Perturbation approach to elastic post-buckling analysis

Computers and Structures

Volumn 66, Issue 5, 1998, Pages 585-595

  Casciaro, R ^a   Garcea, G ^a   Attanasio, G ^b   Giordano, F ^b  

^a UNIVERSITY OF CALABRIA   (Italy)

^b ALENIA SPAZIO   (Italy)

Author keywords

Finite elements; Nonlinear analysis; Perturbation method

Indexed keywords

ALGORITHMS; BUCKLING; ELASTICITY; FINITE ELEMENT METHOD; KINEMATICS; PERTURBATION TECHNIQUES; SENSITIVITY ANALYSIS; STRUCTURAL ANALYSIS;

KOITER PERTURBATION METHOD; NONLINEAR ANALYSIS;

COMPUTER SIMULATION;

EID: 0032017756     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7949(97)00112-0     Document Type: Article

References (48)

1. Koiter, W. T., On the stability of elastic equilibrium. Thesis, Delft, 1945. English transl. NASA TT-F10, p. 883, 1967 and AFFDL/TR70-25, 1970.
2. Budiansky, B., Theory of buckling and post-buckling of elastic structures. In Advances in Applied Mechanics, Vol. 14. Academic Press, New York, 1974.
3. Arbocz, J. and Hol, J. M. A. M. Koiter's stability theory in a computer-aided engineering (CAE) environment. International Journal of Solids and Structures, 1990, 26(9/10), 945-973.
4. Gallagher, R. H., Perturbation procedures in nonlinear finite element analysis. In Proceedings of the International Conference on Computational Methods in Nonlinear Mechanics, Austin, TX, 1974.
5. Hafta, R. T., Mallet, R. H. and Nachbar, W. Adaptation of Koiter method to finite element analysis of snap-trought buckling behavior. International Journal of Solids and Structures, 1971, 7, 1427-1445.
6. Connor, J. J. and Morin, N., Perturbation techniques in the analysis of geometrically nonlinear shells. In High Speed Computing of Elastic Structures, Vol. 2, ed. F. De Veubeke. University of Liege, 1971, pp. 683-706.
7. Lang, T. E. and Hartz, B. J., Finite element matrix formulation of post-buckling stability and imperfection sensitivity. In High Speed Computing of Elastic Structures, Vol. 2, ed. F. De Veubeke. University of Liege, 1971, pp. 727-758.
8. Hangai, Y. and Kawamata, S., Perturbation method in the analysis of geometrically nonlinear and stability problems. In Advances in Computational Methods in Structural Mechanics and Design, ed. T. Oden. UAH Press, The University of Alabama, 1972, pp. 473-492.
9. Hangay Y. and Kawamata, S., Analysis of geometrically nonlinear and stability problems by static perturbation method. Report no. 143, Institute of Industrial Science, University of Tokyo, Jen, 1973.
10. Ecer, A., Application of the finite element method for the analysis of the imperfection sensitivity of structures. In Discrete Methods in engineering. Etas Libri, Milano, 1974.
11. Casciaro, R. Di Carlo, A. and Pignataro, M., A finite element technique for bifurcation analysis. In 14th IUTAM Congress, Delft, The Netherlands, August-September 1976. Report II-192, Istituto di Scienza delle Costruzioni dell'Università di Roma, Roma, 1976.
12. Endou, A., Hangay, Y. and Kawamata, S., Post-buckling analysis of elastic shells of revolution by the finite element method. Report no. 164, Institute of Industrial Science, University of Tokyo, December 1976.
13. Besseling, J. F. Derivatives of deformation parameters for bar elements and their use in buckling and post-buckling analysis. Comparative Methods in Applied Mechanical Engineering, 1977, 12, 97-124.
14. Casciaro, R. and Aristodemo, M., Perturbation analysis of geometrically nonlinear structures. In International Conference on Finite elements nonlinear solid and structural mechanics, Geilo, Norway, August-September 1977.
15. Carnoy, E. Postbuckling analysis of elastic structures by the finite element methods. Comparative Methods in Applied Mechanical Engineering, 1980, 23, 143-174.
16. Besseling, J. F. Nonlinear theory for elastic beams and rods and its finite element rapresentation. Comparative Methods in Applied Mechanical Engineering, 1982, 31, 205-220.
17. Pignataro, M., Di Carlo, A. and Casciaro, R. On nonlinear beam model from the point of view of computational post-buckling analysis. International Journal of Solids and Structures, 1982, 18, 327-347.
18. Casciaro, R., Lanzo, A. D. and Salerno, G., Computational problems in elastic structural stability. In Nonlinear Problems in Engineering, Proc. of ENEA Workshops on Nonlinear Dynamics, Vol. 4, ed. C. Carmignani and G. Maino. Rome, 6-7 May 1991. World Scientific, Singapore, Vol. 4, 1991.
19. Casciaro, R., Salerno, G. and Lanzo, A. D. Finite element asymptotic analysis of slender elastic structures: a simple approach. International Journal of Numerical Methods in Engineering, 1992, 35, 1397-1426.
20. Salerno, G. How to recognize the order of infinitesimal mechanisms: a numerical approach. International Journal of Numerical Methods in Engineering, 1992, 35, 1351-1395.
21. Lanzo, A. D., G. Garcea and R. Casciaro, Analisi perturbativa ad elementi finiti HC di strutture a pannelli sottili. In Atti del XI Congresso AIMETA, Trento, Italy, Settembre-Ottobre 1992.
22. Flores, F. G. and Godoy, L. A. Elastic postbuckling analysis via finite element and perturbation techniques. Part 1: formulation. International Journal of Numerical Methods in Engineering, 1992, 33, 1775-1794.
