Limit Analysis of Structures at Thermal Cycling

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Springer Science & Business Media, Nov 30, 1980 - Science - 537 pages
 

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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
References
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
References
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
Index
533
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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.

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