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A coupled integral–differential quadrature and B-spline-based multi-step technique for transient analysis of VSCL plates

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Abstract

Based on the three-dimensional theory of elasticity, the transient response of variable stiffness composite laminated (VSCL) plates with curvilinear fibers subjected to time-dependent concentrated load on elastic foundation is investigated. The fiber orientation angle varies linearly with respect to the in-plane coordinate in each layer. The layerwise theory in conjunction with a mixed integral–differential quadrature method is used to discretize the equations of motion and relevant boundary conditions in the spatial domain with arbitrary boundary conditions. Then, a novel multi-step method based on B-spline curves is presented to obtain a solution for the resulting system of ordinary differential equations in the temporal domain. Simplicity, accuracy and reliability of the novel combined I-DQ approach and in particular the multi-step techniques with respect to the Newmark time integration scheme are demonstrated. By performed comparison studies with available solutions in the open literature, the convergence and accuracy of the presented technique are demonstrated. Finally, the effects of fiber orientation, different geometric parameters, boundary conditions and elastic foundation coefficients on the transient behavior of the VSCL plates are parametrically studied. It is expected that the presented multi-step technique is to be used in a variety of science and engineering problems in future studies.

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References

  1. Leissa, A.W., Martin, A.F.: Vibration and buckling of rectangular composite plates with variable fiber spacing. Compos. Struct. 14, 339–357 (1990)

    Article  Google Scholar 

  2. Hyer, M.W., Charette, R.F.: Use of curvilinear fiber format in composite structure design. AIAA J. 29, 1011–1015 (1991)

    Article  Google Scholar 

  3. Curry, J.M., Johnson, E.R., Starnes, J.H.: Effect of dropped plies on the strength of graphite-epoxy laminates. AIAA J. 30, 449–456 (1992)

    Article  Google Scholar 

  4. Gürdal, Z., Olmedo, R.A.: In-plane response of laminates with spatially varying fiber orientations: variable stiffness panel concept. AIAA J. 31, 751–758 (1993)

    Article  MATH  Google Scholar 

  5. Parthasarathy, V.N., Kodiyalam, S., Davis, J.E.: Optimization of tow fiber paths for composite design. In: Proceedings of the 36th Structural Dynamics and Materials Conference. New Orleans, pp. 1031–1041 (1995)

  6. Abdallah, M.M., Setoodeh, S.H., Gurdal, Z.: Design of variable stiffness composite panels for maximum fundamental frequency using lamination parameters. Compos. Struct. 81, 283–291 (2007)

    Article  Google Scholar 

  7. Nik, M.A., Fayazbakhsh, K., Pasini, D., Lessard, L.: Variable stiffness composite panels: effects of stiffness variation on the in-plane and buckling response. Compos. Part A Appl. Sci. Manuf. 39, 911–922 (2008)

    Article  Google Scholar 

  8. Honda, S., Narita, Y., Sasaki, K.: Maximizing the fundamental frequency of laminated composite plates with optimally shaped curvilinear fibers. J. Syst. Des. Dyn. 3, 867–876 (2009)

    Google Scholar 

  9. Wu, Z., Weaver, P.M., Raju, G., Kim, B.C.: Buckling analysis and optimisation of variable angle tow composite plates. Thin Walled Struct. 60, 163–172 (2012)

    Article  Google Scholar 

  10. Raju, G., Wu, Z., Kim, B.C., Weaver, P.M.: Prebuckling and buckling analysis of variable angle tow plates with general boundary conditions. Compos. Struct. 94, 2961–2970 (2012)

    Article  Google Scholar 

  11. Houmat, A.: Nonlinear free vibration of laminated composite rectangular plates with curvilinear fibers. Compos. Struct. 106, 211–224 (2013)

    Article  Google Scholar 

  12. Liu, W., Butler, R.: Buckling optimization of variable-angle-tow panels using the infinite-strip method. AIAA J. 51, 1442–1449 (2013)

    Article  Google Scholar 

  13. Akbarzadeh, A.H., Arian Nik, M., Pasini, D.: The role of shear deformation in laminated plates with curvilinear fiber paths and embedded defects. Compos. Struct. 118, 217–227 (2014)

    Article  Google Scholar 

  14. Yazdani, S., Ribeiro, P., Rodrigues, J.D.: A p-version layerwise model for large deflection of composite plates with curvilinear fibres. Compos. Struct. 108, 181–190 (2014)

    Article  Google Scholar 

  15. Tornabene, F., Fantuzzi, N., Bacciocchi, M., Viola, E.: 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. Compos. Part B Eng. 81, 196–230 (2015)

    Article  Google Scholar 

  16. Venkatachari, A., Natarajan, S., Haboussi, M., Ganapathi, M.: Environmental effects on the free vibration of curvilinear fibre composite laminates with cutouts. Compos. Part B Eng. 88, 131–138 (2016)

    Article  Google Scholar 

  17. Tornabene, F., Fantuzzi, N., Bacciocchi, M.: Higher-order structural theories for the static analysis of doubly-curved laminated composite panels reinforced by curvilinear fibers. Thin Walled Struct. 102, 222–245 (2016)

    Article  Google Scholar 

  18. Heydarpour, Y., Aghdam, M.M.: A hybrid Bézier based multi-step method and differential quadrature for 3D transient response of variable stiffness composite plates. Compos. Struct. 154, 344–359 (2016)

