A nonlinear programming approach to kinematic shakedown analysis of frictional materials

International Journal of Solids and Structures

Volumn 43, Issue 21, 2006, Pages 6594-6614

  Li, H X ^a   Yu, H S ^b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

Finite element method; Frictional materials; Kinematic theorem; Nonlinear programming; Shakedown analysis

Indexed keywords

ELASTICITY; FINITE ELEMENT METHOD; KINEMATICS; NONLINEAR EQUATIONS; NUMERICAL METHODS; STRESS ANALYSIS; THEOREM PROVING;

FRICTIONAL MATERIALS; KINEMATIC THEOREM; PLASTIC DISSIPATION; SHAKEDOWN ANALYSIS;

NONLINEAR PROGRAMMING;

EID: 33748528076     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2006.01.009     Document Type: Article

References (43)

1. Boulbibane M., and Weichert D. Application of shakedown theory to soils with non associated flow rules. Mech. Res. Commun. 24 (1997) 513-519
2. Carvelli V., Cen Z.Z., Liu Y.H., and Maier G. Shakedown analysis of defective pressure vessels by a kinematic approach. Arch. Appl. Mech. 69 (1999) 751-764
3. Chen H.F., and Ponter A.R.S. Shakedown and limit analyses for 3-D structures using the linear matching method. Int. J. Pressure Vessels Piping 78 (2001) 443-451
4. Collins I.F., and Boulbibane M. Geomechanical analysis of unbound pavements based on shakedown theory. J. Geotech. Geoenviron. Eng., ASCE 126 (2000) 50-59
5. Collins I.F., and Cliffe P.F. Shakedown in frictional materials under moving surface loads. Int. J. Numer. Anal. Methods Geom. 11 (1987) 409-420
6. Collins, I.F., Wang, A.P., 1992. Shakedown analysis of layered pavements. Report No. 505, School of Engineering, University of Auckland, New Zealand.
7. Feng X.Q., and Liu X.S. On shakedown of three-dimensional elastoplastic strain-hardening structures. Int. J. Plast. 12 (1997) 1241-1256
8. Genna F. A nonlinear inequality, finite element approach to the direct computation of shakedown load safety factors. Int. J. Mech. Sci. 30 (1988) 769-789
9. Hachemi A., and Weichert D. Numerical shakedown analysis of damaged structures. Comput. Methods Appl. Mech. Eng. 160 (1998) 57-70
10. Hamadouche M.A., and Weichert D. Application of shakedown theory to soil dynamics. Mech. Res. Commun. 26 (1999) 565-574
11. Himmelblau D.M. Applied Nonlinear Programming (1972), McGraw-Hill Book Company, New York
12. Huh H., and Yang W.H. A general algorithm for limit solutions of plane stress problems. Int. J. Solids Struct. 28 (1991) 727-738
13. Johnson K.L. The application of shakedown principles in rolling and sliding contact. Eur. J. Mech. A-Solids 11 Special Issue (1992) 155-172
14. Khoi V.D., Yan A.M., and Huang N.D. A dual form for discretized kinematic formulation in shakedown analysis. Int. J. Solids Struct. 41 (2004) 267-277
15. Koiter W.T. General theorems for elastic-plastic bodies. In: Sneddon I.N., and Hill R. (Eds). Progress in Solid Mechanics (1960), North-Holland, Amsterdam 165-221
16. König J.A. On upper bounds to shakedown loads. ZAMM 59 (1979) 349-354
17. König J.A. Shakedown of Elastic-plastic Structure (1987), Elsevier, Amsterdam
18. Li H.X., and Yu H.S. Kinematic limit analysis of frictional materials using nonlinear programming. Int. J. Solids Struct. 42 (2005) 4058-4076
19. Li H.X., Liu Y.H., Feng X.Q., and Cen Z.Z. Limit analysis of ductile composites based on homogenization theory. Proc. Roy. Soc. Lond. A 459 (2003) 659-675
20. Liu Y.H., Cen Z.Z., and Xu B.Y. A numerical method for plastic limit analysis of 3-D structures. Int. J. Solids Struct. 32 (1995) 1645-1658
