Displacement-controlled method and its applications to material non-linearity

International Journal for Numerical and Analytical Methods in Geomechanics

Volumn 29, Issue 3, 2005, Pages 209-226

  Zheng, H ^a   Liu, D F ^a   Lee, C F ^b   Tham, L G ^b  

^a CHINA THREE GORGES UNIVERSITY   (China)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Displacement controlled method (DCM); Finite element analysis; Load controlled method (LCM)

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; MECHANICS; NUMERICAL ANALYSIS; PROBLEM SOLVING; THEOREM PROVING;

GEOMECHANICS; LOAD DISTRIBUTION; LOAD-CONTROLLED METHOD (LCM); NONLINEAR PROBLEMS;

GEOTECHNICAL ENGINEERING;

FINITE ELEMENT METHOD; NONLINEARITY;

EID: 14844364046     PISSN: 03639061     EISSN: None     Source Type: Journal    
DOI: 10.1002/nag.410     Document Type: Article

References (30)

1. Crisfield MA. Non-Linear Finite Element Analysis of Solids and Structures, vol. 1. Wiley: New York, 1991.
2. Zienkiewicz OC, Taylor RL. The Finite Element Method, vol. 2. McGraw-Hill: New York, 1991.
3. Chen C. Efficient and reliable accelerated constant stiffness algorithms for the solution of non-linear problems. International Journal for Numerical Methods in Engineering 1992; 35:481-490.
4. Thmoas JN. An improved accelerated initial stress procedure for elasto-plastic finite element analysis. International Journal for Numerical and Analytical Methods in Geomechanics 1984; 8: 358-379.
5. Sloan SW, Sheng D, Abbo AJ. Accelerated initial stiffness scheme for elasto-plasticity. International Journal for Numerical and Analytical Methods in Geomechanics 2000; 24:579-599.
6. Crisfield MA. Accelerated and damping the modified Newton Raphson method. Computers and Structures 1984; 18:395-407.
7. Potts DM, Ganendra DA. A comparison of solution strategies for non-linear finite element analysis of geotechnical problems. In Proceedings of Third International Conference on Computational Plasticity, vol. 2, Owen DRJ, Onate E, Hinton E (eds). International Center for Numerical Methods in Engineering, Barcelona, 1992; 803-814.
8. Bergan PG. Solution algorithms for nonlinear structural problems. Computers and structures 1980; 12:497-509.
9. Wright EW, Gaylord EH. Analysis of unbraced multistory steel rigid frames. Journal of the Structural Division (ASCE) 1968; 94:1143-1163.
10. Sharifi P, Popov EP. Nonlinear buckling analysis of sandwich arches. Journal of the Engineering Mechanics Division (ASCE) 1971; 97:1397-1412.
11. Zienkiewicz OC. Incremental displacement in non-linear analysis. International Journal for Numerical Methods in Engineering 1971; 3:587-592.
12. Haisler WE, Stricklin JA, Key JE. Displacement incrementation in non-linear structural analysis by the self-correcting method. International Journal for Numerical Methods in Engineering 1977; 11:3-10.
13. Batoz JL, Dhatt G. Incremental displacement algorithms for nonlinear problems. International Journal for Numerical Methods in Engineering 1979; 14:1262-1267.
14. Riks E. An incremental approach to the solution of snapping and buckling problems. International Journal of Solids and Structures 1979; 15:529-551.
15. Crisfield MA. A faster incremental/iterative solution procedure that handles 'snap-through'. Computers and Structures 1981; 13: 55-62.
16. Wempner GA. Discrete approximations related to nonlinear theories of solids. International Journal of Solids and Structures 1971; 7:1581-1599.
17. Runesson K, Samuelsson A, Bernspang L. Numerical technique in plasticity including solution advancement control.International Journal for Numerical Methods in Engineering 1986; 22:769-788.
18. Clarke MJ, Hancock MJA. A study of incremental-iterative strategies for non-linear analysis. International Journal for Numerical Methods in Engineering 1990; 29:1365-1391.
19. Siddiquee MSA, Tanka T, Tatsuoka F. Tracing the equilibrium path by dynamic relaxation in materially for nonlinear problems. International Journal for Numerical Analytical Methods in Geomechanics 1995; 19:749-767.
20. Hager WW. Updating the inverse of a matrix. SIAM Review 1989; 31:221-239.
21. Abbo AJ, Sloan SW. An automatic load stepping algorithm with error control. International Journal for Numerical Methods in Engineering 1996; 39:1737-1759.
22. Lei J, Yanan M. Approximate Theory and Numerical Methods for Bifurcation Problems. The Press of Wuhan University: Wuhan, 1993.
23. Bellini PX, Chulya A. An improved automatic incremental algorithm for efficient solution of nonlinear finite element equations. Computers and Structures 1987; 26:99-110.
24. Sloan SW. Substepping schemes for the numerical integration of elastoplastic stress-strain relation. International Journal for Numerical Methods in Engineering 1987; 24:893-911.
25. Owen DJR, Hinton E. Finite Element in Plasticity: Theory and Practice Pineridge Press: Swansea, 1980.
26. Wang R, Huang WB, Huang ZP. The Introduction to Plastic Mechanics. The Press of Peking University: Beijing, 1992.
27. Duncan JM. State of the art: limit equilibrium and finite-element analysis of slopes. Journal of Geotechnical Engineering Division (ASCE) 1996; 122(7):577-596.
28. Abramson LW, Lee TS, Sharma S, Boyce GM. Slope Stability and Stabilization Methods. Wiley: Chichester, 1995.
29. Griffiths DV, Lane PA. Slope stability analysis by finite elements. Géotechnique 1999; 49(3):387-403.
30. Chen ZY, Morgenstern NR. Extensions to the generalized method of slices for stability analysis. Canadian Geotechnical Journal 1983; 20(1):104-109.