## Limit Analysis of Structures at Thermal Cycling |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Analysis of simple elasticplastic systems under variable repeated loading and temperature | 1 |

12 Oneparameter systems Some additional remarks | 13 |

13 Twoparameter systems | 20 |

14 Influence of strainhardening on the cycle stabilization and shakedown conditions at single and repeated deformations | 30 |

15 Peculiarities of structural behaviour under thermal actions | 36 |

References | 40 |

Fundamental theorems of the shakedown theory | 43 |

22 Statical shakedown theorem Generalization to thermal effects Further development of the statical theorem | 50 |

67 Using the shakedown diagram to evaluate the loadcarrying capacity of structures under variable repeated loading | 264 |

68 Analysis of some test results and adoption of shakedown safety factors | 268 |

69 Tests and analysis of the rotor disc of a radialaxialflow turbine | 274 |

References | 281 |

Shakedown of plates | 283 |

71 Alternating mechanical loading of a circular plate | 284 |

72 Shakedown of a simply supported circular plate at thermal cycling | 288 |

73 Clamped circular plate | 292 |

23 Kinematical shakedown theorem | 56 |

24 Introduction of a fictitious yield surface and restatement of the statical theorem Formulation of the shakedown problem connected with a nontrivi... | 62 |

25 Construction and properties of the fictitious yield surface | 65 |

26 Restatement of the kinematical theorem Conditions for limit states following from both restated shakedown theorems | 71 |

