Extended limit analysis of strain softening frames involving 2nd-order geometric nonlinearity and limited ductility

CMES - Computer Modeling in Engineering and Sciences

Volumn 42, Issue 3, 2009, Pages 217-256

  Tangaramvong, S ^a   Tin Loi, F ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Complementarity problem; Geometric nonlinearity; Limit analysis; Limited ductility; Material nonlinearity; Nonconvex optimization

Indexed keywords

COMPLEMENTARITY PROBLEM; GEOMETRIC NONLINEARITY; LIMIT ANALYSIS; LIMITED DUCTILITY; MATERIAL NONLINEARITY; NONCONVEX OPTIMIZATION;

MODEL STRUCTURES;

DUCTILITY;

EID: 67649858820     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (44)

1. Ardito, R.; Cocchetti, G.; Maier, G. (2008): On structural safety assessment by load factor maximization in piecewise linear plasticity. European Journal of Mechanics A-Solids, vol. 27, pp. 859-881.
2. Armero, E; Ehrlich, D. (2006): Numerical modeling of softening hinges in thin Euler-Bernoulli beams. Computers and Structures, vol. 84, pp. 641-656.
3. Bolzon, G.; Corigliano, A. (1997): A discrete formulation for elastic solids with damaging interfaces. Computer Methods in Applied Mechanics and Engineering, vol. 140, pp. 329-359.
4. Bolzon, G.; Tin-Loi, E (1999): Physical instability and geometric effects in frames. Engineering Structures, vol. 21, pp. 557-567.
5. Brooke, A.; Kendick, D.; Meeraus, A.; Raman, R. (1998): GAMS: a user's guide. Gams Development Corporation, Washington DC.
6. Carvelli, V.; Maier, G.; Taliercio, A. (2000): Kinematic limit analysis of periodic heterogeneous media. CMES: Computer Modeling in Engineering and Sciences, vol. 1, pp. 19-30.
7. Chen, S. S.; Liu, Y. H.; Cen, Z. Z. (2008): A combined approach of the MLPG method and nonlinear programming for lower-bound limit analysis. CMES: Computer Modeling in Engineering and Sciences, vol. 28, pp. 39-55.
8. Cocchetti, G.; Maier, G. (2003): Elastic-plastic and limit-state analyses of frames with softening plastic-hinge models by mathematical programming. International Journal of Solids and Structures, vol. 40, pp. 7219-7244.
9. Cocchetti, G.; Maier, G.; Shen, X. P. (2002): Piecewise linear models for interfaces and mixed mode cohesive cracks. CMES: Computer Modeling in Engineering and Sciences, vol. 3, pp. 279-298.
10. Cottle, R. W.; Pang, J. S.; Stone, R. E. (1992): The Linear Complementarity Problem. Academic Press, San Diego.
11. DeDonato, O.; Maier, G. (1972): Mathematical programming methods for the inelastic analysis of reinforced concrete frames allowing for limited rotation capacity. International Journal for Numerical Methods in Engineering, vol. 4, pp. 307-329.
12. DeFreitas, J. A. T.; LloydSmith, D. (1984-85): Elastoplastic analysis of planar structures for large displacements. Journal of Structural Mechanics, vol. 12, pp. 419-445.
13. Dirkse, S. P.; Ferris, M. C. (1995): The PATH solver: A nonmonotone stabilization scheme for mixed complementarity problems. Optimization Methods and Software, vol. 5, pp. 123-156.
14. Drud, A. S. (1994): CONOPT - a large-scale GRG code. ORSA Journal on Computing, vol. 6, pp. 207-216.
15. Ehrlich, D.; Armero, F. (2005): Finite element methods for the analysis of softening plastic hinges in beams and frames. Computational Mechanics, vol. 35, pp.237-264.
16. Ferris, M. C. (1998): MATLAB and GAMS: Interfacing Optimization and Visualization Software. Technical Report TR98-19, Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, 1998.
17. Ferris, M. C.; Pang, J. S. (1997): Engineering and economic applications of complementarity problems. SI AM Review, vol. 39, pp. 669-713.
18. Ferris, M. C.; Tin-Loi, F. (1999): On the solution of a minimum weight elasto- plastic problem involving displacement and complementarity constraints. Computer Methods in Applied Mechanics and Engineering, vol. 174, pp. 107-120.
19. Ferris, M. C; Tin-Loi, F. (2001): Limit analysis of frictional block assemblies as a mathematical program with complementarity constraints. International Journal of Mechanical Sciences, vol. 43, pp. 209-224.
20. Franchi, A.; Cohn, M. Z. (1980): Computer analysis for elastic-plastic structures. Computer Methods in Applied Mechanics and Engineering, vol. 21, pp. 271-294.
