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Static analysis of functionally graded plate using nonlinear classical plate theory with von-Karman strains

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The present study is based on the nonlinear bending analysis of an FGM plate with Von-Karman strain based on the non-linear classical plate theory (NLCPT) with in-plane displacement and moderate rotation. Non-linear bending analysis based on stresses and transverse deflections is then carried out for the plate for the complex solution obtained using an analytical method viz. Navier’s method. The equations of motion and boundary conditions are obtained using the Principle of Minimum Potential Energy (PMPE) method and material property is graded in thickness direction according to simple power-law distribution in terms of volume fractions of the constituents. The effect of the span-to-thickness ratio and FGM exponent on the maximum central deflection and stresses are studied. The results show that the response is transitional with respect to ceramic and metal and the complex solution predicts the real behavior of stresses and deflections in the functionally graded plate. The functionally graded plate is found to be more effective for moderately thick and thick plates, which is inferred by a complex nature of the solution. For FGM plates, the transverse deflection is in-between to that of metal and ceramic rich plates. The complex nature of the solution also gives information about the stress distribution in the thickness direction.
Rocznik
Strony
707--726
Opis fizyczny
Bibliogr. 25 poz., rys., wykr.
Twórcy
autor
  • Mechanical and Industrial Engineering Department Indian Institute of Technology, Roorkee Roorkee, Uttarakhand-247667, INDIA
autor
  • Mechanical and Industrial Engineering Department Indian Institute of Technology, Roorkee Roorkee, Uttarakhand-247667, INDIA
Bibliografia
  • [1] Koizumi M. and Niino M. (1995): Overview of FGM research in Japan. – MRS Bulletin, vol.20, No.1, pp.19- 24.
  • [2] Mortensen A. and Suresh S. (1995): Functionally graded materials and metal-ceramic composites. – Part I: Processing, International Materials Reviews, vol.40, No.6, pp.239-265.
  • [3] Wang S.S. (1983): Fracture mechanics for delamination problems in composite materials. – Journal of Composite Materials, vol.17, No.3, pp.210-223.
  • [4] Niino M., Hirai T. and Watanabe R. (1987): The functionally gradient materials. – Journal of the Japan Society for Composite Materials, vol.13, pp.257-264.
  • [5] Report (1992) on: Fundamental study on relaxation of thermal stress for high temperature material by tailoring the graded structure. – Department of Science and Technology Agency.
  • [6] Marin L. (2005): Numerical solution of the Cauchy problem for steady-state heat transfer in two dimensional functionally graded materials. – International Journal of Solids Structures, vol.42, pp.4338-4351.
  • [7] Müller E., Drašar C., Schilz J. and Kaysser W.A. (2003): Functionally graded materials for sensor and energy applications. – Materials Science and Engineering: A, vol.362, pp.17-30.
  • [8] Niino M., Kisara K. and Mori M. (2005): Feasibility study of FGM technology in space solar power systems (SPSS). – Materials Science Forum, vol.492, pp.163–168.
  • [9] Levy S. (1942): Bending of rectangular plates with large deflections. – NACA Technology Note 846, pp.1–46.
  • [10] Kant T. and Swaminathan K. (2001): Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher order refined theory. – Composite Structures, vol.53, pp.73–85.
  • [11] Huang M., Ma X.Q., Sakiyama T., Matuda H. and Morita C. (2005): Free vibration analysis of orthotropic rectangular plates with variable thickness and general boundary conditions. – Journal of Sound and Vibration, vol.288, No.4–5, pp.931–955.
  • [12] Ke L.L. and Wang Y.S. (2011): Size effect on dynamic stability of functionally graded microbeams based on a modified couple stress theory. – Composite Structures, vol.93, No.2, pp.342–350.
  • [13] Thai H.T. and Choi D.H. (2013): Size-dependent functionally graded Kirchhoff and Mindlin plate models based on a modified couple stress theory. – Composite Structures, vol.95, pp.142–153.
  • [14] Thai H.T. and Kim S.E. (2013): A size-dependent functionally graded Reddy plate model based on a modified couple stress theory. – Composite Part B Engineering, vol.45, No.1, pp.1636–1645.
  • [15] Thai H.T. and T.P. Vo (2013): A size-dependent functionally graded sinusoidal plate model based on a modified couple stress theory. – Composite Structures, vol.96, pp.376–383.
  • [16] Thai H.T. and Vo T.P. (2013): A new sinusoidal shear deformation theory for bending, buckling, and vibration of functionally graded plates. – Applied Mathematical Modelling, vol.37, No.5, pp.3269–3281.
  • [17] Reddy B.S., Kumar J.S., Reddy C.E. and Kumar K.V. (2014): Static analysis of functionally graded plates using higher-order shear deformation theory- International Journal of Applied Science and Engineering vol. 17, no. April 2013, pp. 23–41.
  • [18] Kumar R. (2016): Meshless analysis of functionally graded plate with different algebraic shear deformation theories. – International Journal for Innovative Research in Science and Technology, vol.2, No.8, pp.106–111.
  • [19] Setoodeh A.R. and Shojaee M. (2016): Application of TW-DQ method to nonlinear free vibration analysis of FG carbon nanotube-reinforced composite quadrilateral plates. – Thin-Walled Structures, vol.108, pp.1–11.
  • [20] 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. (2011): Bending of FGM plates by a sinusoidal plate formulation and collocation with radial basis functions. – Mechanics Research Communications, vol.38, No.5, pp.368–371.
  • [21] 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. (2012): A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates. – Composite Structures, vol.94, No.5, pp.1814–1825.
  • [22] 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. (2012): A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates. – Composite Part B Engineering, vol.43, No.2, pp.711–725.
  • [23] 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. (2013): 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. – Composite Part B Engineering, vol.44, No.1, pp.657–674.
  • [24] Hassaine T., Tounsi A., Abbes E. and Bedia A. (2013): Analytical solution for bending analysis of functionally graded plates. – Scientia Iranian, vol.20, No.3, pp.516–523.
  • [25] Kulkarni K., Singh B.N. and Maiti D.K. (2015): Analytical solution for bending and buckling analysis of functionally graded plates using inverse trigonometric shear deformation theory. – Composite Structures, vol.134, pp.147–157.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-d60fb2f1-e6bb-438d-b4c9-c3e52837bf52
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