Skip to main content
SpringerLink
Log in

Static and Free Vibration Analysis of Functionally Graded Shells Using a Cell-Based Smoothed Discrete Shear Gap Method and Triangular Elements

  • Conference paper
  • First Online:
Proceedings of the International Conference on Advances in Computational Mechanics 2017 (ACOME 2017)

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

Included in the following conference series:

  • 1374 Accesses

Abstract

A cell-based smoothed discrete shear gap method (CS-DSG3) using three-node triangular element was recently proposed to improve the effectiveness of the discrete shear gap method (DSG3) for static and vibration analyses of isotropic Mindlin plates and shells. In this study, the CS-DSG3 is further extended for static and free vibration responses of functionally graded shells. In the present method, the first-order shear deformation theory is used in the formulation owing to the simplicity and computational efficiency. Several numerical examples are provided to validate high reliability of the CS-DSG3 in comparison with other numerical methods.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
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

Institutional subscriptions

References

  1. Loy C, Lam K, Reddy J (1999) Vibration of functionally graded cylindrical shells. Int J Mech Sci 41:309–324

    Article  MATH  Google Scholar 

  2. Pradhan S, Loy C, Lam K, Reddy J (2000) Vibration characteristics of functionally graded cylindrical shells under various boundary conditions. Appl Acoust 61:111–129

    Article  Google Scholar 

  3. Aghdam M, Bigdeli K, Shahmansouri N (2010) A semi-analytical solution for bending of moderately thick doubly curved functionally graded panels. Mech Adv Mater Struct 17:320–327

    Article  Google Scholar 

  4. Su Z, Jin G, Shi S, Ye T, Jia X (2014) A unified solution for vibration analysis of functionally graded cylindrical, conical shells and annular plates with general boundary conditions. Int J Mech Sci 80(3/2014):62–80

    Google Scholar 

  5. Zhao X, Lee YY, Liew KM (2009) Thermoelastic and vibration analysis of functionally graded cylindrical shells. Int J Mech Sci 51(9/2009):694–707

    Google Scholar 

  6. Oktem A, Mantari J, Soares CG (2012) Static response of functionally graded plates and doubly-curved shells based on a higher order shear deformation theory. Eur J Mech A Solids 36:163–172

    Article  MATH  Google Scholar 

  7. Liu B, Ferreira AJM, Xing YF, Neves AMA (2016) Analysis of functionally graded sandwich and laminated shells using a layerwise theory and a differential quadrature finite element method. Compos Struct 136(2016/02/01/2016):546–553

    Google Scholar 

  8. Liu G, Nguyen T (2010) Smoothed finite element methods. CRC Press, Taylor and Francis Group, NewYork

    Google Scholar 

  9. Liu G, Dai K, Nguyen T (2007) A smoothed finite element method for mechanics problems. Comput Mech 39:859–877

    Article  MATH  Google Scholar 

  10. Liu G, Nguyen T, Dai K, Lam K (2007) Theoretical aspects of the smoothed finite element method (SFEM). Int J Numer Methods Eng 71:902–930

    Article  MathSciNet  MATH  Google Scholar 

  11. Liu G, Nguyen-Xuan H, Nguyen-Thoi T (2010) A theoretical study on the smoothed FEM (S-FEM) models: Properties, accuracy and convergence rates. Int J Numer Methods Eng 84:1222–1256

    Article  MathSciNet  MATH  Google Scholar 

  12. Liu GR, Nguyen-Thoi T, Nguyen-Xuan H, Dai KY, Lam KY (2009) On the essence and the evaluation of the shape functions for the smoothed finite element method (SFEM). Int J Numer Methods Eng 77:1863–1869

    Article  MATH  Google Scholar 

  13. Nguyen T, Liu G, Dai K, Lam K (2007) Selective smoothed finite element method. Tsinghua Sci Technol 12:497–508

    Article  MathSciNet  Google Scholar 

  14. Liu GR, Nguyen-Thoi T, Nguyen-Xuan H, Lam KY (2009) A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems. Comput Struct 87(1/2009):14–26

    Google Scholar 

  15. Nguyen-Thoi T, Liu G, Nguyen-Xuan H (2009) Additional properties of the node-based smoothed finite element method (NS-FEM) for solid mechanics problems. Int J Comput Methods 6:633–666

    Article  MathSciNet  MATH  Google Scholar 

  16. Nguyen-Thoi T, Liu G, Nguyen-Xuan H, Nguyen-Tran C (2011) Adaptive analysis using the node-based smoothed finite element method (NS-FEM). Inte J Numer Methods Biomed Eng 27:198–218

    Article  MathSciNet  MATH  Google Scholar 

  17. Liu GR, Nguyen-Thoi T, Lam KY (2009) An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids. J Sound Vib 320(3/6/2009):1100–1130

    Google Scholar 

  18. Nguyen-Thoi T, Liu G, Nguyen-Xuan H (2011) An n-sided polygonal edge-based smoothed finite element method (nES-FEM) for solid mechanics. Inte J Numer Methods Biomed Eng 27:1446–1472

    MATH  Google Scholar 

  19. Nguyen-Thoi T, Liu G, Lam K, Zhang G (2009) A face-based smoothed finite element method (FS-FEM) for 3D linear and geometrically non-linear solid mechanics problems using 4-node tetrahedral elements. Int J Numer Methods Eng 78:324–353

