Efficient Zigzag Theory for Static and Free Vibration Response of Rectangular FGM Panels

  • Authors

    • T. Das
    • J. K Nath
    2018-12-13
    https://doi.org/10.14419/ijet.v7i4.39.23817
  • Free vibration, Functionally graded material, FGM panel, Static analysis, Zigzag theory.

  • Abstract

    An efficient zigzag theory is presented for static and free vibration response of rectangular panels whose layers are made up of a number of functionally graded materials. In order to create a suitable FGM panel laminate, an analytical formulation is developed using an efficient zigzag theory. Different FGM layers have been stacked one over another and perfect interlaminar bonding is assumed between them. As far as manufacturing of such FGM panel is concerned, the technique of 3D printing can be utilized to create it through a single continuous operation. The resulting analytical model is used to identify critical locations and parameters that are responsible for material failure as well as material property variation across panel thickness to enhance productivity and quality of the designed panel. The technique will significantly reduce the time and computational cost involved with analysis of FGM materials and will provide a basis for finite element implementation.

     

     

  • References

    1. [1] Koizumi M., FGM Activities in Japan, Composites: Part B, vol. 28B, pp. 1–4, 1997.

      [2] Birman V., and Byrd L.W., Modelling and Analysis of Functionally Graded Materials and Structures, Appl. Mech. Rev., vol. 60, pp. 195–216, 2007.

      [3] Jha D.K., Kant T., and Singh R.K., A Critical Review of Recent Research on Functionally Graded Plates, Compos. Struct., vol. 96, pp. 833–49, 2013.

      [4] Swaminathan K., Naveenkumar D.T., Zenkour A.M., and Carrera E., Stress,Vibration and Buckling Analyses of FGM Plates-A State-of-The-Art Review, Compos. Struct., vol. 120, pp. 10–31, 2015.

      [5] Thai H., and Kim S., A Review of Theories for The Modeling and Analysis of Functionally Graded Plates and Shells, Compos. Struct., vol. 128, pp. 70—86, 2015.

      [6] Kashtalyan M., and Menshykova M., Three-Dimensional Elasticity Solution for Sandwich Panels With a Functionally Graded Core, Compos. Struct., vol. 87, pp. 36–43, 2009.

      [7] Li Q., Iu V.P., and Kou K.P., Three-Dimensional Vibration Analysis of Functionally Graded Material Sandwich Plates, J. Sound Vib., vol. 311, pp. 498–515, 2008.

      [8] Fantuzzi N., Brischetto S., Tornabene F., and Viola E., 2D and 3D Shell Models For The Free Vibration Investigation of Functionally Graded Cylindrical and Spherical Panels, Compos. Struct., vol. 154, pp. 573–590, 2016.

      [9] Wu C.P., and Li H.Y., The RMVT- and PVD-Based Finite Layer Methods For The Three-Dimensional Analysis of Multilayered Composite and FGM Plates, Compos. Struct., vol. 92, pp. 2476–2496, 2010a.

      [10] Nguyen T.K., Sab K., and Bonnet G., First-Order Shear Deformation Plate Models For Functionally Graded Materials, Compos. Struct., vol. 83, pp. 25–36, 2008.

      [11] Yang C., Jin G., Ye X., and Liu Z., A Modified Fourier-Ritz Solution For Vibration and Damping Analysis of Sandwich Plates With Viscoelastic and Functionally Graded Materials, Int. J. Mech. Sci., vol. 106, pp. 1–18, 2016.

      [12] Bernardo G.M.S., Damasio F.R., Silva T.A.N., and Loja M.A.R., A Study On The Structural Behaviour of FGM Plates Static and Free Vibrations Analyses, Compos. Struct., vol. 136, pp. 124–138, 2016.

      [13] Wu C.P., and Li H.Y., An RMVT-Based Third-Order Shear Deformation Theory of Multilayered Functionally Graded Material Plates, Compos. Struct., vol. 92, pp. 2591–2605, 2010b.

      [14] Zenkour A.M., A Comprehensive Analysis of Functionally Graded Sandwich Plates: Part 1-Deflection and Stresses, Int. J. Solids Struct., vol. 42, pp. 5224–5242, 2005a.

      [15] Zenkour A.M., A Comprehensive Analysis of Functionally Graded Sandwich Plates: Part 2-Buckling and Free Vibration, Int. J. Solids Struct., vol. 42, pp. 5243–5258, 2005b.

      [16] Mantari J.L., and Soares C. G., Five-Unknowns Generalized Hybrid-Type Quasi-3D HSDT For Advanced Composite Plates, Appl. Math. Model., vol. 39, pp. 5598–5615, 2015.

      [17] Mantari J.L., and Granados E.V., A Refined FSDT For The Static Analysis of Functionally Graded Sandwich Plates, Thin Wall. Struct., vol. 90, pp. 150–158, 2015a.

