Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aboustit, B.L. and Reddy, D.V. (1980). Finite element linear programming approach to foundation shakedown, Soils Under Cyclic and Transient Loading, (Editors: G.N. Pande and O.C. Zienkiewicz).
Belytschko, T. (1972). Plane stress shakedown analysis by finite elements. Int. J. Mech. Sci., Vol 14, 619–625.
Bleich, H. (1932). Uber die Bemessung statisch unbestimmter Stahltragwerke unter Berucksichtigung des elastisch-plastischen Verhaltens des Baustoffes, Bauingenieur; Vol 19/20,261.
Boulbibane, M. and Ponter, A.R.S. (2006). The linear matching method for the shakedown analysis of geotechnical problems. Int. J. Num. Analy. Meth. Geomech., Vol 30, 157–179.
Calladine, C.R. (1985). Plasticity for Engineers, Ellis Horwood.
Capurso, M. (1974). A displacement bounding principle in shakedown of structures subjected to cyclic loads. Int. J. Solids structures, Vol 10, 77–92.
Collins, I.F. and Cliffe, P.F. (1987). Shakedown in frictional materials under moving surface loads. Int. J. Num. Analy. Meth. Geomech., Vol 11, 409–420.
Collins, I.F., Wang, A.P. and Saunders, L.R, (1993). Shakedown in layered pavements under moving surface loads. Int. J. Num. Analy. Meth. Geomech., Vol 17, 165–174.
Drucker, D.C., Prager, W. and Greenberg, H.J. (1952). Extended limit design theorems for continuous media, Quart. Appl. Math., Vol 9, 381–389.
Gokhfeld, D.A. and Cherniavski, O.F. (1980). Limit Analysis at Thermal Cycling, Shjthoff and Noordhoff.
Gvozdev, A.A. (1936). La determination de la charge de mine pour les systemes hyperstatiques subissant des deformations plastiques, Proc. Conf. Plastic Deformation, Ac Sc. USSR, 19.
Hamilton, G.M. (1983). Explicit equations for the stresses beeath a sliding spherical contact, Proc. Inst. Mech. Eng., Vol 197c, 53–59.
Hill, R. (1950). The Mathematical Theory of Plasticity, Clarendon Press, Oxford.
Hill, R. (1951). On the state of stress in a plastic-rigid body at the yield point, Phil. Mag., Vol 42, 868–875.
Hills, D.A. and Sackfield, A. (1984). Yield and shakedown states in the contact of generally curved bodies, J. Strain Analy., Vol 19, 9–14.
Himmelblau, D.M. (1972). Applied Nonlinear Programming, McGraw-Hill Book Company, New York.
Huh, H. and Yang, W.H. (1991). A general algorithm for limit solutions of plane stress problems. Int. J. Solids and Structures., Vol. 28, 727–738.
Johnson, K.L. (1962). A shakedown limit in rolling contact, Proc. 4th US Nat. Congress Appl. Mech., ASME, Berkeley, 28.
Johnson, K.L. (1985). Contact Mechanics, Cambridge University Press.
Johnson, K.L. (1992). The application of shakedown principles in rolling and sliding contact, Eur: J. Mech. A/Solids, Vol 11, 155–172.
Johnson, K.L. and Jefferis, J.A. (1963). Plastic flow and residual stresses in rolling and sliding contact, Proc. Inst. Mech. Eng: Symp. Fatigue in Rolling Contact, Vol 177, 54–65.
Kachanov, L.M. (1974). Fundamentals of the Theory of Plasticity. Mir Publishers, Moscow.
Kapoor, A. and Johnson, K.L. (1992). Effect of changes in contact geometry on shakedown of surfaces in rolling/sliding/ contact. Int. J. Mech. Sci., Vol 34, 223–239.
Koiter, W.T. (1960). General theorems for elastic-plastic solids, In: Progress in Solid Mechanics, (Editors: I.N. Sneddon and R. Hill), Vol 1, 167–221.
Konig, J.A. (1987). Shakedown of Elastic-Plastic Structures. Elsevier.
Li, H.X. and Yu, H.S. (2005). Kinematic limit analysis of frictional materials using nonlinear programming. Int. J. Solids Structures, Vol 42, 4058–4076.
Li, H.X. and Yu, H.S. (2006a). A nonlinear programming approach to kinematic shakedown analysis of frictional materials. Int. J. Solids Structures (in press).
