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TECHNICAL PAPERS

Steady-State Limit of Elastoplastic Trusses for the Plastic Shakedown Region

[+] Author and Article Information
K. Uetani, Y. Araki

Graduate School of Engineering, Kyoto University, Sakyo, Kyoto 606-8501, Japan

J. Appl. Mech 67(3), 581-589 (Apr 21, 1999) (9 pages) doi:10.1115/1.1285837 History: Received August 14, 1998; Revised April 21, 1999
Copyright © 2000 by ASME
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References

Koiter, W. T., 1960, “General Theorems for Elastic-Plastic Structures,” Progress in Solid Mechanics, Vol. 1, J. N. Sneddon and R. Hill, eds., North Holland, Amsterdam, pp. 167–221.
Bree,  J., 1967, “Elastic-Plastic Behavior of Thin Tubes Subjected to Internal Pressure and Intermittent High-Heat Fluxes With Application to Fast-Nuclear-Reactor Fuel Elements,” J. Strain Anal., 6, pp. 236–249.
Zarka, J., and Casier, J., 1979, “Elastic-Plastic Response of a Structure to Cyclic Loading: Practical Rules,” Mechanics Today, S. Nemat-Nasser, ed., Pergamon Press, New York, pp. 93–198.
König, J. A., 1987, Shakedown of Elastic-Plastic Structures, Elsevier, Amsterdam.
Nguyen,  Q. S., Gary,  G., and Baylac,  G., 1983, “Interaction Buckling-Progressive Deformation,” Nucl. Eng. Des., 75, pp. 235–243.
Siemaszko,  A., and König,  J. A., 1985, “Analysis of Stability of Incremental Collapse of Skeletal Structures,” J. Struct. Mech., 13, pp. 301–321.
Uetani,  K., and Nakamura,  T., 1983, “Symmetry Limit Theory for Cantilever Beam-Columns Subjected to Cyclic Reversed Bending,” J. Mech. Phys. Solids, 31, pp. 449–484.
Maier, G., Pan, L. G., and Perego, U., 1993, “Geometric Effects on Shakedown and Ratchetting of Axisymmetric Cylindrical Shells Subjected to Variable Thermal Loading,” Eng. Struct., 15 , pp. 453–465.
Uetani,  K., and Araki,  Y., 1999, “Steady-State Limit Analysis of Elastoplastic Trusses Under Cyclic Loads,” Int. J. Solids Struct., 36, pp. 3051–3071.
Hill,  R., 1958, “A General Theory of Uniqueness and Stability in Elastic-Plastic Solids,” J. Mech. Phys. Solids, 6, pp. 236–249.
Drucker,  D. C., Prager,  W., and Greenberg,  H. J., 1952, “Extended Limit Design Theorems for Continuous Media,” Quarterly Appl. Math., 9, pp. 381–389.
Ponter,  A. R. S., and Karadeniz,  S., 1985, “An Extended Shakedown Theory for Structures That Suffer Cyclic Thermal Loadings, Part 1: Theory,” ASME J. Appl. Mech., 52, pp. 877–882.
Ponter,  A. R. S., and Karadeniz,  S., 1985, “An Extended Shakedown Theory for Structures That Suffer Cyclic Thermal Loadings, Part 2: Applications,” ASME J. Appl. Mech., 52, pp. 883–889.
Polizzotto,  C., 1993, “A Study on Plastic Shakedown of Structures, Part I: Basic Properties,” ASME J. Appl. Mech., 60, pp. 318–323.
Polizzotto,  C., 1993, “A Study on Plastic Shakedown of Structures, Part II: Theorems,” ASME J. Appl. Mech., 60, pp. 324–330.
Polizzotto,  C., and Borio,  G., 1996, “Shakedown and Steady-State Responses of Elastic-Plastic Solids in Large Displacements,” Int. J. Solids Struct., 33, pp. 3415–3437.
Uetani, K., 1984, “Symmetry Limit Theory and Steady-State Limit Theory for Elastic-Plastic Beam-Columns Subjected to Repeated Alternating Bending,” Ph.D. thesis, Kyoto University, Kyoto (in Japanese).
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Figures

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Classification of the response in a plane of loading combinations
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The positions and the nodal displacements at the two ends of a truss element
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A bilinear kinematic hardening rule
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Classification of all possible types of the cyclic response
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The equilibrium state Γβ(μ) at which the last loading occurs before Γμ
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Fundamental concepts of the SSL theory: (a) the equilibrium state space and (b) the steady-state space
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(a) The ICL program and (b) the loading process at each amplitude level
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Key differences between (a) the previous method and (b) the present method
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The yielding conditions (a) σμβ(μ)+2σy and (b) σμβ(μ)
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(a) The transition from the elastic range to the strain hardening range and (b) the transition from the straining hardening range to the elastic range
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(a) The two-bar truss and (b) the ten-bar plane truss
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The SSL for (a) the two-bar truss and (b) the ten-bar truss
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The cyclic forced displacement programs: (a) STIDAC and (b) STIDAD
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The SSL and the results of the parametric response analysis
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The relations between U5 and the number of load reversals for the ten-bar truss under (a) ψ̄<ψssl and (b) ψ̄>ψssl
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An example of a new yielding point: (a) the transition in an element where the number of yielding point increases and (b) the transition in another element
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(a) The change of the load factor and (b) the examination of strain reversals

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