Assessments of refined theories for buckling analysis of laminated plates

Composite Structures

Volumn 93, Issue 2, 2011, Pages 456-464

  Nali, P ^a   Carrera, E ^a   Lecca, S ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

Advanced finite elements; Buckling analysis; Higher order plate modelling; Layer Wise description

Indexed keywords

ANISOTROPIC PLATES; BUCKLING ANALYSIS; CARRERA'S UNIFIED FORMULATION; EQUIVALENT SINGLE LAYERS; EXACT SOLUTION; FINITE ELEMENT; FINITE ELEMENTS; HIGHER ORDER PLATE MODELLING; LAMINATED PLATE; LAYER-WISE; LAYER-WISE DESCRIPTION; PRINCIPLE OF VIRTUAL DISPLACEMENTS; REFINED THEORY;

BUCKLING; FINITE ELEMENT METHOD; LAMINATING;

ORTHOTROPIC PLATES;

EID: 79951515675     PISSN: 02638223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruct.2010.08.035     Document Type: Article

References (53)

1. Stein E. Buckling. Encyclopedia of computational mechanics 2004, vol. 2. John Wiley & Sons. E. Stein, R. de Borst, T.J.R. Hughes (Eds.).
2. Bushnell D. Computerized buckling analysis of shells 1985, M. Nihhoff, Dordrecht.
3. Elishakoff I., van Manen S., Vermeulen P.G., Arbocz J. First-order second-moment analysis of the buckling of shells with random imperfections. AIAA J 1987, 25:1113-1117.
4. D'Ottavio M., Carrera E. Variable-kinematics approach for linearized buckling analysis of laminated plates and shells. AIAA J 2010, 48:1987-1997.
5. Timoshenko S.P., Gere J.M. Theory of elastic stability 1961, McGraw-Hill, New York.
6. Jabareen M. Rigorous buckling of laminated cylindrical shells. Thin-Walled Struct 2009, 47:233-240.
7. Buckling of thin-walled circular cylinders. NASA Space Vehicle Design Criteria NASA SP-8007. NASA; 1968.
8. ECSS Draft Standard on Buckling. P.O. Box 299, 2200 AG Noordwijk, The Netherlands: ESA Requirements and Standards Division, ESTEC; 2008.
9. Arbocz J., Starnes J.H. Future directions and challenges in shell stability analysis. Thin-Walled Struct 2002, 40:729-754.
10. Hilburger M.W., Starnes J.H. Effect of imperfections on the buckling response of compression-loaded composite shells. Int J Non-Lin Mech 2002, 37:623-643.
11. Arbocz J., Hilburger M.W. Toward a probabilistic preliminary design criterion for buckling critical composite shells. AIAA J 2005, 43:1823-1827.
12. Leissa AW. Buckling of laminated composite plates and shell panels. Flight Dynamics Laboratory Report No. AFWAL-TR-85-3069; 1985.
13. Leissa A.W. A review of laminated composite plate buckling. Appl Mech Rev 1987, 40(5):555-579.
14. Harris G.Z. The buckling and post buckling behaviour of composite plates under biaxial loading. Int J Mech Sci 1975, 17(3):187-202.
15. Prabhakara M.K. Post-buckling behaviour of simply-supported cross-ply rectangular plates. Aeronaut Quart 1976, 27(4):309-316.
16. Singh G., Sadasiva Rao Y.V.K. Stability of thick angle-ply composite plates. Comput Struct 1988, 29:317-322.
17. Singh G., Sadasiva Rao Y.V.K., Iyengar N.G.R. Buckling of thick layered composite plates under inplane moment loading. Compos Struct 1989, 13(1):35-48.
18. Leissa A.W. Conditions for laminated plates to remain flat under in-plane loading. Compos Struct 1986, 6(4):271-281.
19. Singh G., Venkateswara Rao G., Iyengar N.G.R. Bifurcation buckling in unsymmetrically laminated plates. Compos Eng 1994, 4(2):181-194.
20. Singh G., Venkateswara Rao G., Iyengar N.G.R. Thermal post buckling behaviour of rectangular antisymmetric cross-ply composite plates. Acta Mech 1993, 98:39-50.
21. Matsunaga H. Buckling instabilities of thick elastic plates subjected to in-plane stresses. Comput Struct 1995, 62(1):205-214.
22. Matsunaga H. Vibration and stability of cross-ply laminated composite plates according to a global higher-order plate theory. Comput Struct 2000, 48:231-244.
23. Ahmed Noor K., Jeanne Peters M. Finite element buckling and postbuckling solutions for multilayered composite panels. Finite Elem Anal Des 1994, 15:343-367.
24. Ferreira A.J.M., Barbosa J.T. Buckling behaviour of composite shells. Compos Struct 2000, 50(1):93-98.