27 On the uniqueness of stress state at the limiting cycle | 79 |

28 On the boundedness of inelastic deformation preceding shakedown | 81 |

References | 87 |

Generalized variables in the shakedown analysis | 91 |

31 General method of constructing an interaction surface | 93 |

32 Fictitious interaction surfaces for a rod under cycling normal stress | 96 |

33 Fictitious interaction surfaces for a stretched rod subjected to cycling torque | 100 |

34 Approximate method of introducing generalized variables in shakedown problems | 107 |

35 Generalized stresses in circular plates under tension and bending | 114 |

36 Formulation of the statical theorem in terms of generalized stresses | 127 |

References | 129 |

Statical methods of solving shakedown problems | 131 |

41 The Pontragin maximum principle and its application to the problems of limit analysis | 134 |

42 Application of the mathematical programming methods to problems of incremental collapse | 145 |

43 Simple examples of solving the shakedown problems via the statical approach by using the simplex method | 150 |

44 Discretization of the continuum in the shakedown problems Finite element method | 164 |

45 Approximate statical methods | 166 |

46 Examples illustrating the use of approximate statical methods in shakedown problems | 169 |

References | 179 |

Kinematical methods of solving the shakedown problems | 183 |

51 Application of the mathematical programming methods to shakedown problems in the kinematical formulation | 185 |

52 Solution to the problem of incremental collapse of a plane disc by means of the simplex method | 192 |

53 Approximate kinematical method of determining parameters of the limiting cycle Simple examples | 202 |

54 Incremental collapse of a thickwalled tube subjected to thermal cycling and internal pressure | 210 |

55 Overload method Conditions for incremental collapse of a spherical vessel under variable repeated temperature | 213 |

56 Full shakedown analysis of a beam under simultaneous steady tension and variable repeated bending | 220 |

References | 225 |

Carrying capacity of a turbine disc under single and repeated loading | 227 |

61 Limit analysis of rotating disc Global and partial collapse mechanisms | 229 |

62 Some additional remarks on the evaluation of carrying capacity of discs | 235 |

63 Shakedown of plane disc at cyclic variation of angular velocity and temperature | 237 |

64 Influence of creep on the shakedown conditions | 245 |

65 Shakedown analysis of rotating nonuniformly heated discs of arbitrary profiles | 249 |

66 Peculiarities of incremental collapse analysis of rotor discs of radialflow turbine | 261 |

74 Circular plate with rigid boss | 307 |

75 Rectangular plates and plates of arbitrary shapes Upper bounds on the limiting cycle parameters | 313 |

76 Shakedown of perforated plates | 323 |

336 | |

Shakedown of shells at mechanical and thermal cycling | 339 |

81 Cylindrical shell under ring load and thermal cycling | 340 |

82 Limit analysis of cylindrical elasticplastic shells by the Pontragin maximum principle | 355 |

83 Shakedown of cylindrical shells under moving mechanical load | 366 |

84 Incremental collapse of a conical shell | 372 |

85 Shakedown of spherical shells | 383 |

86 Combustion chamber of liquid fuel rocket engine | 391 |

87 Fast nuclear reactor fuel element | 395 |

References | 404 |

Strain accumulation at thermal cycling under negligible mechanical loading | 407 |

91 Strain accumulation conditions based on the kinematical theorem of shakedown Influence of the type of temperature field | 408 |

92 Repeated action of moving heat source on a bar system | 412 |

93 Ratchetting of a thin cylindrical shell under repeated action of quasistationary temperature field | 417 |

94 Ratchetting of a crystallizer of a semicontinuous tube casting machine | 425 |

95 Ratchetting of a conical shelltype structure slag container | 434 |

96 Experimental investigation of deformations under variable repeated action of quasistationary in the moving coordinate system temperature fields | 447 |

97 Incremental buckling at thermal fluctuations Control and interpretation of experiments the presentday concepts | 456 |

98 Incremental buckling at thermal cycling as demonstrated on a bar system | 466 |

99 Conditions for progressive warping in the light of shakedown theory | 472 |

910 Examples of progressive warping analysis | 475 |

References | 484 |

Some contact problems in the shakedown theory | 487 |

102 Contact problems in the shakedown theory Kinematical method of analysis | 495 |

103 Strain accumulation in a semiplane on which a rigid disc is rolling | 501 |

504 | |

Inelastic shakedown in steady stress cycles | 505 |

111 Existence and uniqueness of a steady stress cycle | 507 |

112 Stress and strain rate analysis in steady cycles Different formulations of the problem | 511 |

113 Particular cases of the problem of steady stress cycle calculation The Melan theorem Strain accumulation conditions at advanced alternating plast... | 514 |

114 Stress and strain rate analysis in steady cycles Another variational formulation and its consequences | 521 |

115 Evaluation of steady cycle characteristics under quasi stationary external actions | 528 |

533 | |

### Common terms and phrases

alternating flow alternating plastic flow applied approximate assumed behaviour bending bending moment collapse mechanism considered constraints coordinate corresponding creep cross-section cyclic deflection determined disc elastic moduli elastic stresses elastic-plastic element equation external actions fictitious interaction fictitious yield curve fictitious yield surface formulation function Gokhfeld heating hoop hoop stresses incremental collapse condition increments per cycle inequality kinematical theorem limit analysis limit equilibrium limiting cycle parameters linear programming loading program magnitude maximum maximum principle Melan Moscow obtained plane plastic deformation plastic hinge plastic strain rates radial radius ratchetting relationships residual stresses Russian self-equilibrating semi-cycle shakedown conditions shakedown diagram shakedown domain shakedown problems shakedown theory shown in Fig simplex method situation solution steady cycle strain accumulation strain-hardening stress distribution structures suitable temperature field thermal cycling thermal stresses thermo-elastic stresses thickness time-independent tube turbine values variable repeated loading variable stresses yield condition yield point yield stress

### Popular passages

Page 485 - The Progressive Buckling of Plates Subjected to Cycles of Longitudinal Strain,

Page xxvii - Thermal Stresses with Applications to Airplanes, Missiles, Turbines, and Nuclear Reactors, McGraw-Hill, New York, 1957. 29 Moxham, KE, "Compression in Welded Web Plates,

Page 486 - Limit Analysis of Rotationally Symmetric Plates and Shells,* Prentice-Hall, Englewood Cliffs, NJ, 1963.