Skip to main content

A Best Theory Diagram for Metallic and Laminated Shells

  • Chapter
  • First Online:

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 15))

Abstract

In this work, refinements of classical theories are proposed in order to analyze isotropic, orthotropic and laminated plates and shells. Higher order theories have been implemented according to the Carrera Unified Formulation (CUF) and, for a given problem, the effectiveness of each employed generalized displacement variable has been established, varying the thickness ratio, the orthotropic ratio and the stacking sequence of the lay-out. A number of theories have therefore been constructed imposing a given error with respect to the available ’best solution’. The results have been restricted to the problems for which closed-form solutions are available. These show that the terms that have to be used according to a given error varies from problem to problem, but they also vary when the variable that has to be evaluated (displacement, stress components) is changed.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berdichevsky, V.L.: Variational-asymptotic method of shell theory construction. PMM Vol. 43, 664–667 (1979)

    Google Scholar 

  2. Berdichevsky, V.L., Misyura, V.: Effect of accuracy loss in classical shell theory. Journal of Applied Mechanics Vol. 59, 217–223 (1992)

    Article  Google Scholar 

  3. Carrera, E.: A class of two-dimensional theories for anisotropic multilayered plates analysis. Atti della accademia delle scienze di Torino. Classe di scienze fisiche matematiche e naturali Vol.19–20, 1–39 (1995)

    Google Scholar 

  4. Carrera, E.: Evaluation of layer-wise mixed theories for laminated plates analysis. AIAA Journal Vol. 26, 830–839 (1998)

    Article  Google Scholar 

  5. Carrera, E.: A study of transverse normal stress effect on vibration of multilayered plates and shells. Journal of Sound and Vibration Vol. 225, No. 5, 803–829 (1999)

    Article  Google Scholar 

  6. Carrera, E.: Multilayered shell theories that account for a layer-wise mixed description. Part I: Governing equations. AIAA Journal Vol. 37, 1107–1116 (1999)

    Article  Google Scholar 

  7. Carrera, E.: Multilayered shell theories that account for a layer-wise mixed description. Part II: Numerical evaluations. AIAA Journal Vol. 37, 1117–1124 (1999)

    Article  Google Scholar 

  8. Carrera, E.: Developments, ideas and evaluations based upon the Reissner’s mixed variational theorem in the modeling of multilayered plates and shells. Applied Mechanics Reviews Vol. 54, 301–329 (2001)

    Article  Google Scholar 

  9. Carrera, E.: Theories and finite elements for multilayered plates and shells. Archives of Computational Methods in Engineering Vol. 9, No. 2, 87–140 (2002)

    Article  Google Scholar 

  10. Carrera, E.: Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking. Archives of Computational Methods in Engineering Vol. 10, No. 3, 216–296 (2003)

    Article  Google Scholar 

  11. Carrera, E.: Historical review of zig-zag theories for multilayered plates and shells. Applied Mechanics Reviews Vol. 56, 287–308 (2003)

    Article  Google Scholar 

  12. Carrera, E., Brischetto, S.: Analysis of thickness locking in classical, refined and mixed theories for layered shells. Composite Structures Vol. 85, No. 1, 83–90 (2008)

    Article  Google Scholar 

  13. Carrera, E., Giunta, G., Brischetto, S.: Hierarchical closed form solutions for plates bent by localized transverse loadings: Journal of Zhejiang University SCIENCE B Vol. 8, 1026–1037 (2007)

    Article  Google Scholar 

  14. Carrera, E., Miglioretti, F., Petrolo, M.: Accuracy of refined finite elements for laminated plate analysis. Composite Structures Vol. 93, 1311–1327 (2011)

    Article  Google Scholar 

  15. Carrera, E., Petrolo, M.: Guidelines and recommendations to construct refinements of classical theories for metallic and composite plates. AIAA Journal Vol. 48, No. 12, 2852–2866 (2010)

    Article  Google Scholar 

  16. Carrera, E., Petrolo, M., Miglioretti, F.: Guidelines and recommendations on the use of higher-order finite elements for bending analysis of plates. International Journal for Computational Methods in Engineering Science and Mechanics, in press

    Google Scholar 

  17. Cicala, P.: Sulla teoria elastica della parete sottile. Giornale del Genio Civile Vol. 4, 6 and 9 (1959)

    Google Scholar 

  18. Cicala, P.: Systematic approximation approach to linear shell theory. Levrotto e Bella, Torino (1965)

    Google Scholar 

  19. Fettahlioglu, O.A., Steele, C.R.: Asymptotic solutions for orthotropic non-homogeneous shells of revolution. ASME J. Appl. Mech. Vol. 44, 753–758 (1974)

    Article  Google Scholar 

  20. Gol’denweizer, A.L.: Theory of thin elastic shells. International Series of Monograph in Aeronautics and Astronautics, Pergamon Press, New York (1961)

    Google Scholar 

  21. Grigolyuk, E.I., Kulikov, G.M.: General directions of the development of theory of shells. Mekhanica Kompozitnykh Materialov Vol. 24, 287–298 (1988)

    Google Scholar 

  22. Kapania, K.: A review on the analysis of laminated shells.. ASME J. Pressure Vessel Technol. Vol. 111, No. 2, 88–96 (1989)