      [18] Zenkour A.M., Bending Analysis of Functionally Graded Sandwich Plates Using a Simple Four-Unknown Shear and Normal Deformations Theory, J. Sand. Struct. Mater., vol. 15, pp. 629–656, 2013.

      [19] Thai H.T., and Choi D.H., A Simple First-Order Shear Deformation Theory For The Bending and Free Vibration Analysis of Functionally Graded Plates, Compos. Struct., vol. 101, pp. 332–340, 2013.

      [20] Thai C.H., Kulasegaram S., Tran L.V., and Nguyen-Xuan H., Generalized Shear Deformation Theory For Functionally Graded Isotropic and Sandwich Plates Based on Isogeometric Approach, Comput. Struct., vol. 141, pp. 94–112, 2014a.

      [21] Bennoun M., Houari M.S.A., and Tounsi A., A Novel Five-Variable Refined Plate Theory For Vibration Analysis of Functionally Graded Sandwich Plates, Mech. Adv. Mater. Struct., vol. 23, pp. 423–431, 2016.

      [22] Nguyen V.H., Nguyen T.K., Thai H.T., and Vo T.P., A New Inverse Trigonometric Shear Deformation Theory For Isotropic and Functionally Graded Sandwich Plates, Composites: Part B, vol. 66, pp. 233–246, 2014.

      [23] Mahi A., Bedia E.A.A., and Tounsi A., A New Hyperbolic Shear Deformation Theory For Bending and Free Vibration Analysis of Isotropic, Functionally Graded, Sandwich and Laminated Composite Plates, Appl. Math. Model., vol. 39, pp. 2489–2508, 2015.

      [24] Liu M., Cheng Y., and Liu J., High-Order Free Vibration Analysis of Sandwich Plates With Both Functionally Graded Face Sheets and Functionally Graded Flexible Core, Composites: Part B, vol 72, pp. 97–107, 2015.

      [25] Carrera E., Brischetto S., Cinefra M., and Soave M., Refined and Advanced Models For Multilayered Plates and Shells Embedding Functionally Ggraded Material Layers, Mech. Adv. Mater. Struct., vol. 17, pp. 603–621,2010.

      [26] Neves A.M.A., Ferreira A.J.M., Carrera E., Cinefra M., Roque C.M.C., Jorge R.M.N., and Soares C.M.M., A Quasi-3D Hyperbolic Shear Deformation Theory For The Static and Free Vibration Analysis of Functionally Graded Plates, Compos. Struct., vol. 94, pp. 1814–1825, 2012a.

      [27] Neves A.M.A., Ferreira A.J.M., Carrera E., Roque C.M.C., Cinefra M., Jorge R.M.N., and Soares C.M.M., A Quasi-3D Sinusoidal Shear Deformation Theory For The Static and Free Vibration Analysis of Functionally Graded Plates, Composites: Part B, vol. 43, pp. 711–725, 2012b.

      [28] Neves A.M.A., Ferreira A.J.M., Carrera E., Cinefra M., Roque C.M.C., Jorge R.M.N., and Soares C.M.M., Static, Free Vibration and Buckling Analysis of Isotropic and Sandwich Functionally Graded Plates Using a Quasi-3D Higher-Order Shear Deformation Theory and a Meshless Technique, Composites: Part B, vol. 44, pp. 657–674, 2013.

      [29] Alipour M.M., and Shariyat M., An Elasticity-Equilibrium-Based Zigzag Theory For Axisymmetric Bending and Stress Analysis of The Functionally Graded Circular Sandwich Plates, Using a Maclaurin-Type Series Solution, Eur. J. Mech. A/Solids, vol. 34, pp. 78–101, 2012.

      [30] Alipour M.M., and Shariyat M., Analytical Zigzag-Elasticity Transient and Forced Dynamic Stress and Displacement Response Prediction of The Annular FGM Sandwich Plates, Compos. Struct., vol. 106, pp. 426–445, 2013.

      [31] Voigt W., Uber die beziehung zwischen den beiden elastizit¨atskonstanten isotroper k¨orper. Wied Ann Phys 1889; 38: 573—87.

      [32] Kapuria S., Patni M., and Yasin M.Y., A quadrilateral shallow shell element based on the third-order theory for functionally graded plates and shells and the inaccuracy of rule of mixtures, Eur. J. Mech. A/Solids 49 (2015) 268–282.

      [33] Reddy J.N., Cheng Z.Q., Three-dimensional thermomechanical deformations of functionally graded rectangular plates, Eur. J. Mech. A/Solids 20 (2001) 841–855.

  • Downloads

  • How to Cite

    Das, T., & K Nath, J. (2018). Efficient Zigzag Theory for Static and Free Vibration Response of Rectangular FGM Panels. International Journal of Engineering & Technology, 7(4.39), 94-104. https://doi.org/10.14419/ijet.v7i4.39.23817

    Received date: 2018-12-12

    Accepted date: 2018-12-12

    Published date: 2018-12-13