Kinematical approach to the shakedown analysis of some structures
Authors:
D. C. Pham and H. Stumpf
Journal:
Quart. Appl. Math. 52 (1994), 707-719
MSC:
Primary 73E50; Secondary 73E20, 73K99, 73V25
DOI:
https://doi.org/10.1090/qam/1306045
MathSciNet review:
MR1306045
Full-text PDF Free Access
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Abstract: From Koiter’s kinematical shakedown theorem, a new variational problem is deduced, which does not contain integrals over a time parameter and gives an upper bound on the safety factor. For a broad class of practical problems, including planar bar systems subjected to combined axial and bending loads, it leads to the exact value of the shakedown factor. The possible inadaptation modes (incremental, alternating, or mixed) on the shakedown boundary are determined.
A. A. Gvozdev, The determination of the value of the collapse load of statically indeterminate systems undergoing Plastic Deformation, Proc. Conf. on Plastic Deformation, USSR Acad. Sci., 1938, p. 19
D. C. Drucker, W. Prager, and H. J. Greenberg, Extended limit design theorems for continuous media, Quart. Appl. Math. 9, 381–389 (1951)
R. Hill, On the state of stress in a plastic-rigid body at the yield point, Philos. Mag. 42, 868–875 (1951)
E. Melan, Zur Plastizität des räumlichen Kontinuums, Ing. Arch. 9, 116–126 (1938)
W. T. Koiter, General theorems for elastic-plastic solids, Progress in Solid Mech., Vol. I, 1963, pp. 165–221
B. G. Neal and P. S. Symonds, A method for calculating the failure load for a framed structure subjected to fluctuating loads, J. Inst. Civil Engrs. 35, 186–197 (1950)
J. Heyman, Plastic design of frames, Cambridge Univ. Press, London and New York, 1971
J. B. Martin, Plasticity: Fundamentals and general results, MIT Press, Cambridge, MA, 1975
M. Z. Cohn and G. Maier, eds., Engineering plasticity by mathematical programming, Pergamon Press, New York and Oxford, 1979
D. A. Gokhfeld and O. F. Cherniavski, Limit analysis of structures at thermal cycling, Groningen, 1980
J. A. König, Shakedown of elastic-plastic structures, Elsevier, Amsterdam, 1987
D. L. Smith, ed., Mathematical programming methods in structural plasticity, Springer-Verlag, New York, 1990
T. Belytschko, Plane stress shakedown analysis by finite elements, Internat. J. Mech. Sci. 14, 619–625 (1972)
D. Weichert and J. Gross-Weege, The numerical assessment of elastic-plastic sheets under variable mechanical and thermal loads using a simplified two surface yield condition, Internat. J. Mech. Sci. 30, 757–767 (1988)
D. A. Gokhfeld, Some problems of plates and shells, Proc. VI-th Soviet Conf. Plates and Shells, Baku. Izd. Nauka, 284–291 (1966)
A. Sawczuk, Evaluation of upper bounds to shakedown loads for shells, J. Mech. Phys. Solids 17, 291–301 (1969)
H. Stumpf and Le Khanh Chau, On shakedown of elastoplastic shells, Quart. Appl. Math. 49, 781–793 (1991)
H. Stumpf, Theoretical and computational aspects in the shakedown analysis of finite elastoplasticity, Internat. J. Plasticity 9, 583–602 (1993)
A. A. Gvozdev, The determination of the value of the collapse load of statically indeterminate systems undergoing Plastic Deformation, Proc. Conf. on Plastic Deformation, USSR Acad. Sci., 1938, p. 19
D. C. Drucker, W. Prager, and H. J. Greenberg, Extended limit design theorems for continuous media, Quart. Appl. Math. 9, 381–389 (1951)
R. Hill, On the state of stress in a plastic-rigid body at the yield point, Philos. Mag. 42, 868–875 (1951)
E. Melan, Zur Plastizität des räumlichen Kontinuums, Ing. Arch. 9, 116–126 (1938)
W. T. Koiter, General theorems for elastic-plastic solids, Progress in Solid Mech., Vol. I, 1963, pp. 165–221
B. G. Neal and P. S. Symonds, A method for calculating the failure load for a framed structure subjected to fluctuating loads, J. Inst. Civil Engrs. 35, 186–197 (1950)
J. Heyman, Plastic design of frames, Cambridge Univ. Press, London and New York, 1971
J. B. Martin, Plasticity: Fundamentals and general results, MIT Press, Cambridge, MA, 1975
M. Z. Cohn and G. Maier, eds., Engineering plasticity by mathematical programming, Pergamon Press, New York and Oxford, 1979
D. A. Gokhfeld and O. F. Cherniavski, Limit analysis of structures at thermal cycling, Groningen, 1980
J. A. König, Shakedown of elastic-plastic structures, Elsevier, Amsterdam, 1987
D. L. Smith, ed., Mathematical programming methods in structural plasticity, Springer-Verlag, New York, 1990
T. Belytschko, Plane stress shakedown analysis by finite elements, Internat. J. Mech. Sci. 14, 619–625 (1972)
D. Weichert and J. Gross-Weege, The numerical assessment of elastic-plastic sheets under variable mechanical and thermal loads using a simplified two surface yield condition, Internat. J. Mech. Sci. 30, 757–767 (1988)
D. A. Gokhfeld, Some problems of plates and shells, Proc. VI-th Soviet Conf. Plates and Shells, Baku. Izd. Nauka, 284–291 (1966)
A. Sawczuk, Evaluation of upper bounds to shakedown loads for shells, J. Mech. Phys. Solids 17, 291–301 (1969)
H. Stumpf and Le Khanh Chau, On shakedown of elastoplastic shells, Quart. Appl. Math. 49, 781–793 (1991)
H. Stumpf, Theoretical and computational aspects in the shakedown analysis of finite elastoplasticity, Internat. J. Plasticity 9, 583–602 (1993)
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Article copyright:
© Copyright 1994
American Mathematical Society