21. Maier G. Shakedown theory in perfect elastoplasticity with associated and nonassociated flow-laws: a finite element linear programming approach. Meccanica 4 (1969) 250-260
22. Maier, G., Carvelli, G., Cocchetti, G., 2000. On direct methods of shakedown and limit analysis. In: Plenary Lecture, 4th Euromech Solid Mechanics Conference, Metz, June 2000.
23. Melan E. Theorie Statisch Unbestimmter Tragwerke aus iddalplastischem baustoff. Sitzungsbericht der Akademie der Wissenschafien (Wien) Abt. IIA 195 (1938) 145-195
24. Morelle P. Numerical shakedown analysis of axisymmetric sandwich shells: an upper bound formulation. Int. J. Numer. Methods Eng. 23 (1986) 2071-2088
25. Ponter A.R.S., and Engelhardt M. Shakedown limits for a general yield condition: implementation and application for a von Mises yield condition. Eur. J. Mech. A-Solids 19 (2000) 423-445
26. Raad L., Weichert D., and Najm W. Stability of multilayer systems under repeated loads. Transp. Res. Record 1207 (1988) 181-186
27. Radovsky B.S., and Murashina N.V. Shakedown of subgrade soil under repeated loading. Transp. Res. Record 1547 (1996) 82-88
28. Shapiro J.F. Mathematical Programming: Structures and Algorithms (1979), A Wiley-Interscience Publication, New York
29. Sharp R.W., and Booker J.R. Shakedown of pavements under moving surface loads. J. Transp. Eng., ASCE 110 (1984) 1-14
30. Shiau S.H., and Yu H.S. Load and displacement prediction for shakedown analysis of layered pavements. Transp. Res. Record 1730 (2000) 117-124
31. Stein E., Zhang G., and Konig J.A. Shakedown with nonlinear strain-hardening including structural computation using finite element method. Int. J. Plast. 8 (1992) 1-31
32. Stein E., Zhang G., and Huang Y. Modeling and computation of shakedown problems for nonlinear hardening materials. Comput. Methods Appl. Mech. Eng. 103 (1993) 247-272
33. Weichert D. Shakedown at finite displacement: a note on Melan's theorem. Mech. Res. Commun. 11 (1984) 121-127
34. Weichert D., and Gross W.J. On the influence of geometrical nonlinearities on the shakedown of elastic-plastic structures. Int. J. Plast. 2 (1986) 135-148
35. Weichert D., Hachemi A., and Schwabe F. Shakedown analysis of composites. Mech. Res. Commun. 26 (1999) 309-318
36. Weichert D., Hachemi A., and Schwabe F. Application of shakedown analysis to the plastic design of composites. Arch. Appl. Mech. 69 (1999) 623-633
37. Xue M.D., Wang X.F., Williams F.W., and Xu B.Y. Lower-bound shakedown analysis of axisymmetric structures subjected to variable mechanical and thermal loads. Int. J. Mech. Sci. 39 (1997) 965-976
38. Yu H.S. Three-dimensional analytical solutions for shakedown of cohesive-frictional materials under moving surface loads. Proc. Roy. Soc. London A 461 (2005) 1951-1964
39. Yu H.S., and Hossain M.Z. Lower bound shakedown analysis of layered pavements using discontinuous stress field. Comput. Methods Appl. Mech. Eng. 167 (1998) 209-222
40. Zhang Y.G. An iteration algorithm for kinematic shakedown analysis. Comput. Methods Appl. Mech. Eng. 127 (1995) 217-226
41. Zhang Y.G., and Lu M.W. An algorithm for plastic limit analysis. Comp. Methods Appl. Mech. Engrg. 126 (1995) 333-341
42. Zhang P.X., Lu M.W., and Hwang K. A mathematical programming algorithm for limit analysis. Acta Mech. Sin. 7 (1991) 267-274
43. Zouain N., Borges L., and Silveira J.L. An algorithm for shakedown analysis with nonlinear yield functions. Comput. Methods Appl. Mech. Eng. 191 (2002) 2463-2481