A 3D solution for angle-ply cylindrical shell panel supported arbitrarily on its boundaries using extended Kantorovich method

Abstract

Structural components such as shell with arbitrarily supported boundary condition and angle-ply material configuration require an efficient theory to accurately predict its three-dimensional (3D) deformations and stresses. Here, a generalized 3D solution using the multiterm extended Kantorovich method (EKM) is presented for a cylindrical shell panel. In this work, the governing equation of the problem is obtained using the mixed type Reissner’s principle from shell equilibrium and constitutive relations in the cylindrical coordinate system. Further, two sets of simultaneous ordinary differential equations (ODEs) are obtained iteratively by applying the EKM. This reduction in partial differential equations to ODEs has highly increased the accuracy and convergence of the process. This solution has provided very accurate results with just two terms in the series (multiterm) expansion, and results are obtained after just one or two iteration steps for angle-ply laminates. Transverse stresses including boundary effects have been accurately predicted by presently developed solution in and around the vicinity of the clamped edge where a 3D finite element (FE) fails otherwise.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

References

  1. 1.

    Piggott, M.R., Zhang, W.: Fracture toughness of angle ply laminates. ESIS Publ. 32, 445–454 (2003)

    Google Scholar 

  2. 2.

    Alipour, M.M.: An analytical approach for bending and stress analysis of cross/angle-ply laminated composite plates under arbitrary non-uniform loads and elastic foundations. Arch. Civ. Mech. Eng. 16(2), 193–210 (2016)

    Article  Google Scholar 

  3. 3.

    Chen, W.Q., Lee, K.Y.: State-space approach for statics and dynamics of angle-ply laminated cylindrical panels in cylindrical bending. Int. J. Mech. Sci. 47(3), 374–87 (2005)

    Article  Google Scholar 

  4. 4.

    Kant, T.: A critical review and some results of recently developed refined theories of fiber-reinforced laminated composites and sandwiches. Compos. Struct. 23(4), 293–312 (1993)

    Article  Google Scholar 

  5. 5.

    Wu, C.P., Chiu, K.H., Wang, Y.M.: A review on the three-dimensional analytical approaches of multilayered and functionally graded piezoelectric plates and shells. Comput. Mater. Continua. 8(2), 93–132 (2008)

    Google Scholar 

  6. 6.

    Qatu, M.S., Asadi, E., Wang, W.: Review of recent literature on static analyses of composite shells: 2000–2010. Open J. Compos. Mater. 2(03), 61 (2012)

    Article  Google Scholar 

  7. 7.

    Benjeddou, A.: Advances in piezoelectric finite element modeling of adaptive structural elements: a survey. Comput. Struct. 76(1–3), 347–63 (2000)

    Article  Google Scholar 

  8. 8.

    Carrera, E.: Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking. Arch. Comput. Method E 10(3), 215–96 (2003)

    MathSciNet  Article  Google Scholar 

  9. 9.

    Liew, K.M., Zhao, X., Ferreira, A.J.: A review of meshless methods for laminated and functionally graded plates and shells. Compos. Struct. 93(8), 2031–41 (2011)

    Article  Google Scholar 

  10. 10.

    Wu, C.P., Liu, Y.C.: A review of semi-analytical numerical methods for laminated composite and multilayered functionally graded elastic/piezoelectric plates and shells. Compos. Struct. 147, 1–5 (2016)

    Article  Google Scholar 

  11. 11.

    Ren, J.G.: Exact solutions for laminated cylindrical shells in cylindrical bending. Compos. Sci. Technol. 29(3), 169–87 (1987)

    Article  Google Scholar 

  12. 12.

    Varadan, T.K., Bhaskar, K.: Bending of laminated orthotropic cylindrical shells—an elasticity approach. Compos. Struct. 17(2), 141–56 (1991)

    Article  Google Scholar 

  13. 13.

    Bhaskar, K., Varadan, T.K.: Exact elasticity solution for laminated anisotropic cylindrical shells. J. Appl. Mech. 60(1), 41–7 (1993)

    Article  Google Scholar 

  14. 14.

    Bhaskar, K., Varadan, T.K.: A benchmark elasticity solution for an axisymmetrically loaded angle-ply cylindrical shell. Compos. Eng. 3(11), 1065–73 (1993)

    Article  Google Scholar 

  15. 15.

    Hawkes, T.D., Soldatos, K.P.: Three-dimensional axisymmetric vibrations of orthotropic and cross-ply laminated hollow cylinders. AIAA J. 30(4), 1089–98 (1992)

    Article  Google Scholar 

  16. 16.

