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Shock and Vibration
Volume 2016, Article ID 2373862, 17 pages
http://dx.doi.org/10.1155/2016/2373862
Research Article

Boundary Conditions in 2D Numerical and 3D Exact Models for Cylindrical Bending Analysis of Functionally Graded Structures

1DICAM Department, University of Bologna, Bologna, Italy
2Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Torino, Italy

Received 8 August 2016; Revised 19 October 2016; Accepted 26 October 2016

Academic Editor: Yuri S. Karinski

Copyright © 2016 F. Tornabene et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. W. Q. Chen, J. B. Cai, and G. R. Ye, “Responses of cross-ply laminates with viscous interfaces in cylindrical bending,” Computer Methods in Applied Mechanics and Engineering, vol. 194, no. 6–8, pp. 823–835, 2005. View at Publisher · View at Google Scholar · View at Scopus
  2. W. Q. Chen and K. Y. Lee, “Three-dimensional exact analysis of angle-ply laminates in cylindrical bending with interfacial damage via state-space method,” Composite Structures, vol. 64, no. 3-4, pp. 275–283, 2004. View at Publisher · View at Google Scholar · View at Scopus
  3. W. Q. Chen and K. Y. Lee, “Time-dependent behaviors of angle-ply laminates with viscous interfaces in cylindrical bending,” European Journal of Mechanics—A/Solids, vol. 23, no. 2, pp. 235–245, 2004. View at Publisher · View at Google Scholar · View at Scopus
  4. A. H. Gandhi and H. K. Raval, “Analytical and empirical modeling of top roller position for three-roller cylindrical bending of plates and its experimental verification,” Journal of Materials Processing Technology, vol. 197, no. 1–3, pp. 268–278, 2008. View at Publisher · View at Google Scholar · View at Scopus
  5. S. Oral and H. Darendeliler, “The optimum die profile for the cylindrical bending of plates,” Journal of Materials Processing Technology, vol. 70, no. 1–3, pp. 151–155, 1997. View at Publisher · View at Google Scholar · View at Scopus
  6. V. A. Jairazbhoy, P. Petukhov, and J. Qu, “Large deflection of thin plates in cylindrical bending—non-unique solutions,” International Journal of Solids and Structures, vol. 45, no. 11-12, pp. 3203–3218, 2008. View at Publisher · View at Google Scholar · View at Scopus
  7. A. Lebée and K. Sab, “A bending-gradient model for thick plates, part II: closed-form solutions for cylindrical bending of laminates,” International Journal of Solids and Structures, vol. 48, no. 20, pp. 2889–2901, 2011. View at Publisher · View at Google Scholar · View at Scopus
  8. P. V. Nimbolkar and I. M. Jain, “Cylindrical bending of elastic plates,” Procedia Materials Science, vol. 10, pp. 793–802, 2015. View at Publisher · View at Google Scholar
  9. A. S. Sayyad and Y. M. Ghugal, “A nth-order shear deformation theory for composite laminates in cylindrical bending,” Curved and Layered Structures, vol. 2, no. 1, pp. 290–300, 2015. View at Publisher · View at Google Scholar
  10. N. J. Pagano, “Exact solutions for composite laminates in cylindrical bending,” Journal of Composite Materials, vol. 3, no. 3, pp. 398–411, 1969. View at Publisher · View at Google Scholar
  11. N. J. Pagano and A. S. D. Wang, “Further study of composite laminates under cylindrical bending,” Journal of Composite Materials, vol. 5, pp. 421–428, 1971. View at Publisher · View at Google Scholar · View at Scopus
  12. N. Saeedi, K. Sab, and J.-F. Caron, “Cylindrical bending of multilayered plates with multi-delamination via a layerwise stress approach,” Composite Structures, vol. 95, pp. 728–739, 2013. View at Publisher · View at Google Scholar · View at Scopus
  13. X.-P. Shu and K. P. Soldatos, “Cylindrical bending of angle-ply laminates subjected to different sets of edge boundary conditions,” International Journal of Solids and Structures, vol. 37, no. 31, pp. 4289–4307, 2000. View at Publisher · View at Google Scholar · View at Scopus
  14. Z. G. Bian, W. Q. Chen, C. W. Lim, and N. Zhang, “Analytical solutions for single- and multi-span functionally graded plates in cylindrical bending,” International Journal of Solids and Structures, vol. 42, no. 24-25, pp. 6433–6456, 2005. View at Publisher · View at Google Scholar · View at Scopus
  15. H. M. Navazi and H. Haddadpour, “Nonlinear cylindrical bending analysis of shear deformable functionally graded plates under different loadings using analytical methods,” International Journal of Mechanical Sciences, vol. 50, no. 12, pp. 1650–1657, 2008. View at Publisher · View at Google Scholar · View at Scopus
  16. W. Q. Chen, J. Ying, J. B. Cai, and G. R. Ye, “Benchmark solution of imperfect angle-ply laminated rectangular plates in cylindrical bending with surface piezoelectric layers as actuator and sensor,” Computers and Structures, vol. 82, no. 22, pp. 1773–1784, 2004. View at Publisher · View at Google Scholar · View at Scopus