    Article  MathSciNet  MATH  Google Scholar 

  20. Cui X, Liu G, Li G, Zhao X, Nguyen-Thoi T, Sun G (2008) A smoothed finite element method (SFEM) for linear and geometrically nonlinear analysis of plates and shells. Comput Model Eng Sci 28:109–125

    MathSciNet  MATH  Google Scholar 

  21. Nguyen-Thoi T, Phung-Van P, Luong-Van H, Nguyen-Van H, Nguyen-Xuan H (2012) A cell-based smoothed three-node Mindlin plate element (CS-MIN3) for static and free vibration analyses of plates. Comput Mech:1–17

    Google Scholar 

  22. Nguyen-Xuan H, Liu G, Thai-Hoang CA, Nguyen-Thoi T (2010) An edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates Comput Methods Appl Mech Eng 199:471–489

    Google Scholar 

  23. Nguyen-Thoi T, Phung-Van P, Thai-Hoang C, Nguyen-Xuan H (2013). A cell-based smoothed discrete shear gap method (CS-DSG3) using triangular elements for static and free vibration analyses of shell structures. Int J Mech Sci 74(9/2013):32–45

    Google Scholar 

  24. Bletzinger K-U, Bischoff M, Ramm E (2000) A unified approach for shear-locking-free triangular and rectangular shell finite elements. Comput Struct 75(4/2000):321–334

    Google Scholar 

  25. Nguyen-Thoi T, Bui-Xuan T, Phung-Van P, Nguyen-Xuan H, Ngo-Thanh P (2013) Static, free vibration and buckling analyses of stiffened plates by CS-FEM-DSG3 using triangular elements. Comput Struct 125:100–113

    Article  Google Scholar 

  26. Phung-Van P, Nguyen-Thoi T, Tran LV, Nguyen-Xuan H (2013) A cell-based smoothed discrete shear gap method (CS-DSG3) based on the C 0-type higher-order shear deformation theory for static and free vibration analyses of functionally graded plates. Comput Mater Sci 79:857–872

    Article  Google Scholar 

  27. Phung-Van P, Nguyen-Thoi T, Le-Dinh T, Nguyen-Xuan H (2013) Static and free vibration analyses and dynamic control of composite plates integrated with piezoelectric sensors and actuators by the cell-based smoothed discrete shear gap method (CS-FEM-DSG3). Smart Mater Struct 22:095026

    Article  Google Scholar 

  28. Phung-Van P, Nguyen-Thoi T, Luong-Van H, Thai-Hoang C, Nguyen-Xuan H (2014) A cell-based smoothed discrete shear gap method (CS-FEM-DSG3) using layerwise deformation theory for dynamic response of composite plates resting on viscoelastic foundation. Comput Methods Appl Mech Eng 272:138–159

    Article  MathSciNet  MATH  Google Scholar 

  29. Nguyen-Hoang S, Phung-Van P, Natarajan S, Kim H-G (2016) A combined scheme of edge-based and node-based smoothed finite element methods for Reissner–Mindlin flat shells. Eng Comput 32:267–284 (SCIE-Springer)

    Google Scholar 

  30. Nguyen-Thoi T, Phung-Van P, Nguyen-Xuan H, Thai-Hoang C (2012) A cell-based smoothed discrete shear gap method using triangular elements for static and free vibration analyses of Reissner-Mindlin plates. Int J Numer Methods Eng 91:705–741

    Article  MathSciNet  MATH  Google Scholar 

  31. Alijani F, Amabili M, Karagiozis K, Bakhtiari-Nejad F (2011) Nonlinear vibrations of functionally graded doubly curved shallow shells. J Sound Vib 330:1432–1454

    Article  Google Scholar 

  32. Matsunaga H (2008) Free vibration and stability of functionally graded shallow shells according to a 2D higher-order deformation theory. Compos Struct 84:132–146

    Article  Google Scholar 

  33. Chorfi S, Houmat A (2010) Non-linear free vibration of a functionally graded doubly-curved shallow shell of elliptical plan-form. Compos Struct 92:2573–2581

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tran Dai Nghia University, Ho Chi Minh City, Vietnam

    D. Le-Xuan & V. Tran-The

  2. Le Qui Don University, Hanoi, Vietnam

    H. Pham-Quoc

  3. Faculty of Mechanical Technology, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam

    N. Nguyen-Van

Authors
  1. D. Le-Xuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Pham-Quoc
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. Tran-The
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. N. Nguyen-Van
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Le-Xuan .

Editor information

Editors and Affiliations

  1. CIR Technology, Ho Chi Minh City University of Technology, Ho Chi Minh, Vietnam

    Hung Nguyen-Xuan

  2. Faculty of Engineering and Architecture, Ghent University, Ghent, Belgium

    Phuc Phung-Van

  3. Computational Mechanics, Bauhaus-University Weimar, Weimar, Germany

    Timon Rabczuk

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Le-Xuan, D., Pham-Quoc, H., Tran-The, V., Nguyen-Van, N. (2018). Static and Free Vibration Analysis of Functionally Graded Shells Using a Cell-Based Smoothed Discrete Shear Gap Method and Triangular Elements. In: Nguyen-Xuan, H., Phung-Van, P., Rabczuk, T. (eds) Proceedings of the International Conference on Advances in Computational Mechanics 2017. ACOME 2017. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-10-7149-2_26

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-7149-2_26

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-7148-5

  • Online ISBN: 978-981-10-7149-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation