Skip to main content
SpringerLink
Log in

Isogeometric layerwise formulation for bending and free vibration analysis of laminated composite plates

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

This study proposes a new plate formulation based on a generalized layerwise theory in the isogeometric analysis (IGA) framework to investigate the bending and free vibration behavior of a laminated composite plate. All degrees of freedom in the isogeometric formulation are only associated with the displacements (i.e., rotation-free). In IGA, NURBS functions are used both to construct the geometry and to approximate the field variables. Merits of utilizing IGA include: the exact geometrical description, high accuracy and efficiancy, higher-order smoothness. The displacement-based layerwise theory assumes an individual displacement field expansion inside each layer, and the transverse displacement component is regarded to be \(C^{0}\)-continuous at the layer interfaces, thus yielding a more precise description of the stress states. The \(C^{0}\) continuity enforcement across the thickness in the present formulation is easily implemented by virtue of the knot insertion technique of IGA. The capability of the present isogeometric layerwise formulation in analyzing the static and dynamic responses is evidenced by conducting some numerical tests available in the open literature and comparing the computed outcomes with the reference data.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations.

References

  1. Liew, K.M., Pan, Z.Z., Zhang, L.W.: An overview of layerwise theories for composite laminates and structures: development, numerical implementation and application. Compos. Struct. 216, 240–259 (2001)

    Article  Google Scholar 

  2. Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd edn. CRC Press, Boca Raton (2004)

    MATH  Google Scholar 

  3. Khandan, R., Noroozi, S., Sewell, P., Vinney, J.: The development of laminated composite plate theories: a review. J. Mater. Sci. 47, 5901–5910 (2012)

    Article  Google Scholar 

  4. Liew, K.M.: Solving the vibration of thick symmetric laminates by Reissner/Mindlin plate theory and the p-Titz method. J. Sound Vib. 198, 343–360 (1996)

    Article  Google Scholar 

  5. Ferreira, A.J.M.: A formulation of the multiquadric radial basis function method for the analysis of laminated composite plates. Compos. Struct. 59, 385–392 (2003)

    Article  Google Scholar 

  6. Liew, K.M., Huang, Y.Q., Reddy, J.N.: Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method. Comput. Methods Appl. Mech. Eng. 192, 2203–2222 (2003)

    Article  Google Scholar 

  7. Ferreira, A.J.M., Castro, L.M.S., Bertoluzza, S.: A high order collocation method for the static and vibration analysis of composite plates using a first-order theory. Compos. Struct. 89, 424–432 (2009)

    Article  Google Scholar 

  8. Reddy, J.N.: Exact solutions of moderately thick laminated shells. J. Eng. Mech. 110, 794–809 (1984)

    Article  Google Scholar 

  9. Cho, K.N., Bert, C.W., Striz, A.G.: Free vibration of laminated rectangular plates analyzed by higher-order individual-layer theory. J. Sound Vib. 145, 429–442 (1991)

    Article  Google Scholar 

  10. Khdeir, A.A., Librescu, L.: Analysis of symmetric cross-ply laminated elastic plates using a higher-order theory. Part II. Buckling and free vibration. Compos. Struct. 9, 259–277 (1988)

    Article  Google Scholar 

  11. Ali, J.S.M., Bhaskar, K., Varadan, T.K.: A new theory for accurate thermal/mechanical flexural analysis of symmetric laminated plates. Compos. Struct. 45, 227–232 (1993)

    Article  Google Scholar 

  12. Wu, C.P., Chen, W.Y.: Vibration and stability of laminated plates based on a local higher-order plate theory. J. Sound Vib. 177, 503–520 (1994)

    Article  Google Scholar 

  13. Matsunaga, H.: Vibration and stability of cross-ply laminated composite plates according to a global higher-order plate theory. Compos. Struct. 48, 231–244 (2000)

    Article  Google Scholar 

  14. Jian, W.S., Nakatani, A., Kitagawa, H.: Vibration analysis of fully clamped arbitrarily laminated plate. Compos. Struct. 63, 115–122 (2004)

    Article  Google Scholar 

  15. Ferreira, A.J.M., Batra, R.C., Roque, C.M.C., Qian, L.F., Jorge, R.M.N.: Natural frequencies of functionally graded plates by a mesh-less method. Compos. Struct. 75, 593–600 (2006)

    Article  Google Scholar 

  16. Zhen, W., Wanji, C.: Free vibration of laminated composite and sandwich plates using global–local higher-order theory. J. Sound Vib. 298, 333–349 (2006)

    Article  Google Scholar 

  17. Xiang, S., Wang, K.M.: Free vibration analysis of symmetric laminated composite plates by trigonometric shear deformation theory and inverse multiquadric RBF. Thin Walled Struct. 47, 304–310 (2009)

    Article  Google Scholar 

  18. Adim, B., Daouadji, T.H., Rabahi, A.: A simple higher order shear deformation theory for mechanical behavior of laminated composite plates. Int. J. Adv. Struct. Eng. 8, 103–117 (2016)

    Article  Google Scholar 

  19. Nosier, A., Kapania, R.K., Reddy, J.N.: Free vibration analysis of laminated plates using a layerwise theory. AIAA J. 31, 2335–2346 (1993)

