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Thermo-mechanical behavior of functionally graded circular sector plates

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Abstract

By reformulating the governing equations of the first-order theory into those describing the interior and edge-zone problems of the plate, closed-form solutions are presented for analysis of functionally graded circular sector plates with vertex angle \({\theta_0 \leq \pi /2}\) whose radial edges are simply supported and subjected to transverse loading and heat conduction through the plate thickness. Various types of clamped, simply supported, and free-edge boundary supports are considered on the circular edge of the plate. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. The effects of material property, boundary conditions, sector angle \({\theta_0}\), and boundary-layer phenomena on various response quantities in a circular sector plate are studied and discussed. Under a mechanical load, radial stress resultants in an FG circular sector plate with various clamped supports are zero, and consequently, their responses are seen to be identical. Simply supported FG circular sector plates which are immovable in radial direction do not show a neutral plane in bending, while in FG circular sector plates with other types of boundary supports this plane exists and its z-coordinate depends on the material constant. It is observed that the boundary-layer width is approximately equal to the plate thickness both in thermal and mechanical loadings with the boundary-layer effects being the strongest near a free edge.

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References

  1. Koizumi M.: The concept of FGM. Ceram. Trans. Funct. Gradient Mater. 34, 3–10 (1993)

    Google Scholar 

  2. Kobayashi H., Turvey G.J.: Elastic small deflection analysis of annular sector Mindlin plates. Int. J. Mech. Sci. 36, 811–827 (1994)

    Article  MATH  Google Scholar 

  3. Ambartsumyan, S.A.: Theory of anisotropic plates (translated from the Russian by T. Cheron). Technomic Publishing Co, Inc; (1970)

  4. Cheung M.S., Chan M.Y.T.: Static and dynamic analysis of thin and thick sectorial plates by the finite strip method. Comput. Struct. 14, 79–88 (1981)

    Article  Google Scholar 

  5. Liu F.L., Liew K.M.: Differential quadrature element method for static analysis of Reissner-Mindlin polar plates. Int. J. Solids Struct. 36, 5101–5123 (1999)

    Article  MATH  Google Scholar 

  6. Lim G.T., Wang C.M.: Bending of annular sectorial plates using Kirchhoff results. Eur. J. Mech. A/Solids 19, 1041–1057 (2000)

    Article  MATH  Google Scholar 

  7. Kim K., Yoo C.H.: Analytical solution to flexural responses of annular sector thin-plates. Thin-Walled Struct. 48, 879–887 (2010)

    Article  Google Scholar 

  8. Aghdam M.M., Mohammadi M., Erfanian V.: Bending analysis of thin annular sector plates using extended Kantorovich method. Thin-Walled Struct. 45, 983–990 (2007)

    Article  Google Scholar 

  9. Aghdam M.M., Shahmansouri M., Mohammadi M.: Extended Kantorovich method for static analysis of moderately thick functionally graded sector plates. Math. Comput. Simul. 86, 118–130 (2012)

    Article  MathSciNet  Google Scholar 

  10. Mousavi S.M., Tahani M.: Analytical solution for bending of moderately thick radially functionally graded sector plates with general boundary conditions using multi-term extended Kantorovich method. Compos. B Eng. 43, 1405–1416 (2012)

    Article  Google Scholar 

  11. Jomehzadeh E., Saidi A.R.: Atashipour SR, An analytical approach for stress analysis of functionally graded annular sector plates. Mater. Des. 30, 3679–3685 (2009)

    Article  Google Scholar 

  12. Saidi A.R., Hejripoor F., Jomehzadeh E.: On the stress singularities and boundary layer in moderately thick functionally graded sectorial plates. Appl. Math. Model. 34, 3478–3492 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. Huang C.S., McGee O.G., Leissa A.W.: Exact Analytical solutions for free vibration of thick sectorial plates with simply-supported radial edges. Int. J. Solids Struct. 31(11), 1609–1631 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  14. Huang C.S., Ho K.H.: An analytical solution for vibrations of a polarly orthotropic Mindlin sectorial plate with simply-supported radial edges. J. Sound Vib. 273, 277–294 (2004)

    Article  Google Scholar 

  15. Nie G.J., Zhong Z.: Vibration analysis of functionally graded annular sectorial plates with simply-supported radial edges. Compos. Struct. 84, 167–176 (2008)

