A consistent refinement of first-order shear deformation theory for laminated composite and sandwich plates using improved zigzag kinematics

Journal of Mechanics of Materials and Structures

Volumn 5, Issue 2, 2010, Pages 341-367

  Tessler, Alexander ^a   Di Sciuva, Marco ^b   Gherlone, Marco ^b  

^a NASA LANGLEY RESEARCH CENTER   (United States)

^b POLITECNICO DI TORINO   (Italy)

Author keywords

First order shear deformation plate theory; Laminated composite plates; Sandwich plates; Virtual work principle; Zigzag kinematics

Indexed keywords

FIRST-ORDER SHEAR DEFORMATION; LAMINATED COMPOSITE PLATES; SANDWICH PLATES; VIRTUAL WORK PRINCIPLE; ZIGZAG KINEMATICS;

DELAMINATION; KINEMATICS; LAMINATED COMPOSITES; LAMINATING; PIECEWISE LINEAR TECHNIQUES; SHEAR DEFORMATION;

PLATES (STRUCTURAL COMPONENTS);

EID: 77957891488     PISSN: 15593959     EISSN: None     Source Type: Journal    
DOI: 10.2140/jomms.2010.5.341     Document Type: Article

References (43)

1. S. A. Ambartsumyan, Russian source, State Publishing House for Physical and Mathematical Literature, Moscow, 1961. Translated in "Theory of anisotropic shells", NASA Technical translation TT F-118, 1964, http://tinyurl.com/NASA-TT-F-118.
2. G. Arfken, Mathematical methods for physicists, 3rd ed., Academic Press, Orlando, FL, 1985.
3. R. C. Averill, "Static and dynamic response of moderately thick laminated beams with damage", Compos. Eng. 4:4 (1994), 381-395.
4. R. C. Averill and Y. C. Yip, "Development of simple, robust finite elements based on refined theories for thick laminated beams", Comput. Struct. 59:3 (1996), 529-546.
5. A. Barut, E. Madenci, T. Anderson, and A. Tessler, "Equivalent single layer theory for a complete stress field in sandwich panels under arbitrary distributed loading", Compos. Struct. 58:4 (2002), 483-495.
6. M. Cho and R. R. Parmerter, "An efficient higher-order plate theory for laminated composites", Compos. Struct. 20:2 (1992), 113-123.
7. M. Cho and R. R. Parmerter, "Efficient higher order composite plate theory for general lamination configurations", AIAA J. 31:7 (1993), 1299-1306.
8. G. M. Cook and A. Tessler, "A {3, 2}-order bending theory for laminated composite and sandwich beams", Compos. B Eng. 29:5 (1998), 565-576.
9. M. Di Sciuva, "A refinement of the transverse shear deformation theory for multilayered orthotropic plates", in Atti del VII Congresso Nazionale AIDAA (Naples, 1983), edited by A. Marchese, ESA, Rome, 1984. Also in Aerotecnica Missili e Spazio 63 (1984), 84-92.
10. M. Di Sciuva, "A refined transverse shear deformation theory for multilayered anisotropic plates", Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 118 (1984), 279-295.
11. M. Di Sciuva, "Development of an anisotropic, multilayered, shear-deformable rectangular plate element", Comput. Struct. 21:4 (1985), 789-796.
12. M. Di Sciuva, "Evaluation of some multilayered, shear-deformable plate elements", pp. 394-400 in A collection of technical papers: AIAA/ASME/ASCE/AHS 26th Structures, Structural Dynamics and Materials Conference (Orlando, FL, 1985), vol. 1, AIAA, New York, 1985. Paper 85-0717.
13. M. Di Sciuva, "Bending, vibration and buckling of simply supported thick multilayered orthotropic plates: an evaluation of a new displacement model", J. Sound Vib. 105:3 (1986), 425-442.
14. M. Di Sciuva, "An improved shear-deformation theory for moderately thick multilayered anisotropic shells and plates", J. Appl. Mech. (ASME) 54:3 (1987), 589-596.
15. M. Di Sciuva, "Further refinement in the transverse shear deformation theory for multilayered composite plates", Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 124:5-6 (1990), 248-268.
16. M. Di Sciuva, "Multilayered anisotropic plate models with continuous interlaminar stresses", Compos. Struct. 22:3 (1992), 149-168.
17. M. Di Sciuva, M. Gherlone, and L. Librescu, "Implications of damaged interfaces and of other nonclassical effects on the load carrying capacity of multilayered composite shallow shells", Int. J. Non-Linear Mech. 37:4-5 (2002), 851-867.