  17. W. Q. Chen and K. Y. Lee, “Exact solution of angle-ply piezoelectric laminates in cylindrical bending with interfacial imperfections,” Composite Structures, vol. 65, no. 3-4, pp. 329–337, 2004. View at Publisher · View at Google Scholar · View at Scopus
  18. T. Kant and S. M. Shiyekar, “Cylindrical bending of piezoelectric laminates with a higher order shear and normal deformation theory,” Computers and Structures, vol. 86, no. 15-16, pp. 1594–1603, 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. P. Lu, H. P. Lee, and C. Lu, “An exact solution for functionally graded piezoelectric laminates in cylindrical bending,” International Journal of Mechanical Sciences, vol. 47, no. 3, pp. 437–438, 2005. View at Publisher · View at Google Scholar · View at Scopus
  20. W. Yan, J. Wang, and W. Q. Chen, “Cylindrical bending responses of angle-ply piezoelectric laminates with viscoelastic interfaces,” Applied Mathematical Modelling, vol. 38, no. 24, pp. 6018–6030, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. Y. Y. Zhou, W. Q. Chen, and C. F. Lü, “Semi-analytical solution for orthotropic piezoelectric laminates in cylindrical bending with interfacial imperfections,” Composite Structures, vol. 92, no. 4, pp. 1009–1018, 2010. View at Publisher · View at Google Scholar · View at Scopus
  22. G. P. Dube, S. Kapuria, and P. C. Dumir, “Exact piezothermoelastic solution of a simply-supported orthotropic flat panel in cylindrical bending,” International Journal of Mechanical Sciences, vol. 38, pp. 374–387, 1996. View at Google Scholar
  23. V. N. Pilipchuk, V. L. Berdichevsky, and R. A. Ibrahim, “Thermo-mechanical coupling in cylindrical bending of sandwich plates,” Composite Structures, vol. 92, no. 11, pp. 2632–2640, 2010. View at Publisher · View at Google Scholar · View at Scopus
  24. C. Zhang, S. Di, and N. Zhang, “A new procedure for static analysis of thermo-electric laminated composite plates under cylindrical bending,” Composite Structures, vol. 56, no. 2, pp. 131–140, 2002. View at Publisher · View at Google Scholar · View at Scopus
  25. W. Q. Chen and K. Y. Lee, “State-space approach for statics and dynamics of angle-ply laminated cylindrical panels in cylindrical bending,” International Journal of Mechanical Sciences, vol. 47, no. 3, pp. 374–387, 2005. View at Publisher · View at Google Scholar · View at Scopus
  26. C.-P. Wu and Y.-S. Syu, “Exact solutions of functionally graded piezoelectric shells under cylindrical bending,” International Journal of Solids and Structures, vol. 44, no. 20, pp. 6450–6472, 2007. View at Publisher · View at Google Scholar · View at Scopus
  27. W. Yan, J. Ying, and W. Q. Chen, “The behavior of angle-ply laminated cylindrical shells with viscoelastic interfaces in cylindrical bending,” Composite Structures, vol. 78, no. 4, pp. 551–559, 2007. View at Publisher · View at Google Scholar · View at Scopus
  28. S. Brischetto, F. Tornabene, N. Fantuzzi, and E. Viola, “3D exact and 2D generalized differential quadrature models for free vibration analysis of functionally graded plates and cylinders,” Meccanica, vol. 51, no. 9, pp. 2059–2098, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. N. Fantuzzi, S. Brischetto, F. Tornabene, and E. Viola, “2D and 3D shell models for the free vibration investigation of functionally graded cylindrical and spherical panels,” Composite Structures, vol. 154, pp. 573–590, 2016. View at Publisher · View at Google Scholar
  30. S. Brischetto and R. Torre, “Exact 3D solutions and finite element 2D models for free vibration analysis of plates and cylinders,” Curved and Layered Structures, vol. 1, no. 1, pp. 59–92, 2014. View at Publisher · View at Google Scholar
  31. F. Tornabene, S. Brischetto, N. Fantuzzi, and E. Viola, “Numerical and exact models for free vibration analysis of cylindrical and spherical shell panels,” Composites Part B: Engineering, vol. 81, pp. 231–250, 2015. View at Publisher · View at Google Scholar · View at Scopus
  32. S. Brischetto, “Exact elasticity solution for natural frequencies of functionally graded simply-supported structures,” Computer Modeling in Engineering & Sciences, vol. 95, no. 5, pp. 391–430, 2013. View at Google Scholar · View at Scopus
  33. S. Brischetto, “Three-dimensional exact free vibration analysis of spherical, cylindrical, and flat one-layered panels,” Shock and Vibration, vol. 2014, Article ID 479738, 29 pages, 2014. View at Publisher · View at Google Scholar · View at Scopus
