Upper and lower bound limit analysis of plates using FEM and second-order cone programming

Computers and Structures

Volumn 88, Issue 1-2, 2010, Pages 65-73

  Le, Canh V ^a   Nguyen Xuan, H ^b   Nguyen Dang, H ^c  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

^b UNIVERSITY OF NATURAL SCIENCES   (Viet Nam)

^c UNIVERSITY OF LIÈGE   (Belgium)

Author keywords

Criterion of mean; Displacement and equilibrium models; Limit analysis; Second order cone programming; Upper and lower bounds

Indexed keywords

CRITERION OF MEAN; DISPLACEMENT AND EQUILIBRIUM MODELS; LIMIT ANALYSIS; SECOND ORDER CONE PROGRAMMING; UPPER AND LOWER BOUNDS;

CONTROL THEORY;

EID: 70350763849     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2009.08.011     Document Type: Article

References (32)

1. Johansen K.W. Yield-line theory (1962), Cement and Concrete Association, London
2. Wood R.H. Plastic and elastic design of slabs and plates (1961), Thames and Hudson, London
3. Hodge P.G.J., and Belytschko T. Numerical methods for the limit analysis of plates. Trans ASME, J Appl Mech 35 (1968) 796-802
4. Christiansen E., and Larsen S. Computations in limit analysis for plastic plates. Int J Numer Methods Eng 19 (1983) 169-184
5. Andersen K.D., Christiansen E., and Overton M.L. Computing limit loads by minimizing a sum of norms. SIAM J Sci Comput 19 (1998) 1046-1062
6. Capsoni A., and Corradi L. Limit analysis of plates - a finite element formulation. Struct Eng Mech 8 (1999) 325-341
7. Krabbenhoft K., and Damkilde L. Lower bound limit analysis of slabs with nonlinear yield criteria. Comput Struct 80 (2002) 2043-2057
8. Yan A.M., and Nguyen-Dang H. Limit analysis of cracked structures by mathematical programming and finite element technique. Comput Mech 24 (1999) 319-333
9. Yan A.M., Jospin R.J., and Nguyen-Dang H. An enhance pipe elbow element - application in plastic limit analysis of pipe structures. Int J Numer Methods Eng 46 (1999) 409-431
10. Phan-Hong Q, Nguyen-Dang H. Limit analysis of 2D structures using gliding line mechanism generated by rigid finite elements, Collection of papers from Prof. Nguyen-Dang Hungs former students. Vietnam National University, Ho Chi Minh City Publishing House; 2006. p. 447-60.
11. Clough R, Tocher J. Finite element stiffness matrices for analysis of plates in bending. In: Proceedings of the conference on matrix methods in structural mechanics, Ohio,Wright Patterson A.F.B.; 1965.
12. Morley L.S.D. The triangular equilibrium problem in the solution of plate bending problems. Aero Quart 19 (1968) 149-169
13. Gaudrat V.F. A Newton type algorithm for plastic limit analysis. Comput Methods Appl Mech Eng 88 (1991) 207-224
14. Zouain N., Herskovits J., Borges L.A., and Feijoo R.A. An iterative algorithm for limit analysis with nonlinear yield functions. Int J Solids Struct 30 (1993) 1397-1417
15. Yan A.M., and Nguyen-Dang H. Kinematical shakedown analysis with temperature-dependent yield stress. Int J Numer Methods Eng 50 (2001) 1145-1168
16. Nguyen-Dang H, Yan AM, Vu DK. Duality in kinematical approaches of limit and shakedown analysis of structures, complementary, duality and symmetry in nonlinear mechanics. In: Gao David, editor. Shanghai IUTAM symposium; 2004. p. 128-48.
17. Andersen K.D., Christiansen E., and Overton M.L. An efficient primal-dual interior-point method for minimizing a sum of Euclidean norms. SIAM J Sci Comput 22 (2001) 243-262
18. Andersen E.D., Roos C., and Terlaky T. On implementing a primal-dual interior-point method for conic quadratic programming. Math Program 95 (2003) 249-277
19. Mosek, The MOSEK optimization toolbox for MATLAB manual, Mosek ApS; 2008. .
20. Krabbenhoft K., Lyamin A.V., and Sloan S.W. Formulation and solution of some plasticity problems as conic programs. Int J Solids Struct 44 (2007) 1533-1549
21. Makrodimopoulos A., and Martin C.M. Upper bound limit analysis using simplex strain elements and second-order cone programming. Int J Numer Anal Methods Geomech 31 (2006) 835-865
22. Ciria H., Peraire J., and Bonet J. Mesh adaptive computation of upper and lower bounds in limit analysis. Int J Numer Methods Eng 75 (2008) 899-944
23. Munoz J., Bonet J., Huerta A., and Peraire J. Upper and lower bounds in limit analysis: adaptive meshing strategies and discontinuous loading. Int J Numer Methods Eng 77 (2009) 471-501
24. Debongnie JF, Applying pressures on plate equilibrium elements. Technical report, University of Liege, Belgium.
25. Nguyen-Xuan H, Debongnie JF, The equilibrium finite element model and error estimation for plate bending. International Congress Engineering Mechanics Today 2004, Ho Chi Minh City, Vietnam; August 16-20, 2004.
26. Debongnie JF, Nguyen-Xuan H, Nguyen-Huy C, Dual analysis for finite element solutions of plate bending. In: Montero G, Montenegro R, editors. Proceedings of the eighth international conference on computational structures technology, B.H.V. Topping, Stirlingshire, Scotland: Civil-Comp Press; 2006.
27. Nguyen-Dang H. Direct limit analysis via rigid-plastic finite elements. Comput Methods Appl Mech Eng 8 (1976) 81-116
28. Christiansen E, Limit analysis of collapse states, Handbook of numerical analysis, vol. IV, Amsterdam: North-Holland; 1996. p. 193312 [chapter II].
29. Le C.V., Gilbert M., and Askes H. Limit analysis of plates using the EFG method and second-order cone programming. Int J Numer Methods Eng 78 (2009) 1532-1552
30. Nguyen-Dang H., and Konig J.A. A finite element formulation for shakedown problems using a yield criterion of the mean. Comput Methods Appl Mech Eng 8 (1976) 179-192
31. Le CV, Nguyen-Xuan H, Nguyen-Dang H. Dual limit analysis of bending plates. In: Proceeding of third international conference on advanced computational methods in engineering, Ghent - Belgium; 2005.
32. Hopkins H., and Wang A. Load-carrying capacities for circular plates of perfectly-plastic material with arbitrary yield condition. J Mech Phys Solids 3 (1954) 117-129