    Article  Google Scholar 

  20. Roque, C.M.C., Ferreira, A.J.M., Jorge, R.M.N.: Modelling of composite and sandwich plates by a trigonometric layerwise deformation theory and radial basis functions. Compos. Part B Eng. 36, 559–572 (2005)

    Article  Google Scholar 

  21. Shariyat, M.: Thermal buckling analysis of rectangular composite plates with temperature dependent properties based on layerwise theory. Thin Walled Struct. 45, 439–452 (2007)

    Article  Google Scholar 

  22. Cetkovic, M.: Thermo-mechanical bending of laminated composite and sandwich plates using layerwise displacement model. Compos. Struct. 125, 388–399 (2015)

    Article  Google Scholar 

  23. Rakocevic, M., Popopvic, S., Ivanisevic, N.: A computational method for laminated composite plates based on layerwise theory. Compos. Part B Eng. 122, 202–218 (2017)

    Article  Google Scholar 

  24. Hughes, T.J.R., Cottrell, J.A., Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Eng. 194, 4135–4195 (2005)

    Article  MathSciNet  Google Scholar 

  25. Liu, N., Jeffers, A.E.: A geometrically exact isogeometric Kirchhoff plate: feature-preserving automatic meshing and C1 rational triangular Bézier spline discretizations. Int. J. Numer. Methods Eng. 115, 395–409 (2018)

    Article  Google Scholar 

  26. Liu, N., Jeffers, A.E.: Feature-preserving rational Bézier triangles for isogeometric analysis of higher-order gradient damage models. Comput. Methods Appl. Mech. Eng. 357, 112585 (2019)

    Article  Google Scholar 

  27. Do, V.N.V., Jeon, J.T., Lee, C.H.: Dynamic analysis of carbon nanotube reinforced composite plates by using Bézier extraction based isogeometric finite element combined with higher-order shear deformation theory. Mech. Mater. 142, 103307 (2020)

    Article  Google Scholar 

  28. Liu, N., Jeffers, A.E.: Adaptive isogeometric analysis in structural frames using a layer-based discretization to model spread of plasticity. Comput. Struct. 196, 1–11 (2018)

    Article  Google Scholar 

  29. Kapoor, H., Kapania, R.K.: Geometrically nonlinear NURBS isogeometric finite element analysis of laminated composite plates. Compos. Struct. 94, 3434–3447 (2012)

    Article  Google Scholar 

  30. Nguyen, V.P., Nguyen-Xuan, H.: High-order b-splines based finite elements for delamination analysis of laminated composites. Compos. Struct. 102, 261–275 (2013)

    Article  Google Scholar 

  31. Guo, Y., Ruess, M., Gürdal, Z.: A contact extended isogeometric layerwise approach for the buckling analysis of delaminated composites. Compos. Struct. 116, 55–66 (2014)

    Article  Google Scholar 

  32. Guo, Y., Nagy, A.P., Gürdal, Z.: A layerwise theory for laminated composites in the framework of isogeometric analysis. Compos. Struct. 107, 447–457 (2014)

    Article  Google Scholar 

  33. Liu, N., Beata, P.A., Jeffers, A.E.: A mixed isogeometric analysis and control volume approach for heat transfer analysis of nonuniformly heated plates. Numer. Heat Transf. B Fundam. 75, 347–362 (2019)

    Article  Google Scholar 

  34. Liu, N., Ren, X., Lua, J.: An isogeometric continuum shell element for modeling the nonlinear response of functionally graded material structures. Compos. Struct. 237, 111893 (2020)

    Article  Google Scholar 

  35. Liu, N., Jeffers, A.E.: Isogeometric analysis of laminated composite and functionally graded sandwich plates based on a layerwise displacement theory. Compos. Struct. 176, 143–153 (2017)

    Article  Google Scholar 

  36. Sheikh, A.H., Topdar, P., Halder, S.: An appropriate FE model for through-thickness variation of displacement and potential in thin/moderately thick smart laminates. Compos. Struct. 51, 401–409 (2001)

    Article  Google Scholar 

  37. Pagano, N.J.: Exact solutions for rectangular bidirectional composites. J. Compos. Mater. 4, 20–34 (1970)

    Article  Google Scholar 

  38. Ferreira, A.J.M., Carrera, E., Cinefra, E.M., Viola, E., Tornabene, F., Fantuzzi, F.N., Zenkour, A.M.: Analysis of thick isotropic and cross-ply laminated plates by generalized differential quadrature method and a unified formulation. Compos. Part B Eng. 58, 544–552 (2014)

    Article  Google Scholar 

  39. Noor, A.K.: Stability of multilayered composite plates. Fibre Sci. Technol. 8, 81–89 (1975)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIT) (No. 2020R1F1A1075346).

Author information

Authors and Affiliations

  1. Applied Computational Civil and Structural Engineering Research Group, Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Vuong Nguyen Van Do

  2. Department of Civil and Environmental Engineering, Daelim University College, 29, Imgok-ro, Dongan-ku, Anyang-si, Gyeonggi-do, 13916, Republic of Korea

    Chin-Hyung Lee

Authors
  1. Vuong Nguyen Van Do
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chin-Hyung Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chin-Hyung Lee.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

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

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Van Do, V.N., Lee, CH. Isogeometric layerwise formulation for bending and free vibration analysis of laminated composite plates. Acta Mech 232, 1329–1351 (2021). https://doi.org/10.1007/s00707-020-02900-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-020-02900-7

Search

Navigation