompressible Fluid", doi
  109. Yield-point Ring Load Filled Circular Cylindrical Shells", doi
  110. Zur Plastizitat des Raumlichen Kontinuums", doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.