Elastic-plastic and limit-state analyses of frames with softening plastic-hinge models by mathematical programming

International Journal of Solids and Structures

Volumn 40, Issue 25, 2003, Pages 7219-7244

  Cocchetti, G ^a   Maier, G ^a  

^a POLITECNICO DI MILANO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ELASTICITY; FINITE ELEMENT METHOD; LOADS (FORCES); MATHEMATICAL PROGRAMMING; PLASTIC DEFORMATION; PLASTICITY; STRESS ANALYSIS;

COMPLEMENTARITY THEORY;

STRUCTURAL FRAMES;

LOADING; STRUCTURAL COMPONENT;

EID: 0242274303     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(03)00363-9     Document Type: Article

References (71)

1. Anderheggen E. Glanzer G. Steffen P. Polyhedral yield surfaces in the element nodal force space Computers and Structures 78 2000 111-121
2. Avery P. Mahendran M. Refined plastic hinge analysis of steel frame structures comprising non-compact sections. I: formulation, II: verification Advances in Structural Engineering 3 2000 291-325
3. Bažant Z.P. Scaling of failure of beams, frames and plates with softening hinges Meccanica 36 2001 67-77
4. Bažant Z.P. Pan J. Pijaudier-Cabot G. Softening in reinforced concrete beams and frames Journal of Structural Engineering 113 1987 2333-2347
5. Bažant Z.P. Jiràsek M. Softening-induced dynamic localization instability: seismic damage in frames Proceedings of the ASCE, Journal of Engineering Mechanics 122 1996 1149-1158
6. Bažant Z.P. Cedolin L. Stability of Structures 1991 Oxford University Press New York
7. Belytschko T. Liu W.K. Moran B. Nonlinear finite element analysis for continua and structures 2000 Wiley Chichester
8. Ben-Tal A. Nemirovski A. On polyhedral approximations of the second-order cone Mathematics of Operations Research 26 2001 193-205
9. Biolzi L. Labuz J.F. Global instability and bifurcation in beams composed of rock-like materials International Journal of Solids and Structures 30 1993 359-370
10. Bolzon G. Maier G. Tin-Loi F. Holonomic and nonholonomic simulations of quasi-brittle fracture: a comparative study of mathematical programming approaches Wittmann F.H Fracture Mechanics of Concrete Structures 1995 885-898 Aedificatio Publishers Freiburg
11. Bolzon G. Maier G. Tin-Loi F. On multiplicity of solutions in quasi-brittle fracture computations Computational Mechanics 19 1997 511-516
12. Bolzon G. Ghilotti D. Maier G. Strength of periodic elastic-brittle composites evaluated through homogenization and parameter identification European Journal of Mechanics/Solids 21 2002 355-378
13. Bolzon G. Tin-Loi F. Physical instability and geometric effects in frames Engineering Structures 21 1999 557-567
14. Capurso M. Limit analysis of continuous media with piecewise linear yield condition Meccanica 6 1971 53-58
15. Capurso M. Maier G. Incremental elastoplastic analysis and quadratic optimization Meccanica 4 1970 107-116
16. Cen Z. Maier G. Bifurcations and instabilities in fracture of cohesive-softening structures: a boundary element analysis Fatigue and Fracture of Engineering Materials and Structures 15 1992 911-928
17. Cocchetti G. Maier G. Shen X.P. Piecewise linear models for interfaces and mixed mode cohesive cracks Computer Modeling in Engineering and Sciences 3 2002 279-298
18. Cohn M. Maier G. Engineering Plasticity by Mathematical Programming 1979 Pergamon Press
19. Comi C. Corigliano A. Maier G. Dynamic analysis of elastoplastic-softening discretized structures Proceedings of the ASCE, Journal of Engineering Mechanics 118 1992 2352-2375
20. Corradi L. Maier G. A matrix theory of elastic-locking structures Meccanica 4 1969 298-313
21. Cottle R.W. Pang J.S. Stone R.E. The Linear Complementarity Problem 1992 Academic Press San Diego