25. Ferreira A.J.M., Fasshauer G.E., Batra R.C. Natural frequencies of thick plates made of orthotropic, monoclinic, and hexagonal materials by a meshless method. J Sound Vib 2009, 319(3-5):984-992.
26. Carrera E. A class of two dimensional theories for multilayered plates analysis, Atti Accademia delle Scienze di Torino. Mem Sci Fis 1995, 19-20:49-87.
27. Ferreira A.J.M. Polyharmonic (thin-plate) splines in the analysis of composite plates. Int J Mech Sci 2004, 46:1549-1569.
28. Carrera E. Historical review of zig-zag theories for multilayered plates and shells. Appl Mech Rev 2003, 56:287-308.
29. Lekhnitskii S.G. Strength calculation of composite beams. Vestnik inzhen i tekhnikov 1935, 9.
30. Ambartusumian S.A. On a theory of bending of anisotropic plate. Investiia Akad Nauk SSSR Ot Tekh Nauk 1958, 4.
31. Reissner E. On a certain mixed variational theory and a proposed application. Int J Numer Methods Eng 1984, 20:1366-1368.
32. Carrera E. Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking. Arch Comput Methods Eng 2003, 10(3):215-296.
33. Carrera L.DeMasiE. Classical and advanced multilayered plate elements based upon PVD and RMVT. Part 1. Derivation of finite element matrice. Int J Numer Methods Eng 2002, 55:191-231.
34. Carrera E. Single layer vs multilayer plate modellings on the base of reissner's mixed theorem. AIAA J 2000, 38(2):342-352.
35. Carrera E. An assessment of mixed and classical theories on global and local response of multilayered orthotropic plates. Compos Struct 2000, 50:183-198.
36. Carrera E., Giunta G. Hierarchical evaluation of failure parameters in composite plates. AIAA J 2009, 47:692-702.
37. Cauchy A.L. Sur lequilibre et le mouvement dune plaque solide. Exercises de Matematique 1828, 3:328-355.
38. Poisson S.D. Memoire sur lequilibre et le mouvement des corps elastique. Mem Acad Sci 1829, 8:353-570.
39. Kirchhoff G. Uber das gleichgewicht und die bewegung einer elastishen scheibe. J Angew Math 1850, 40:51-88.
40. Reissner E. The effect of transverse shear deformation on the bending of elastic plates. J Appl Mech 1945, 12:69-76.
41. Mindlin R.D. Influence of rotatory inertia and shear in flexural motions of isotropic elastic plates. J Appl Mech 1951, 18:1031-1036.
42. Carrera E., Brischetto S. Analysis of thickness locking in classical, refined and mixed multilayered plate theories. Compos Struct 2008, 82:549-562.
43. Carrera E., Brischetto S., Nali P. Variational statements and computational models for multifield problems and multilayered structures. MAMS 2008, 15(3):182-198. [special issue].
44. Crisfield MA. Non-linear finite element analysis of solids and structures. The Atrium, Southern Gate, Chichester, West Sussex, England: Wiley & Sons Ltd.; 1991.
45. Bathe K.J. Finite element procedures 1996, Prentice-Hall, Inc., Upper Saddle River (NJ).
46. Zienkiewicz O.C., Taylor R.L., Zhu J.Z. The finite element method: Its basis and fundamentals 2005, Elsevier Butterworth-Heinemann Linacre House, Jordan Hill, Oxford. 6th ed.
47. Carrera E. Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking. Arch Comput Methods Eng 2003, 10:215-297.
48. Carrera E., Cinefra M., Nali P. MITC technique extended to variable kinematic multilayered plate elements. Compos Struct 2010, 92:1888-1895.
49. Leissa AW. Vibration of plates. NASA SP-160; 1969.
50. Brunelle E.J., Robertson S.R. Vibrations of an initially stressed thick plate. J Sound Vib 1976, 45:405-416.
51. Reddy J.N., Phan P.H. Stability and vibration of isotropic, orthotropic and laminated plates according to a higher order shear deformation theory. J Sound Vib 1985, 98:157-170.
52. Doong J.L. Vibration and stability of an initially stressed thick plate according to a high-order deformation theory. J Sound Vib 1987, 113(3, 22):425-440.
53. Matsunaga H. Free vibration and stability of thick elastic plates subjected to in-plane forces. Int J Solids Struct 1994, 31(22):3113-3124.