  34. S. Brischetto, “A continuum elastic three-dimensional model for natural frequencies of single-walled carbon nanotubes,” Composites Part B: Engineering, vol. 61, pp. 222–228, 2014. View at Publisher · View at Google Scholar · View at Scopus
  35. S. Brischetto, “An exact 3d solution for free vibrations of multilayered cross-ply composite and sandwich plates and shells,” International Journal of Applied Mechanics, vol. 6, no. 6, Article ID 1450076, 42 pages, 2014. View at Publisher · View at Google Scholar · View at Scopus
  36. S. Brischetto, “A continuum shell model including van der Waals interaction for free vibrations of double-walled carbon nanotubes,” CMES-Computer Modeling in Engineering and Sciences, vol. 104, no. 4, pp. 305–327, 2015. View at Google Scholar · View at Scopus
  37. S. Brischetto, F. Tornabene, N. Fantuzzi, and M. Bacciocchi, “Refined 2D and exact 3D shell models for the free vibration analysis of single- and double-walled carbon nanotubes,” Technologies, vol. 3, no. 4, pp. 259–284, 2015. View at Publisher · View at Google Scholar
  38. S. Brischetto, “Convergence analysis of the exponential matrix method for the solution of 3D equilibrium equations for free vibration analysis of plates and shells,” Composites Part B: Engineering, vol. 98, pp. 453–471, 2016. View at Publisher · View at Google Scholar
  39. S. Brischetto, “Exact and approximate shell geometry in the free vibration analysis of one-layered and multilayered structures,” International Journal of Mechanical Sciences, vol. 113, pp. 81–93, 2016. View at Publisher · View at Google Scholar
  40. S. Brischetto, “Curvature approximation effects in the free vibration analysis of functionally graded shells,” International Journal of Applied Mechanics, 2016. View at Publisher · View at Google Scholar
  41. F. Tornabene, N. Fantuzzi, F. Ubertini, and E. Viola, “Strong formulation finite element method based on differential quadrature: a survey,” Applied Mechanics Reviews, vol. 67, no. 2, Article ID 020801, pp. 1–55, 2015. View at Publisher · View at Google Scholar · View at Scopus
  42. F. Tornabene, E. Viola, and N. Fantuzzi, “General higher-order equivalent single layer theory for free vibrations of doubly-curved laminated composite shells and panels,” Composite Structures, vol. 104, pp. 94–117, 2013. View at Publisher · View at Google Scholar · View at Scopus
  43. N. Fantuzzi, F. Tornabene, E. Viola, and A. J. Ferreira, “A strong formulation finite element method (SFEM) based on RBF and GDQ techniques for the static and dynamic analyses of laminated plates of arbitrary shape,” Meccanica, vol. 49, no. 10, pp. 2503–2542, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  44. F. Tornabene, N. Fantuzzi, and M. Bacciocchi, “Free vibrations of free-form doubly-curved shells made of functionally graded materials using higher-order equivalent single layer theories,” Composites Part B: Engineering, vol. 67, pp. 490–509, 2014. View at Publisher · View at Google Scholar · View at Scopus
  45. F. Tornabene and E. Viola, “Static analysis of functionally graded doubly-curved shells and panels of revolution,” Meccanica, vol. 48, no. 4, pp. 901–930, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  46. F. Tornabene, N. Fantuzzi, M. Bacciocchi, and R. Dimitri, “Dynamic analysis of thick and thin elliptic shell structures made of laminated composite materials,” Composite Structures, vol. 133, pp. 278–299, 2015. View at Publisher · View at Google Scholar · View at Scopus
  47. F. Tornabene, N. Fantuzzi, M. Bacciocchi, and E. Viola, “Higher-order theories for the free vibrations of doubly-curved laminated panels with curvilinear reinforcing fibers by means of a local version of the GDQ method,” Composites Part B: Engineering, vol. 81, pp. 196–230, 2015. View at Publisher · View at Google Scholar · View at Scopus
  48. F. Tornabene, N. Fantuzzi, M. Bacciocchi, and R. Dimitri, “Free vibrations of composite oval and elliptic cylinders by the generalized differential quadrature method,” Thin-Walled Structures, vol. 97, pp. 114–129, 2015. View at Publisher · View at Google Scholar · View at Scopus
  49. F. Tornabene and J. N. Reddy, “FGM and laminated doubly-curved and degenerate shells resting on nonlinear elastic foundations: a GDQ solution for static analysis with a posteriori stress and strain recovery,” Journal of the Indian Institute of Science, vol. 93, no. 4, pp. 635–688, 2013. View at Google Scholar · View at MathSciNet
  50. N. Fantuzzi, F. Tornabene, and E. Viola, “Four-parameter functionally graded cracked plates of arbitrary shape: a GDQFEM solution for free vibrations,” Mechanics of Advanced Materials and Structures, vol. 23, no. 1, pp. 89–107, 2016. View at Publisher · View at Google Scholar · View at Scopus