Finite element limit analysis of anisotropic structures

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 41-43, 2006, Pages 5422-5436

  Corradi, Leone ^a   Luzzi, Lelio ^a   Vena, Pasquale ^a  

^a POLITECNICO DI MILANO   (Italy)

Author keywords

Anisotropic plasticity; Finite element method; Limit analysis; Natural approach

Indexed keywords

COMPRESSIVE STRENGTH; FAILURE (MECHANICAL); FINITE ELEMENT METHOD; PLASTICITY; POLYNOMIALS; STRAIN RATE; STRESSES; TENSORS;

ANISOTROPIC MATERIALS; ANISOTROPIC PLASTICITY; LIMIT ANALYSIS; NATURAL APPROACH;

ANISOTROPY;

ANISOTROPY; COMPRESSIVE STRENGTH; FAILURE (MECHANICAL); FINITE ELEMENT METHOD; PLASTICITY; POLYNOMIALS; STRAIN RATE; STRESSES; TENSORS;

EID: 33745332610     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.06.032     Document Type: Article

References (36)

1. A. Charnes, H.J. Greenberg, Plastic collapse and linear programming, Technical Report 506, American Mathematical Society, 1951.
2. In: Cohn M.Z., and Maier G. (Eds). Engineering Plasticity by Mathematical Programming (1979), Pergamon Press, New York
3. Belytschko T., and Hodge Jr. Ph.D. Plane stress limit analysis by finite elements. ASCE, J. Engrg. Mech. Div. 96 (1970) 931-944
4. Bottero A., Negre R., Pastor J., and Turgeman S. Finite element method and limit analysis theory for soil mechanics problems. Comput. Methods Appl. Mech. Engrg. 22 (1980) 131-149
5. Casciaro R., and Cascini L. A mixed formulation and mixed finite elements for limit analysis. Int. J. Numer. Methods Engrg. 18 (1982) 211-243
6. Yang G. Panpenalty finite element programming for plastic limit analysis. Comput. Struct. 28 (1988) 749-755
7. Hu H., and Yang W.H. A general algorithm for limit solutions of plane stress problems. Int. J. Solids Struct. 28 (1991) 727-738
8. 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
9. Sloan S.W., and Kleeman P.W. Upper bound limit analysis using discontinuous velocity fields. Comput. Methods Appl. Mech. Engrg. 127 (1995) 293-314
10. Jiang G.L. Nonlinear finite element formulation of kinematic limit analysis. Int. J. Numer. Methods Engrg. 38 (1995) 2775-2807
11. Capsoni A., and Corradi L. A finite element formulation of the rigid-plastic limit analysis problem. Int. J. Numer. Methods Engrg. 40 (1997) 2063-2086
12. Ponter A.R.S., and Carter K.F. Limit state solutions based on elastic solutions with a spatially varying elastic modulus. Comput. Methods Appl. Mech. Engrg. 140 (1997) 237-258
13. Hodge Jr. Ph.D., and Belytschko T. Numerical methods for the limit analysis of plates. ASME, J. Appl. Mech. 35 (1968) 796-802
14. Christiansen E., and Andersen K.D. Computation of collapse states with von Mises type yield condition. Int. J. Numer. Methods Engrg. 46 (1999) 1185-1202
15. Christiansen E., and Pedersen O.S. Automatic mesh refinement in limit analysis. Int. J. Numer. Methods Engrg. 50 (2001) 1331-1346
16. J.H. Argyris, Continua and discontinua, in: Proceedings of the First Conference on Matrix Methods in Structural Mechanics, AFFDL-TR 66-88, Dayton, Ohio, 1966, pp. 11-92.
17. Argyris J.H., Balmer H., Doltsinis J.St., Dunne P.C., Haase M., Muller M., and Scharpf D.W. Finite element method: the natural approach. Comput. Methods Appl. Mech. Engrg. 17/18 (1979) 1-106
18. Ponter A.R.S., Fuschi P., and Engelhardt M. Limit analysis for general class of yield conditions. Eur. J. Mech.-A/Solids 19 (2000) 401-421
19. Capsoni A., Corradi L., and Vena P. Limit analysis of orthotropic structures based on Hill's yield condition. Int. J. Solids Struct. 38 (2001) 3945-3963
20. Capsoni A., Corradi L., and Vena P. Limit analysis of anisotropic structures based on the kinematic theorem. Int. J. Plasticity 17 (2001) 1531-1549
21. Corradi L., and Vena P. Limit analysis of orthotropic plates. Int. J. Plasticity 19 (2003) 1543-1566
22. Pan L., and Seshari R. Limit analysis for anisotropic solids using variational principle and repeated finite element analysis. Trans. CSME 28 (2004) 89-107
23. Tsai S.W., and Wu E.M. A general theory of strength of anisotropic materials. J. Compos. Mater. 8 (1971) 58-80
24. Martin J.B. Plasticity: Fundamentals and General Results (1975), MIT Press, Cambridge, MA
25. Simo J.C., and Rifai M.S. A class of assumed strain methods and the method of incompatible modes. Int. J. Numer. Methods Engrg. 29 (1990) 1595-1638
26. Hill R. A theory of the yielding and plastic flow of anisotropic materials. Proc. Roy. Soc. A 193 (1947) 281-297
27. Harvey J.F. Theory and Design of Pressure Vessels (1985), Van Nostrans, New York
28. Corradi L., Luzzi L., and Trudi F. Collapse of thick cylinders under radial pressure and axial load. ASME, J. Appl. Mech. 72 (2005) 564-569
29. Barlat F., Lege D.J., and Brem J.C. A six component yield function for anisotropic materials. Int. J. Plasticity 7 (1991) 693-712
30. Zienkiewicz O.C., and Taylor R.L. The Finite Element Method vol. 2 (1989), McGraw-Hill, London, UK
31. Capsoni A., and Corradi L. Limit analysis of plates: A finite element formulation. Struct. Engrg. Mech. 8 (1999) 325-341
32. Corradi L., and Panzeri N. Post-collapse analysis of plates and shells based on a rigid-plastic version of the TRIC element. Comput. Methods Appl. Mech. Engrg. 192 (2003) 3747-3775
33. Argyris J.H., Tenek L., and Oloffson L. TRIC: a simple but sophisticated 3-node triangular element based on six rigid-body and 12 straining modes for fast computational simulations of arbitrary isotropic and laminated composite shells. Comput. Methods Appl. Mech. Engrg. 145 (1997) 11-85
34. Argyris J.H., Papadrakakis M., Apostolopoulou C., and Koutsourelakis S. The TRIC shell element: theoretical and numerical investigation. Comput. Methods Appl. Mech. Engrg. 182 (2000) 217-245
35. Argyris J.H., Papadrakakis M., and Karapitta L. Elasto-plastic analysis of shells with triangular element TRIC. Comput. Methods Appl. Mech. Engrg. 191 (2002) 3613-3636
36. Zheng Q.S., and Betten J. The formulation of constitutive equations for fiber-reinforced composites in plane problems. Part II. Arch. Appl. Mech. 65 (1995) 161-177