    Article  Google Scholar 

  16. Hosseini-Hashemi Sh., Taher H.R.D., Akhavan H.: Vibration analysis of radially FGM sectorial plates of variable thickness on elastic foundations. Compos. Struct. 92, 1734–1743 (2010)

    Article  Google Scholar 

  17. Hosseini-Hashemi Sh., Akhavan H., Taher H.R.D., Daemi N., Alibeigloo A.: Differential quadrature analysis of functionally graded circular and annular sector plates on elastic foundations. Mater. Des. 31, 1871–1880 (2010)

    Article  Google Scholar 

  18. Tahouneh V., Yas M.H.: 3-D free vibration analysis of thick functionally graded annular sector plates on Pasternak elastic foundation via 2-D differential quadrature method. Acta Mech. 223, 1879–1897 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  19. Mindlin R.D.: Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates. J. Appl. Mech. 18, 31–38 (1951)

    MATH  Google Scholar 

  20. Reissner E.: The effect of transverse shear deformation on the bending of elastic plates. J. Appl. Mech. 12, 69–77 (1945)

    MathSciNet  Google Scholar 

  21. Reissner E.: On bending of elastic plates. Q. Appl. Math. 5, 55–68 (1947)

    MathSciNet  MATH  Google Scholar 

  22. Nosier A., Yavari A., Sarkani S.: Study of edge-zone equation of Mindlin-Reissner plate theory. J. Eng. Mech. 126, 647–651 (2000)

    Article  Google Scholar 

  23. Nosier A., Yavari A., Sarkani S.: On a boundary layer phenomenon in Mindlin-Reissner plate theory for laminated circular sector plates. Acta Mech. 151, 149–161 (2001)

    Article  MATH  Google Scholar 

  24. Nosier A., Fallah F.: Reformulation of Mindlin-Reissner governing equations of functionally graded circular plates. Acta Mech. 198, 209–233 (2008)

    Article  MATH  Google Scholar 

  25. Saidi R., Hasani Baferani A.: Thermal buckling analysis of moderately thick functionally graded annular sector plates. Compos. Struct. 92, 1744–1752 (2010)

    Article  Google Scholar 

  26. Reddy J.N., Chin C.D.: Thermo-mechanical analysis of functionally graded cylinders and plates. J. Therm. Stress. 21, 593–626 (1998)

    Article  Google Scholar 

  27. Fung Y.C., Tong P.: Classical and Computational Solid Mechanics. World Scientific, New Jersey (2001)

    Book  MATH  Google Scholar 

  28. Reddy J.N.: Theory and Analysis of Elastic Plates. Taylor & Francis, Philadelphia (1999)

    Google Scholar 

  29. Mansfield E.H.: The bending and stretching of plates. Cambridge University Press, Cambridge (1989)

    Book  MATH  Google Scholar 

  30. Huang C.S., McGee O.G., Leissa M.A.: Exact analytical solutions for free vibrations of thick sectorial plates with simply-supported radial edges. Int. J. Solids Struct. 31(11), 1609–1631 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  31. Huang C.S., Chang M.T.: Corner stress singularities in an FGM thin plate. Int. J. Solids Struct. 44, 2802–2819 (2007)

    Article  MATH  Google Scholar 

  32. Timoshenko S., Woinowsky S.K.: Theory of Plates and Shells. McGraw-Hill Inc, Boston (1959)

    Google Scholar 

  33. Abrate S.: Functionally graded plates behave like homogeneous plates. Compos. B Eng. 39, 151–158 (2008)

    Article  Google Scholar 

  34. Zhang D.G., Zhou Y.H.: A theoretical analysis of FGM thin plates based on physical neutral surface. Comput. Mater. Sci. 44(2), 716–720 (2008)

    Article  Google Scholar 

  35. Singha M.K., Prakash T., Ganapathi M.: Finite element analysis of functionally graded plates under transverse load. Finite Elem. Anal. Des. 47(4), 453–460 (2011)

    Article  Google Scholar 

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  1. Sharif University of Technology, Azadi Ave., P.O. Box 11365-9567, Tehran, Iran

    F. Fallah & A. Nosier

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  1. F. Fallah
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  2. A. Nosier
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Fallah, F., Nosier, A. Thermo-mechanical behavior of functionally graded circular sector plates. Acta Mech 226, 37–54 (2015). https://doi.org/10.1007/s00707-014-1140-2

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  • DOI: https://doi.org/10.1007/s00707-014-1140-2

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