    Google Scholar 

  23. Kapania, K., Raciti , S.: Recent advances in analysis of aminated beams and plates, part I: Shear effects and buckling. AIAA Journal Vol. 27, No. 7, 923–935 (1989)

    Article  Google Scholar 

  24. Kapania, K., Raciti, S.: Recent advances in analysis of laminated beams and plates. part II: Vibrations and wave propagation. AIAA Journal Vol. 27, No. 7, 935–946 (1989)

    Article  Google Scholar 

  25. Kirchhoff, G.: Uber das gleichgewicht und die bewegung einer elastischen scheibe. J. Angew. Math. Vol. 40, 51–88 (1850)

    Google Scholar 

  26. Koiter, W.T.: On the foundations of the linear theory of thin elastic shell. Proc. Kon. Nederl. Akad. Wetensch. Vol. 73, 169–195 (1970)

    Google Scholar 

  27. Librescu, L.: Elasto-statics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures. Noordhoff Int, Leyden, Netherland (1976)

    Google Scholar 

  28. Librescu, L., Reddy, J.N.: A critical review and generalization of transverse shear deformable anisotropic plates, euromech colloquium 219, kassel. Refined Dynamical Theories of Beams, Plates and Shells and Their Applications September 1986, 32–43, I Elishakoff and Irretier (eds), Springer Verlag, Berlin (1986)

    Google Scholar 

  29. Love, A.E.H.: The Mathematical Theory of Elasticity. Fourth ed., Cambridge Univ Press (1927)

    Google Scholar 

  30. Mindlin, R.D.: Influence of rotatory inertia and shear in flexural motions of isotropic elastic plates. ASME J. Appl. Mech. Vol. 18, 1031–1036 (1950)

    Google Scholar 

  31. Naghdi, P.M.: The theory of shells and plates. Handbuch der Phisik Vol. 6, 425–640 (1972)

    Google Scholar 

  32. Noor, A.K., Burton, W.S.: Assessment of shear deformation theories for multilayered composite plates. Appl. Mech. Rev. Vol. 42, No. 1, 1–18 (1989)

    Article  Google Scholar 

  33. Noor, A.K., Burton, W.S.: Assessment of computational models for multilayered composite shells. Appl. Mech. Rev. Vol. 43, No. 4, 67–97 (1989)

    Google Scholar 

  34. Qatu, M.S.: Recent research advances in the dynamic behavior of shells. Part 1: laminated composite shells. Applied Mechanics Reviews Vol. 55, No. 4, 325–350 (2002)

    Article  Google Scholar 

  35. Qatu, M.S.: Recent research advances in the dynamic behavior of shells. Part 2: homogenous shells. Applied Mechanics Reviews Vol. 55, No. 5, 415–434 (2002)

    Article  Google Scholar 

  36. Reddy, J.N.: Mechanics of laminated composite plates and shells. Theory and Analysis. Second ed., CRC Press (2004)

    Google Scholar 

  37. Reddy, J.N., Robbins, D.H.: Theories and computational models for composite laminates. Appl. Mech. Rev. Vol. 47, No. 6, 147–165 (1994)

    Article  Google Scholar 

  38. Reissner, E.: The effect of transverse shear deformation on the bending of elastic plates. ASME J. Appl. Mech. Vol. 12, 69–76 (1945)

    Google Scholar 

  39. Ren, J.G.: Exact solutions for laminated cylindrical shells in cylindrical bending. Composites Science and Technology Vol. 29, 169–187 (1987)

    Article  CAS  Google Scholar 

  40. Spencer, A.J.M., Watson, P., Rogers, T.G.: Stress analysis of laminated circular cylindrical shells. Recent Developments in Composite Materials Structures. Presented at the Winter Annual meeting of ASME, Dallas, Nov. 1990, AD 19, AMD 113, ASME, New York (1990)

    Google Scholar 

  41. Varadan, T.K., Bhaskar, K.: Bending of laminated orthotropic cylindrical shells – an elasticity approach. Composite Structures Vol. 17, 141–156 (1991)

    Article  Google Scholar 

  42. Vlasov, B.F.: On the equations of bending of plates. Dokla Ak Nauk Azerbeijanskoi-SSR Vol. 3, 955–979 (1957)

    Google Scholar 

  43. Widera, D.E.O., Fan, H.: On the derivation of a refined theory for non-homogeneous anisotropic shells of revolution. ASME J. Appl. Mech. Vol. 110, 102–105 (1988)

    Google Scholar 

  44. Widera, D.E.O., Logan, L.: efined theories for nonhomogeneous anisotropic cylindrical shells: Part I-derivation. Journal of the Engineering Mechanics Division Vol. 106, No. 6, 1053–1074 (1980)

    Google Scholar 

Download references

Acknowledgements

The financial support from the Regione Piemonte projects STEPS and MICROCOST is gratefully acknowledged.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Erasmo Carrera .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Carrera, E., Cinefra, M., Petrolo, M. (2011). A Best Theory Diagram for Metallic and Laminated Shells. In: Altenbach, H., Eremeyev, V. (eds) Shell-like Structures. Advanced Structured Materials, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21855-2_45

Download citation

Publish with us

Policies and ethics