22. De Donato O. Maier G. Mathematical programming methods for the inelastic analysis of reinforced concrete frames allowing for limited rotation capacity International Journal for Numerical Methods in Engineering 4 1972 307-329
23. Dirkse S.P. Ferris M.C. The PATH solver: a non-monotone stabilisation scheme for mixed complementarity problems Optimization Methods and Software 5 1995 123-156
24. Facchinei F. Jiang H. Qi L. A smoothing method for mathematical programs with equilibrium constraints Mathematical Programming 85 1999 107-134
25. Feijóo R.A. Zouain N. Formulations in rates and increments for elastic-plastic analysis International Journal for Numerical Methods in Engineering 26 1988 2031-2048
26. Ferris M.C. Mangasarian O.L. Pang J.-S. Complementarity: Applications, Algorithms and Extensions 2001 Kluwer Academic Publishers Dordrecht
27. Ferris M.C. Tin-Loi F. Limit analysis of frictional block assemblies as a mathematical program with complementarity constraints International Journal of Mechanical Sciences 43 2001 209-224
28. Franchi A. Genna F. A stable/neutral equilibrium path for the numerical solution of elastic-plastic softening problems Computer Methods in Applied Mechanics and Engineering 90 1991 921-942
29. Franchi A. Genna F. Corradi L. On the determination of bifurcation and limit points Proceedings of the ASCE, Journal of Engineering Mechanics 124 1998 866-874
30. Gao D.Y. Duality Principles in Nonconvex Systems: Theory, Methods and Applications 1999 Kluwer Academic Publishers Dordrecht
31. Gao D.Y. Ogden R.W. Stavroulakis G.E. Nonsmooth/Nonconvex Mechanics 2001 Kluwer Academic Publishers
32. Gawecki A. Janinska B. Computer analysis of slackened-elastic-plastic beams under non-proportional loads Computer Assisted Mechanical Engineering Science 2 1995 25-40
33. Giambanco F. Elastic-plastic analysis by asymptotic pivoting method Computers and Structures 71 1999 215-238
34. Giannessi F. Jurina L. Maier G. A quadratic complementarity problem related to the optimal design of a pipeline freely resting on a rough sea bottom Engineering Structures 4 1982 186-196
35. Griffin T.B. Reddy B.D. Martin J.B. A numerical study of holonomic approximations to problems in plasticity International Journal for Numerical Methods in Engineering 26 1988 1449-1466
36. Hodge P.G.Jr. Automatic piecewise linearization in ideal plasticity Computer Methods in Applied Mechanics and Engineering 10 1977 249-272
37. Jiràsek M. Analytical and numerical solutions for frames with softening hinges Journal of Engineering Mechanics 123 1997 8-14
38. Jiràsek M. Bažant Z.P. Inelastic analysis of structures 2002 Wiley Chichester, UK
39. Judice J.J. Mitra G. An enumerative method for the solution of linear complementarity problems European Journal of Operations Research 36 1988 122-128
40. Kaliszky S. Plasticity. Theory and Engineering Applications 1989 Elsevier Amsterdam
41. Kaliszky S. Elastoplastic analysis with limited plastic deformations and displacements Mechanical Structures and Machines 24 1996 39-50
42. Kim T.H. Reid S.R. Multiaxial softening hinge model for tubular vehicle roll-over protective structures International Journal of Mechanical Sciences 43 2001 2147-2170
43. Kulkarni M. Belytschko T. Bayliss A. Stability and error analysis for time integrators applied to strain-softening materials Computer Methods in Applied Mechanics and Engineering 124 1995 335-363
44. Liu G.S. Zhang J.Z. A new branch and bound algorithm for solving quadratic programs with linear complementarity constraints Journal of Computational and Applied Mathematics 146 2002 77-87
45. Lloyd Smith D. Mathematical Programming Methods in Structural Plasticity 1990 Springer Verlag New York
46. Lubliner J. Plasticity theory 1990 McMillan Publisher New York