23. Flores, F. G. and Godoy, L. A. Elastic postbuckling analysis via finite element and perturbation techniques. Part 2: application to shells of revolution. International Journal of Numerical Methods in Engineering, 1993, 36, 331-354.
24. Lanzo, A. D., Garcea, G. and Casciaro, R., Analisi perturbativa multimodale ad elementi finiti di strutture a pannelli sottili. In Atti del VII Meccanica Computazionale, Trieste, Italy, 1-3 Giugno, 1993.
25. Attanasio, G., Luongo, V., Minuto, A. and Vannucci, G., Confronto validazione di codici e metodologie di analisi nonlineare per strutture metalliche ed in composito. Report No. 51X94003, ALENIA, Area Aeronautica, Ingegneria Velivoli Trasporto, Pomigliano D'Arco, Napoli, Italy, 1994.
26. a European Users' Conference, Torino, Italy, 19-20 September 1994.
27. Lanzo, A. D., Garcea, G. and Casciaro, R. Koiter's post-buckling analysis of elastic plates. International Journal of Numerical Methods in Engineering, 1995, 38, 2325-2345.
28. Garcea, G. and Lanzo, A. D., Validazione mediante analisi step-by-step di un codice FEM per l'analisi multimodale di strutture elastiche in parete sottile. In Atti del XII Congresso AIMETA, Napoli, Italy, Ottobre 1995.
29. Salerno, G., Figlia, G. and Casciaro, R., Accuratezza ed affidabilità nell'analisi perturbativa alla Koiter. In IX Convegno Italiano Meccanica Computazionale, Catania, Giugno 1995.
30. Salerno, G., Figlia, G. and Casciaro, R., Influenza delle modalità estrapolative nell'analisi asintotica alla Koiter di strutture elastiche snelle. In XII Convegno AIMETA, Napoli, Ottobre 1995.
31. Lanzo, A. D. and Garcea, G., Asymptotic post-buckling analysis of thin-walled structures. In Proceedings of the International Conference on Mechanics of Solids and Materials Engineering, Singapore, 5-7 June 1995.
32. Salerno, G. and Casciaro, R., A monomodal approach to imperfection sensitivity analysis in multimode elastic buckling. In International conference of mechanics of solids and materials engineering, Singapore, 5-7 Giugno 1995.
33. Lanzo, A. D. and Garcea, G. Koiter's analysis of thin-walled structures by a finite element approach. International Journal of Numerical Methods in Engineering, 1996, 39, 3007-3031.
34. Lanzo, A. D. and Garcea, G., Coupled instabilities in thin-walled structures by a FEM implementation of Koiter's approach. In Second International Conference on Coupled Instabilities in Metal Structures, Liege, Belgium, September 5-7 1996.
35. Salerno, G., Secondary bifurcations and attractive paths in monomodal reduction of coupled instability. In Second International Conference on Coupled Instabilities in Metal Structures, Liege, Belgium, September 5-7 1996.
36. Salerno, G., Colletta, G. and Casciaro, R., Attractive post-critical paths and stochastic imperfection sensitivity analysis of nonlinear elastic structures within an FEM context. In Second ECCOMAS International Conference on Numical Methods in Engineering, Paris, France, September 1996.
37. Figlia, G. and Salerno, G., How to choose some meaningful directions for imperfection sensitivity analysis in multimode elastic buckling. In X Convegno Meccanica Computazionale, Padova, Settembre 1996.
38. Lopez, S., Fortino, S. and Lanzo, A. D., Post-buckling analysis of plates by multigrid FEM approach. In Proceedings ECCOMAS'96 Conference, Paris, France, September 1996.
39. Salerno, G. and Casciaro, R. Mode jumping and attrative paths in multimode elastic buckling. International Journal of Numerical Methods in Engineering, 1997, 40, 833-861.
40. Salerno, G. and Lanzo, A. D. A nonlinear beam finite element for the post-buckling analysis of plane frames by Koiter's perturbation approach. Comparative Methods in Applied Engineering, 1997, 146, 325-349.
41. Lanzo, A. D., Analisi di sensibilità alle imperfezioni di strutture in parete sottile in presenza di tensioni residue. In Congresso AIMETA'97, Siena, Settembre 1997.
42. Salerno, G. and Lanzo, A. D., Sull'insensibilità post-critica all'esatezza geometrica ed al modello FEM di strutture staticamente indeterminate. In Congresso AIMETA '97, Siena, Settembre 1997.
43. Di Carlo, A., Pignataro, M. and Rizzi, N. On the proper treatment of axial and shear deformability constraints in post-buckling analysis of beams. Journal of Non-Linear Mechanics, 1981, 16(2), 221-229.
44. Brezzi, F., Cornalba, M. and Di Carlo, A. How to get around a simple quadratic fold. Numerical Mathematics, 1986, 48, 417-427.
45. Aristodemo, M. A high-continuity finite element model for two-dimensional elastic problem. Computers and Structures, 1985, 21, 987-993.
46. Noor, A. K. Recent advances and application of reduction methods. Applied Mechanical Review, 1994, 5, 125-146May.
47. Wittrick, W. H. and Williams, F. W. An algorithm for computing critical buckling loads of elastic structures. Journal of Structural Mechanics, 1973, 1(4), 497-518.
48. Casciaro, R., Lanzo, A. D. and Salerno, G., A new algorithm for nonlinear symmetric eigenvalue problem. Report No. 122, Dipartimento di Strutture, Università della Calabria, Cosenza, Italy, 1990.