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Bending Analysis of Laminated Composite and Sandwich Cylindrical Shells Using Analytical Method and Ansys Calculations

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Mechanics of Composite Materials Aims and scope

The bending analysis of isotropic, laminated composite and cylindrical sandwich shells was carried out using a higher order shear deformation theory which incorporates undetermined integral in the displacement field. The model proposed involves only four variables. Moreover, unlike the conventional FSDTs, the shear correction factor is not necessary. The Hamilton’s principle and the Navier’s method are employed to determine and solve the equations of motion. The present analytical model was compared with other higher-order theories in the literature. In addition, finite element analysis methods were designed to calculate displacements and stresses of shells. Shells are subjected to uniform loads. Results are given for shallow and deep shells and thick to thin. According to the analysis, kinematics, based on the indeterminate integral component, are very effective and enable researchers to investigate laminated plates and shells more accurately than traditional models.

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References

  1. G. Kirchhoff, “Über das Gleichgewicht und die Bewegung einer elastischen Scheibe,” Crelles J., 1850, No. 40, 51-88 (1850).

    Article  Google Scholar 

  2. R. Mindlin, “Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates,” 18, No. 1, 31-38 (1951).

  3. K. M. Liew, X. Zhao, and A. J. Ferreira, “A review of meshless methods for laminated and functionally graded plates and shells,” Compos. Struct., 93, No. 8, 2031-2041 (2011).

    Article  Google Scholar 

  4. A. S. Sayyad and Y. M. Ghugal, “On the free vibration analysis of laminated composite and sandwich plates: a review of recent literature with some numerical results,” Compos. Struct., 129, 177-201 (2015).

    Article  Google Scholar 

  5. T. Kant, “A critical review and some results of recently developed refined theories of fiber-reinforced laminated composites and sandwiches,” Compos Struct., 23, No. 4, 293-312 (1993).

    Article  ADS  Google Scholar 

  6. E. Carrera, “Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking,” Archives of Computational Methods in Eng.., 10, No.3, 215-296 (2003).

    Article  MathSciNet  Google Scholar 

  7. S. S. Sahoo, C. K. Hirwani, S. K. Panda, and D. Sen, “Numerical analysis of vibration and transient behavior of laminated composite curved shallow shell structure, an experimental validation,” Scientia Iranica., 25, No. 4, 2218-2232 (2018).

    Google Scholar 

  8. S. S. Sahoo, S. K. Panda, and T. R. Mahapatra, “Static, free vibration and transient response of laminated composite curved shallow panel–an experimental approach,” Eur. J. Mech.-A/Solids., 59, 95-113 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  9. S. S. Sahoo, S. K. Panda, and V. K. Singh, “Experimental and numerical investigation of static and free vibration responses of woven glass/epoxy laminated composite plate,” Proc. of the Institution of Mech. Engineers, Part L: J. Mater.: Design and Applications., 231, No. 5, 463-478 (2017).

  10. J. N. Reddy and C. F. Liu, “A higher-order shear deformation theory of laminated elastic shells,” Int. J. Eng. Sci., 23, 319-330 (1985).

    Article  Google Scholar 

  11. S. M. R. Khalili, A. Davar, and K. M. Fard, “Free vibration analysis of homogeneous isotropic circular cylindrical shells based on a new three-dimensional refined higher-order theory,” Int. J. Mech. Sci., 56, 1-25 (2012).

    Article  Google Scholar 

  12. J. L. Mantari and C. G. Soares, “Analysis of isotropic and multilayered plates and shells by using a generalized higherorder shear deformation theory,” Compos. Struct., 94, No. 8, 2640-2656 (2012).

    Article  Google Scholar 

  13. J. L. Mantari and C. G. Soares, “Optimized sinusoidal higher order shear deformation theory for the analysis of functionally graded plates and shells,” Compos. Part B., 56, 126-136 (2014).

    Article  Google Scholar 

  14. E. Viola, F. Tornabene, and N. Fantuzzi, “Static analysis of completely doubly-curved laminated shells and panels using general higher-order shear deformation theories,” Compos. Struct., 101, 59-93 (2013).

    Article  Google Scholar 

  15. F. Tornabene and E. Viola, “Static analysis of functionally graded doubly-curved shells and panels of revolution,” Meccanica, 48, 901-930 (2013).

    Article  MathSciNet  Google Scholar 

  16. F. Tornabene, N. Fantuzzi, E. Viola, and E. Carrera, “Static analysis of doubly-curved anisotropic shells and panels using CUF approach, differential geometry and differential quadrature method,” Compos. Struct., 107, 675-697 (2014).

    Article  Google Scholar 

  17. F. Tornabene, N. Fantuzzi, and M. Bacciocchi, “On the mechanics of laminated doubly-curved shells subjected to point and line loads,” Int. J. Eng. Sci., 109, 115-164 (2016).

    Article  MathSciNet  Google Scholar 

  18. F. Tornabene, N. Fantuzzi, M. Bacciocchi, and J. N. Reddy, “A posteriori stress and strain recovery procedure for the static analysis of laminated shells resting on nonlinear elastic foundation,” Compos., Part B., 126, 162-191 (2017).

  19. T. Kant and K. Swaminathan, “Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory,” Compos. Struct., 56, No. 4, 329-344 (2002).