47. Luo Z.-Q. Pang J.-S. Ralph D. Mathematical Programs With Equilibrium Constraints 1996 Cambridge University Press Cambridge
48. Maier G. On elastic-plastic structures with associated stress-strain relations allowing for work softening Meccanica 2 1967 55-64
49. Maier G. On softening flexural behaviour of beams in elastoplasticity Rendiconti dell'Istituto Lombardo di Scienze e Lettere 102 1968 648-677
50. Maier G. A matrix structural theory of piecewise-linear plasticity with interacting yield planes Meccanica 5 1970 55-66
51. Maier, G., 1971. On structural instability due to strain softening, In: "Instability of Continuous Systems", Proceedings of the IUTAM Symposium Herrenalb 1969, Leipholz Editor, pp. 411-417
52. Maier G. Piecewise linearization of yield criteria in structural plasticity Solid Mechanics Archives 2/3 1976 239-281
53. Maier G. Carvelli V. Cocchetti G. On direct methods for shakedown and limit analysis European Journal of Mechanics A/Solids 19 Special Issue 2000 S79-S100
54. Maier G. Comi C. Energy properties of solution to quasi-brittle fracture mechanics problems with piecewise linear cohesive crack models Benallal A. Continuous Damage and Fracture 2000 197-205 Elsevier Amsterdam
55. Maier G. Giacomini S. Paterlini F. Combined elastoplastic and limit analysis via restricted basis linear programming Computer Methods in Applied Mechanics and Engineering 19 1979 21-48
56. Maier G. Zavelani Rossi A. Dotreppe J.C. Equilibrium branching due to flexural softening Proceedings of the ASCE, Journal of the Structural Division 99 (N.EM4) 1973 897-906
57. Massonet, C.H., Save, M., 1978. In: Nelissen, B. (Ed.), Calcul Plastique des Constructions. Angleur, Liegi
58. Mistakidis E.S. Stavroulakis G.E. Nonconvex Optimization in Mechanics 1998 Kluwer Academic Publishers
59. Moré J.J. Wright S.J. Optimization Software Guide 1993 SIAM Publications Philadelphia
60. Olsen P.C. The influence of the linearization of the yield surface on the load-bearing capacity of reinforced concrete slabs Computer Methods in Applied Mechanics and Engineering 162 1998 351-358
61. Palmer A.C. Maier G. Drucker D.C. Normality relations and convexity of yield surfaces for unstable materials or structural elements Transactions of the ASME Journal of Applied Mechanics 1967 464-470
62. Potra F.A. Wright S.J. Interior-point methods Journal of Computational and Applied Mathematics 124 2000 281-302
63. Ralph D. Global convergence of damped Newton's method for nonsmooth equations, via the path search Mathematical Operations and Research 19 1994 352-389
64. Royer-Carfagni G. Can a moment-curvature relationship describe the flexion of softening beams? European Journal of Mechanics A/Solids 20 2001 253-276
65. Simo J.C. Govindjee S. Non-linear B-stability and symmetry preserving return mapping algorithms for plasticity and viscoplasticity International Journal for Numerical Methods in Engineering 31 1991 151-176
66. Tin-Loi F. A yield surface linearization procedure in limit analysis Mechanical Structures and Machines 18 1990 135-149
67. Tin-Loi F. Wong M.B. Nonholonomic computer analysis of elastoplastic frames Computer Methods in Applied Mechanics and Engineering 72 1989 351-364
68. Vanderbei R.J. Shanno D.F. An interior-point algorithm for nonconvex nonlinear programming Computational Optimization and Applications 13 1999 231-252
69. Wakefield R.R. Tin-Loi F. Large scale nonholonomic elastoplastic analysis using a linear complementarity formulation Computer Methods in Applied Mechanics and Engineering 84 1990 229-242
70. Yang Y.B. Kuo S.R. Wu Y.S. Incrementally small-deformation theory for nonlinear analysis of structural frames Engineering Structures 24 2002 783-798
71. Zienkiewicz O.C. Taylor R.L. The Finite Element Method 5th ed. 2000 Butterworth-Heinemann Oxford