18. J.-S. Kim and M. Cho, "Enhanced first-order shear deformation theory for laminated and sandwich plates", J. Appl. Mech.(ASME) 72:6 (2005), 809-817.
19. J.-S. Kim and M. Cho, "Enhanced modeling of laminated and sandwich plates via strain energy transformation", Compos. Sci. Technol. 66:11-12 (2006), 1575-1587.
20. L. Librescu, A. A. Khdeir, and J. N. Reddy, "A comprehensive analysis of the state of stress of elastic anisotropic flat plates using refined theories", Acta Mech. 70:1-4 (1987), 57-81.
21. D. Liu and X. Li, "An overall view of laminate theories based on displacement hypothesis", J. Compos. Mater. 30:14 (1996), 1539-1561.
22. K. H. Lo, R. M. Christensen, and E. M. Wu, "A higher-order theory of plate deformation, 1: Homogeneous plates", J. Appl. Mech.(ASME) 44 (1977), 663-668.
23. K. H. Lo, R. M. Christensen, and E. M. Wu, "A higher-order theory of plate deformation, 2: Laminated plates", J. Appl. Mech.(ASME) 44 (1977), 669-676.
24. MD Nastran: reference guide, Version 2006.0, MSC Software Corporation, Santa Ana, CA, 2006.
25. H. Murakami, "Laminated composite plate theory with improved in-plane responses", J. Appl. Mech.(ASME) 53:3 (1986), 661-666.
26. A. K. Noor and W. S. Burton, "Assessment of shear deformable theories for multilayered composite plates", Appl. Mech. Rev.(ASME) 42:1 (1989), 1-12.
27. A. K. Noor and W. S. Burton, "Three-dimensional solutions for antisymmetrically laminated anisotropic plates", J. Appl. Mech. (ASME) 57:1 (1990), 182-188.
28. N. J. Pagano, "Exact solutions for composite laminates in cylindrical bending", J. Compos. Mater. 3:3 (1969), 398-411.
29. J. N. Reddy, "A simple higher-order theory for laminated composite plates", J. Appl. Mech. (ASME) 51:4 (1984), 745-752.
30. J. N. Reddy, Mechanics of laminated composite plates: theory and analysis, CRC Press, Boca Raton, FL, 1997.
31. J. N. Reddy, Mechanics of laminated composite plates and shells: theory and analysis, 2nd ed., CRC Press, Boca Raton, FL, 2004.
32. K. J. Reddy and K. Vijayakumar, "Lamination-dependent shear deformation models for cylindrical bending of angle-ply laminates", Comput. Struct. 55:4 (1995), 717-725.
33. E. Reissner, "On a certain mixed variational theorem and a proposed application", Int. J. Numer. Methods Eng. 20:7 (1984), 1366-1368.
34. E. Reissner, "Reflections on the theory of elastic plates", Appl. Mech. Rev. (ASME) 38:11 (1985), 1453-1464.
35. C.-T. Sun and J. M. Whitney, "Theories for the dynamic response of laminated plates", AIAA J. 11:2 (1973), 178-183.
36. A. Tessler, "An improved plate theory of {1,2}-order for thick composite laminates", Int. J. Solids Struct. 30:7 (1993), 981-1000.
37. A. Tessler, M. Di Sciuva, and M. Gherlone, "Refinement of Timoshenko beam theory for composite and sandwich beams using zigzag kinematics", Technical report TP-2007-215086, NASA Langley Research Center, Hampton, VA, 2007, Available at http://tinyurl.com/NASA-TP-2007-215086.
38. A. Tessler, M. Di Sciuva, and M. Gherlone, "Refined zigzag theory for laminated composite and sandwich plates", Technical report TP-2009-215561, NASA Langley Research Center, Hampton, VA, 2009, Available at http://tinyurl.com/NASA-TP-2009-215561.
39. A. Toledano and H. Murakami, "A high-order laminated plate theory with improved in-plane responses", Int. J. Solids Struct. 23:1 (1987), 111-131.
40. P. Umasree and K. Bhaskar, "Analytical solutions for flexure of clamped rectangular cross-ply plates using an accurate zig-zag type higher-order theory", Compos. Struct. 74:4 (2006), 426-439.
41. S. Vlachoutsis, "Shear correction factors for plates and shells", Int. J. Numer. Methods Eng. 33:7 (1992), 1537-1552.
42. W. Yu, "Mathematical construction of a Reissner-Mindlin plate theory for composite laminates", Int. J. Solids Struct. 42:26 (2005), 6680-6699.
43. W. Yu, J.-S. Kim, D. H. Hodges, and M. Cho, "A critical evaluation of two Reissner-Mindlin type models for composite laminated plates", Aerosp. Sci. Technol. 12:5 (2008), 408-417.