21. Kamenjarzh, J. A. (1996): Limit Analysis of Solids and Structures. CRC Press, Boca Baton.
22. Kanzow, C. (1996): Some noninterior continuation methods for linear complementarity problems. SIAM Journal on Matrix Analysis and Applications, vol. 17, pp. 851-868.
23. Karakostas, S. M.; Mistakidis, E. S. (2000): Evaluation of the ductility features in steel structures with softening moment-rotation behaviour based on a nonconvex optimization formulation. Engineering Computations, vol. 17, pp. 573-592.
24. Leu, S.-Y.; Chen, J. T. (2006): Sequential limit analysis of rotating hollow cylinders of nonlinear isotropic hardening. CMES: Computer Modeling in Engineering and Sciences, vol. 14, pp. 129-140.
25. Liu, C.-S.; Atluri, S. N. (2008): A fictitious time integration method (FTIM) for solving mixed complementarity problems with applications to non-linear optimization. CMES: Computer Modeling in Engineering and Sciences, vol. 34, pp. 155-178.
26. Long, S. Y.; Liu, K. Y.; Li, G. Y. (2008): An analysis for the elasto-plastic fracture problem by the meshless local Petrov-Galerkin method. CMES: Computer Modeling in Engineering and Sciences, vol. 28, pp. 203-216.
27. Luo, Z. Q.; Pang, J. S.; Ralph, D. (1996): Mathematical Programs with Equilibrium Constraints. Cambridge University Press, Cambridge.
28. Maier, G. (1970): A matrix structural theory of piecewise linear elastoplasticity with interacting yield planes. Meccanica, vol. 5, pp. 54-66.
29. Maier, G. (1971): Incremental plastic analysis in the presence of large displacements and physical instabilizing effects. International Journal of Solids and Structures, vol. 7, pp. 345-372.
30. Maier, G.; Drucker, D. C. (1973): Effects of geometry change on essential features of inelastic behavior. Journal of the Engineering Mechanics Division (ASCE), vol. 99, pp. 819-834.
31. Maier, G.; Giacomini, S.; Paterlini, F. (1979): Combined elastoplastic and limit analysis via restricted basis linear programming. Computer Methods in Applied Mechanics and Engineering, vol. 19, pp. 21-48.
32. Maier, G.; Zavelani, A.; Dotreppe, J. C. (1973): Equilibrium branching due to flexural softening. Journal of the Structural Division (ASCE), vol. 99, pp. 897-906.
33. Massonnet, C. E.; Save, M. A. (1965): Plastic Analysis and Design, Vol I: Beams and Frames. Blaisdell Publishing Co, New York.
34. Przemieniecki, J. S. (1985): Theory of Matrix Structural Analysis. Dover Publication Inc, New York.
35. Tangaramvong, S.; Tin-Loi, F. (2007a): A complementarity approach for elastoplastic analysis of strain softening frames under combined bending and axial force. Engineering Structures, vol. 29, pp. 742-753.
36. Tangaramvong, S.; Tin-Loi, F. (2007b): Limit analysis of strain softening steel frames under pure bending. Journal of Constructional Steel Research, vol. 63, pp. 1151-1159.
37. Tangaramvong, S.; Tin-Loi, F. (2009): Limit analysis of elastoplastic frames considering 2nd-order geometric nonlinearity and displacement constraints. International Journal of Mechanical Sciences, vol. 51, pp. 179-191.
38. Tin-Loi, F. (1999): A smoothing scheme for a minimum weight problem in structural plasticity. Structural Optimization, vol. 17, pp. 279-285.
39. Tin-Loi, F.; Que, N. S. (2002): Nonlinear programming approaches for an inverse problem in quasibrittle fracture. International Journal of Mechanical Sciences, vol. 44, pp. 843-858.
40. Tin-Loi, F.; Tangaramvong, S.; Xia, S. H. (2007): Limit analysis of frames involving unilateral supports with frictional contact. International Journal of Mechanical Sciences, vol. 49, pp. 454-465.
41. Tin-Loi, F.; Tseng, P. (2003): Efficient computation of multiple solutions in quasibrittle fracture analysis. Computer Methods in Applied Mechanics and Engineering, vol. 192, pp. 1377-1388.
42. Tin-Loi, E; Vimonsatit, V. (1996): Nonlinear analysis of semirigid frames: a parametric complementarity approach. Engineering Structures, vol. 18, pp. 115- 124.
43. Tin-Loi, E; Xia, S. H. (2001): Holonomic softening: Models and analysis. Mechanics of Structures and Machines, vol. 29, pp. 65-84.
44. Tonkovic, Z.; Sorić, J.; Skozrit, I. (2008): On numerical modeling of cyclic elastoplastic response of shell structures. CMES: Computer Modeling in Engineering and Sciences, vol. 26, pp. 75-90.