Performance of the p-version finite element method for limit analysis

International Journal of Mechanical Sciences

Volumn 45, Issue 6-7, 2003, Pages 1149-1166

  Tin Loi, F ^a   Ngo, N S ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Collapse loads; Limit analysis; p elements; Plasticity

Indexed keywords

ELASTOPLASTICITY; FINITE ELEMENT METHOD; LOADS (FORCES); STRAIN; STRESSES;

COLLAPSE LOADS;

MECHANICAL ENGINEERING;

EID: 0242657731     PISSN: 00207403     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijmecsci.2003.08.004     Document Type: Article

References (37)

1. Cohn MZ, Maier G, editors. Engineering plasticity by mathematical programming. New York: Pergamon Press; 1979.
2. König J.A. Shakedown of elastic-plastic structures. 1987;Elsevier, Amsterdam.
3. Kamenjarzh J.A. Limit analysis of solids and structures. 1996;CRC Press, Boca Baton.
4. Maier G, Carvelli V, Cocchetti G. On direct methods for shakedown and limit analysis. European Journal of Mechanics A/Solids 2000;19:S79-100 (Special issue).
5. Maier G. On some issues in shakedown analysis. Journal of Applied Mechanics. 68:2001;799-808.
6. Nagtegaal J.C., Parks D.M., Rice J.R. On numerically accurate finite element solutions in the fully plastic range. Computer Methods in Applied Mechanics and Engineering. 4:1974;153-177.
7. Zienkiewicz O.C., Taylor R.L., Too T.M. Reduced integration technique in general analysis of plates and shells. International Journal for Numerical Methods in Engineering. 3:1971;275-290.
8. Hughes T.J.R. Generalization of selective integration procedures to anisotropic and nonlinear media. International Journal for Numerical Methods in Engineering. 15:1980;1413-1418.
9. Simo J.C., Rifai M.S. A class of mixed assumed strain methods and the method of incompatible modes. International Journal for Numerical Methods in Engineering. 29:1990;1595-1638.
10. Sloan S.W., Randolph M.F. Numerical prediction of collapse loads using finite element methods. International Journal for Numerical and Analytical Methods in Geomechanics. 6:1982;47-76.
11. Anderheggen E., Knöpfel H. Finite element limit analysis using linear programming. International Journal of Solids and Structures. 8:1972;1413-1431.
12. Christiansen E. Computation of limit loads. International Journal for Numerical Methods in Engineering. 17:1981;1547-1570.
13. Turgeman S., Guessab B., Guessama M. Yield design theory. an efficient static method formulation European Journal of Mechanics A/Solids. 17:1998;499-513.
14. Yu X., Tin-Loi F. Behavior of four finite elements for direct limit analysis. Loo Y.C., Chowdhury S.H., Fragomeni S. Advances in mechanics of structures and materials. 2002;119-124 Balkema, Lisse.
15. Szabó B.A., Babuška I. Finite element analysis. 1991;Wiley, New York.
16. Szabó BA, Actis RL, Holzer SM. Solution of elastic-plastic stress analysis problems by the p -version of the finite element method. In: Babuška I, Falherty JE, Henshaw WD, Hopcroft JE, Oliger JE, Tezduyar T, editors. IMA volumes in mathematics and its applications, vol. 75: Modeling, mesh generation, and adaptive numerical methods for partial differential equations. New York: Springer; 1995. p. 395-416.
17. Holzer S.M., Yosibash Z. The. p -version of the finite element method in incremental elasto-plastic analysis International Journal for Numerical Methods in Engineering. 39:1996;1859-1878.
18. Jeremić B., Xenophontos C. Application of the. p -version of the finite element method to elasto-plasticity with localization of deformation Communications in Numerical Methods in Engineering. 15:1999;867-876.
19. Düster A., Rank E. The. p -version of the finite element method compared to an adaptive h -version for the deformation theory of plasticity Computer Methods in Applied Mechanics and Engineering. 190:2001;1925-1935.
20. 2 flow theory with non-linear isotropic hardening International Journal for Numerical Methods in Engineering. 53:2002;49-63.
21. Wells G.N., Sluys L.J., de Borst R. A. p -adaptive scheme for overcoming volumetric locking during plastic flow Computer Methods in Applied Mechanics and Engineering. 191:2002;3153-3164.
22. Christiansen E. Limit analysis of collapse states. In: Ciarlet PG, Lions JL, editors. Handbook of numerical analysis, Vol. 4. Amsterdam: North-Holland; 1996. p. 193-312.
23. Sloan S.W. Lower bound limit analysis using finite elements and linear programming. International Journal for Numerical and Analytical Methods in Geomechanics. 12:1988;61-77.
24. Sloan S.W. Upper bound limit analysis using finite elements and linear programming. International Journal for Numerical and Analytical Methods in Geomechanics. 13:1989;263-282.
25. Campion S.D., Jarvis J.L. An investigation of the implementation of the. p -version finite element method Finite Elements in Analysis and Design. 23:1996;1-21.
26. Banerjee U., Suri M. The effect of numerical quadrature in the. p -version of the finite element method Mathematics of Computation. 1-20:199259.
27. Brooke A., Kendrick D., Meeraus A., Raman R. GAMS: a user's guide. 1998;Gams Development Corporation, Washington, DC.
28. Drud A. CONOPT - a large-scale GRG code. ORSA Journal on Computing. 6:1994;207-216.
29. Gill PE, Murray W, Saunders MA, Wright MH. MINOS 5.5 user's guide. Report 83-20R, Department of Operations Research, Stanford University, Stanford, CA, revised 1998.
30. Sloan S.W., Kleeman P.W. Upper bound limit analysis using discontinuous velocity fields. Computer Methods in Applied Mechanics and Engineering. 127:1995;293-314.
31. De Buhan P., Maghous S. A straightforward numerical method for evaluating the ultimate loads of structures. European Journal of Mechanics A/Solids. 14:1995;309-328.
32. Capsoni A., Corradi L. A finite element formulation of the rigid-plastic limit analysis problem. International Journal for Numerical Methods in Engineering. 40:1997;2063-2086.
33. Christiansen E., Andersen K.D. Computation of collapse states with von Mises yield condition. International Journal for Numerical Methods in Engineering. 46:1999;1185-1202.
34. Belytschko T. Plane stress shakedown analysis by finite elements. International Journal of Mechanical Sciences. 14:1972;619-625.
35. Corradi L., Zavelani A. A linear programming approach to shakedown analysis of structures. Computer Methods in Applied Mechanics and Engineering. 3:1974;37-53.
36. Nguyen D.H., Palgen L. Shakedown analysis by displacement method and equilibrium finite elements. Transactions of the Canadian Society of Mechanical Engineering. 61:1980;34-40.
37. Groß-Weege J. On the numerical assessment of the safety factor of elastic-plastic structures under variable loading. International Journal of Mechanical Sciences. 394:1997;417-433.