    Article  Google Scholar 

  19. Lin, P.C.: Bending of cantilever rectangular plate with concentrated load. Appl. Math. Mech. 3, 281–291 (1982)

    Article  MATH  Google Scholar 

  20. Swanson, S.R.: Response of orthotropic sandwich plates to concentrated loading. J. Sandw. Struct. Mater. 2, 270–287 (2000)

    Article  Google Scholar 

  21. Şimşek, M., Kocatürk, T.: Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load. Compos. Struct. 90, 465–473 (2009)

    Article  Google Scholar 

  22. Abali, B.E., Völlmecke, C., Woodward, B., Kashtalyan, M., Guz, I., Müller, W.H.: Three-dimensional elastic deformation of functionally graded isotropic plates under point loading. Compos. Struct. 118, 367–376 (2014)

    Article  Google Scholar 

  23. Aghdam, M.M., Fallah, A., Haghi, P.: Nonlinear initial value ordinary differential equations. In: Dai, L., Jazar, R. N. (eds.) Nonlinear Approaches in Engineering Applications, pp. 117–136. Springer, Switzerland (2015)

  24. Zhang, J.Z., Ng, T.Y., Liew, K.M.: Three-dimensional theory of elasticity for free vibration analysis of composite laminates via layerwise differential quadrature modelling. Int. J. Numer. Methods Eng. 57, 1819–1844 (2003)

    Article  MATH  Google Scholar 

  25. Tornabene, F.: Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution. Comput. Methods Appl. Mech. Eng. 198, 2911–2935 (2009)

    Article  MATH  Google Scholar 

  26. Setoodeh, A.R., Tahani, M., Selahi, E.: Hybrid layerwise-differential quadrature transient dynamic analysis of functionally graded axisymmetric cylindrical shells subjected to dynamic pressure. Compos. Struct. 93, 2663–2670 (2011)

    Article  Google Scholar 

  27. Maleki, S., Tahani, M., Andakhshideh, A.: Transient response of laminated plates with arbitrary laminations and boundary conditions under general dynamic loadings. Arch. Appl. Mech. 82, 615–630 (2012)

    Article  MATH  Google Scholar 

  28. Heydarpour, Y., Malekzadeh, P., Golbahar Haghighi, M.R., Vaghefi, M.: Thermoelastic analysis of rotating laminated functionally graded cylindrical shells using layerwise differential quadrature method. Acta Mech. 223, 81–93 (2012)

    Article  MATH  Google Scholar 

  29. Heydarpour, Y., Aghdam, M.M., Malekzadeh, P.: Free vibration analysis of rotating functionally graded carbon nanotube-reinforced composite truncated conical shells. Compos. Struct. 117, 187–200 (2014)

    Article  MATH  Google Scholar 

  30. Lal, R., Saini, R.: On the use of GDQ for vibration characteristic of non-homogeneous orthotropic rectangular plates of bilinearly varying thickness. Acta Mech. 226, 1605–1620 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  31. Malekzadeh, P., Heydarpour, Y.: Mixed Navier-layerwise differential quadrature three-dimensional static and free vibration analysis of functionally graded carbon nanotube reinforced composite laminated plates. Meccanica 50, 143–167 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  32. Eftekhari, S.A.: A note on mathematical treatment of the Dirac-delta function in the differential quadrature bending and forced vibration analysis of beams and rectangular plates subjected to concentrated loads. Appl. Math. Model. 39, 6223–6242 (2015)

    Article  MathSciNet  Google Scholar 

  33. Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells Theory and Analysis. CRC Press, London (2004)

    MATH  Google Scholar 

  34. Piegl, L., Tiller, W.: The NURBS Book, 2nd edn. Springer, New York (1997)

    Book  MATH  Google Scholar 

  35. Vosoughi, A.R., Malekzadeh, P., Razi, H.: Response of moderately thick laminated composite plates on elastic foundation subjected to moving load. Compos. Struct. 97, 286–295 (2013)

    Article  Google Scholar 

  36. Naserian Nik, A.M., Tahani, M.: Analytical solutions for bending analysis of rectangular laminated plates with arbitrary lamination and boundary conditions. J. Mech. Sci. Technol. 23, 2253–2267 (2009)

    Article  Google Scholar 

  37. Khdeir, A.A., Reddy, J.N.: Exact solutions for the transient response of symmetric cross-ply laminates using a higher-order plate theory. Compos. Sci. Technol. 34, 205–224 (1989)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, School of Engineering, Persian Gulf University, Bushehr, 75168, Iran

    Y. Heydarpour

  2. Department of Mechanical Engineering, Amirkabir University of Technology, Hafez Ave., Tehran, 15875-4413, Iran

    M. M. Aghdam

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  1. Y. Heydarpour
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  2. M. M. Aghdam
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Correspondence to M. M. Aghdam.

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Heydarpour, Y., Aghdam, M.M. A coupled integral–differential quadrature and B-spline-based multi-step technique for transient analysis of VSCL plates. Acta Mech 228, 2965–2986 (2017). https://doi.org/10.1007/s00707-017-1850-3

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  • DOI: https://doi.org/10.1007/s00707-017-1850-3

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