    Jiarang, F., Hongyu, S.: Exact solution for laminated continuous open cylindrical shells. Appl. Math. Mech. 18(11), 1073–86 (1997)

    Article  Google Scholar 

  17. 17.

    Chen, W.Q.: Free vibration analysis of laminated piezoceramic hollow spheres. J. Acoust. Soc. Am. 109(1), 41–50 (2001)

    Article  Google Scholar 

  18. 18.

    Chen, W.Q., Wang, Y.F., Cai, J.B., Ye, G.R.: Three-dimensional analysis of cross-ply laminated cylindrical panels with weak interfaces. Int. J. Solids Struct. 41(9–10), 2429–46 (2004)

    Article  Google Scholar 

  19. 19.

    Yan, W., Ying, J., Chen, W.Q.: The behavior of angle-ply laminated cylindrical shells with viscoelastic interfaces in cylindrical bending. Compos. Struct. 78(4), 551–9 (2007)

    Article  Google Scholar 

  20. 20.

    Lü, C.F., Lim, C.W., Xu, F.: Stress analysis of anisotropic thick laminates in cylindrical bending using a semi-analytical approach. J. Zhejiang Univ.-Sci. A 8(11), 1740–5 (2007)

    Article  Google Scholar 

  21. 21.

    Alibeigloo, A.: Static and vibration analysis of axi-symmetric angle-ply laminated cylindrical shell using state space differential quadrature method. Int. J. Pres. Ves. Pip. 86(11), 738–47 (2009)

    Article  Google Scholar 

  22. 22.

    Sheng, H.Y., Ye, J.Q.: A three-dimensional state space finite element solution for laminated composite cylindrical shells. Comput. Method Appl. M 192(22–24), 2441–59 (2003)

    Article  Google Scholar 

  23. 23.

    Kapuria, S., Kumari, P.: Multiterm extended Kantorovich method for three-dimensional elasticity solution of laminated plates. J. Appl. Mech. 79(6), 061018(1-9) (2012)

    Article  Google Scholar 

  24. 24.

    Kapuria, S., Kumari, P.: Extended Kantorovich method for coupled piezoelasticity solution of piezolaminated plates showing edge effects. Proc. R. Soc. A-Math. Phys. 469(2151), 20120565 (2013)

    MathSciNet  Article  Google Scholar 

  25. 25.

    Kumari, P., Susanta, B., Santosh, K.: Coupled three-dimensional piezoelasticity solution for edge effects in Levy-type rectangular piezolaminated plates using mixed field extended Kantorovich method. Compos. Struct. 140, 491–505 (2016)

    Article  Google Scholar 

  26. 26.

    Kumari, P., Singh, A., Rajapakse, R.K., Kapuria, S.: Three-dimensional static analysis of Levy-type functionally graded plate with in-plane stiffness variation. Compos. Struct. 168, 780–91 (2017)

    Article  Google Scholar 

  27. 27.

    Kumari, P., Kar, S.: Static behavior of arbitrarily supported composite laminated cylindrical shell panels: an analytical 3D elasticity approach. Compos. Struct. 207, 949–965 (2019)

    Article  Google Scholar 

  28. 28.

    Kumari, P., Kapuria, S., Rajapakse, R.K.: Three-dimensional extended Kantorovich solution for Levy-type rectangular laminated plates with edge effects. Compos. Struct. 107, 167–76 (2014)

    Article  Google Scholar 

  29. 29.

    Xu, K., Noor, A.K., Tang, Y.Y.: Three-dimensional solutions for coupled thermoelectroelastic response of multilayered plates. Comput. Method Appl. M 126(3–4), 355–71 (1995)

    Article  Google Scholar 

  30. 30.

    Dumir, P.C., Dube, G.P., Kapuria, S.: Exact piezoelastic solution of simply-supported orthotropic circular cylindrical panel in cylindrical bending. Int. J. Solids Struct. 34(6), 685–702 (1997)

    Article  Google Scholar 

  31. 31.

    ABAQUS/STANDARD. User’s manual. Version 6.9-1 (2009)

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Shranish Kar.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kar, S., Kumari, P. A 3D solution for angle-ply cylindrical shell panel supported arbitrarily on its boundaries using extended Kantorovich method. Int J Adv Eng Sci Appl Math (2020). https://doi.org/10.1007/s12572-020-00267-5

Download citation

Keywords

  • 3D analytical solution
  • Angle-ply shells
  • Arbitrary boundary conditions
  • Boundary effects
  • Multiterm extended Kantorovich method