    Article  Google Scholar 

  20. J. L. Mantari, A. S. Oktem, and C. G. Soares, “A new higher order shear deformation theory for sandwich and composite laminated plates,” Compos., Part B, 43, No. 3, 1489-1499 (2012).

    Article  Google Scholar 

  21. K. Mehar, S. K. Panda, and B. K. Patle, “Thermoelastic vibration and flexural behavior of FG-CNT reinforced composite curved panel,” Int. J. Appl. Mech., 9, No. 4, 1750046 (2017).

  22. P. V. Katariya and S. K. Panda, “Thermal buckling and vibration analysis of laminated composite curved shell panel,” Aircraft Eng. and Aerospace Technol., 88, No. 1, 97-107 (2016).

    Article  Google Scholar 

  23. M. Nebab, S. Benguediab, H. A. Atmane, and F. Bernard, “A simple quasi-3D HDST for dynamic behavior of advanced composite plates with the effect of variables elastic foundations,” Geomech. and Eng., 22, No. 5, 415-431 (2020).

    Google Scholar 

  24. M. Amabili, “Nonlinear vibrations and stability of laminated shells using a modified first-order shear deformation theory,” Eur. J. Mech.-A/Solids., 68, 75-87 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  25. M. Amabili and J. N. Reddy, “A new non-linear higher-order shear deformation theory for large-amplitude vibrations of laminated doubly curved shells,” Int. J. Non-Linear Mech., 45, No. 4, 409-418 (2010).

    Article  ADS  Google Scholar 

  26. M. Amabili and J. N. Reddy, “Nonlinear mechanics of sandwich plates: Layerwise third-order thickness and shear deformation theory,” Compos. Struct., 278, 114693 (2021).

    Article  Google Scholar 

  27. M. Amabili and J. N. Reddy, “The nonlinear, third-order thickness and shear deformation theory for statics and dynamics of laminated composite shells,” Compos. Struct., 244, 112265 (2020).

    Article  Google Scholar 

  28. M. G. Rivera, J. N. Reddy, and M. Amabili, “A continuum eight‐parameter shell finite element for large deformation analysis,” Mech. Adv. Mater. and Struct., 27, No. 7, 551-560 (2020).

    Article  Google Scholar 

  29. M. Amabili, “A new third-order shear deformation theory with non-linearities in shear for static and dynamic analysis of laminated doubly curved shells,” Compos. Struct., 128, 260-273 (2015).

    Article  Google Scholar 

  30. M. Yaylaci, E. Öner, and A. Birinci, “Comparison between Analytical and ANSYS calculations for a receding contact problem,” J. Eng. Mech., 140, No. 9, 04014070 (2014).

  31. O. Allam, K. Draiche, A. A. Bousahla, F. Bourada, A. Tounsi, K. H. Benrahou, and A. Tounsi, “A generalized 4-unknown refined theory for bending and free vibration analysis of laminated composite and sandwich plates and shells,” Computers and Concrete, Int. J., 26, No. 2, 185-201 (2020).

    Google Scholar 

  32. N. Reddy, “A simple higher-order theory for laminated composite plates,” J. Appl. Mech., 51, No. 4, 745-752 (1984).

    Article  ADS  Google Scholar 

  33. R. D. Cook, D. S. Malkus, M. E. Plesha, and R. J. Witt, Concepts and Applications of Finite Element Analysis, Wiley, Singapore (2000).

    Google Scholar 

  34. ANSYS Release 19.2, help.

  35. B. S. Reddy, A. R. Reddy, J. S. Kumar, and K. V. K. Reddy, “Bending analysis of laminated composite plates using finite element method,” Int. J. Eng., Sci. and Technol., 4, No. 2, 177-190 (2012).

  36. E. Asadi, W. Wang, and M. S. Qatu, “Static and vibration analyses of thick deep laminated cylindrical shells using 3D and various shear deformation theories,” Compos. Struct., 94, No. 2, 494-500 (2012).

    Article  Google Scholar 

  37. F. Tornabene, A. Liverani, and G. Caligiana, “Static analysis of laminated composite curved shells and panels of revolution with a posteriori shear and normal stress recovery using generalized differential quadrature method,” Int. J. Mech. Sci., 61, No. 1, 71-87 (2012).

    Article  Google Scholar 

  38. A. S. Sayyad and Y. M. Ghugal, “Stress analysis of laminated composite and sandwich cylindrical shells using a generalized shell theory,” Compos. Mater. and Eng., 2, No. 2, 103-124 (2020).

    Google Scholar 

  39. N. J. Pagano, “Exact solutions for rectangular bidirectional composites and sandwich plates,” J. Compos. Mater., 4, No. 1, 20-34 (1970).

    Article  ADS  Google Scholar 

  40. A. S. Sayyad, and Y. M. Ghugal, “A new shear and normal deformation theory for isotropic, transversely isotropic, laminated composite and sandwich plates,” Int. J. Mech. Mater. Des., 10, No. 3, 247-267 (2014).

    Article  Google Scholar 

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Correspondence to A. A. Bousahla.

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Attia, A., Berrabah, A.T., Bourada, F. et al. Bending Analysis of Laminated Composite and Sandwich Cylindrical Shells Using Analytical Method and Ansys Calculations. Mech Compos Mater 60, 33–48 (2024). https://doi.org/10.1007/s11029-024-10173-7

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  • DOI: https://doi.org/10.1007/s11029-024-10173-7

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