Li, H.X. and Yu, H.S. (2006b). A nonlinear programming approach to kinematic shakedown analysis of composite materials. Int. J. Num. Meth. Eng., Vol 66, 117–146.
Li, H.X. and Yu, H.S. (2006). Three-dimensional solutions for shakedown of layered pavements under moving surface loads. Int. J. Num. Analy. Meth. Geomech. (under review).
Liu, Y.H., Cen, Z.Z. and Xu, B.Y. (1995). A numerical method for plastic limit analysis of 3D structures. Int. J. Solids and Structures., Vol. 32, 1645–1658.
Maier, G. (1969). Shakedown theory in perfect elastoplasticity with associated and nonassociated flow laws: a finite element linear programming approach. Meccanica, Vol 4, 250–260.
Maier, G, Carvelli, G. and Cocchetti, G. (2000). On direct methods of shakedown and limit analysis. Plenary Lecture, 4th Euromech Solid Mechanics Conference, Metz, June.
Melan, E (1938). Zur plastizitat des raumlichen Kontinuums, Ing. Arch., Vol 9, 116–125.
Pande, G.N. (1982). Shakedown of foundations subjected to cyclic loads, Soil Mechanics-Transient and Cyclic Loads, (Editors: G.N. Pande and O.C. Zienkiewicz), 469–489.
Ponter, A.R.S. (1972). An upper bound on the small displacement of elastic perfectly plastic structures. J. Appl. Mech., Vol 39, 959–963.
Ponter, A.R.S. (1976). A general shakedown theorem for inelastic materials. Proc. 3rd Int. Con$ Struct. Mech. Reactor Technology., Section L, Imperial College, London.
Ponter, A.R.S., Hearle, A.D. and Johnson, K.L. (1985). Application of the kinemtical shakedown theorem to rolling and sliding point contacts. J. Mech. Phys. Solids, Vol 33, 339–362.
Prager, W. and Hodge, P.G. (1951). The Theory of Perfectly Plastic Solids, John Wiley and Sons, New York.
Radd, L., Weichert, D. and Najm, W. (1988). Stability of multilayer system under repeated loads. Transport. Res. Rec., Vol 1207, 181–186.
Radovsky, B.S. and Murashina, N.V. (1996). Shakedown of subgrade soil under repeated loading. Transport. Res. Rec., Vol 1547, 82–88.
Sharp, R.W. (1983). Shakedown Analysis and Design of Pavements, PhD Thesis, Sydney University, Australia.
Sharp, R.W. and Booker, J.R. (1984). Shakedown of pavements under moving surface loads. J. Transp. Eng., ASCE, Vol 110, 1–14.
Shiau, S.H. (2001). Numerical Methods for Shakedown Analayis of Pavements, PhD Thesis, University of Newcastle, Australia.
Shiau, S.H. and Yu, H.S. (1999). Shakedown of three-layered pavements. Proc. 7th Int. ConJon Structural Failure and Plasticity, Melbourne, Australia.
Shiau, S.H. and Yu, H.S. (2000a). Load and displacement predictions for shakedown analysis of layered pavements. Transport. Res. Rec., Vol 1730, 117–124.
Shiau, S.H. and Yu, H.S. (2000b). Shakedown analysis of flexible pavements. Proc. John Booker Memorial Symp., 643–653.
Sloan, S.W. (1988). A steepest edge active set algorithm for solving sparse linear programming problems. Int. J. Num. Meth. Eng., Vol. 26, 2671–2685.
Symonds, P.S. and Neal, B.G. (1951). Recent progress in the plastic methods of structural analysis. J. Franklin. Inst., Vol 252, 383–407.
Yu, H.S. (2005). Three-dimensional analytical solutions for shakedown of cohesive frictional materials under moving surface loads. Proc. R. Soc. A., Vol 461, 1951–1964.
Yu, H.S. and Hossain, M.Z. (1998). Lower bound shakedown analysis of layered pavements using discontinuous stress fields. Comput. Meth. Appl. Mech, Eng., Vol 167, 209–222.
Rights and permissions
Copyright information
© 2006 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
(2006). Shakedown Analysis. In: Plasticity and Geotechnics. Advances in Mechanics and Mathematics, vol 13. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-33599-5_13
Download citation
DOI: https://doi.org/10.1007/978-0-387-33599-5_13
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-33597-1
Online ISBN: 978-0-387-33599-5
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)