Analytical Solutions of the FG Thick Plates with In-Plane Stiffness Variation and Porous Substances Using Higher Order Shear Deformation Theory

Document Type: Research Paper

Authors

Department of Engineering, Colleg of Engineering, Fereydan Brabch , Islamic Azad University, Isfahan, Iran

Abstract

This paper presents the governing equations on the rectangular plate with the variation of material stiffness through their thick using higher order shear deformation theory (HSDT). The governing equations are obtained by using Hamilton's principle with regard to variation of Young's modulus in through their thick with regard sinusoidal variation of the displacement field across the thickness. In addition, the effects of the substances in FG-porous plate are investigated.                                  

Keywords


[1] Birman V., Byrd L.W., 2007, Modeling and analysis of functionally graded materials and structures, Applied Mechanics Reviews 60(5): 195-216.
[2] Jha D.K., Kant T., Singh R.K., 2013, A critical review of recent research on functionally graded plates, Composite Structures 96: 833-849.
[3] Cheng Z.Q., Batra R.C., 2000, Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates, Journal of Sound and Vibration 229(4): 879-895.
[4] Navazi H.M., Haddadpour H., Rasekh M., 2006, An analytical solution for nonlinear cylindrical bending of Functionally graded plates, Thin-Walled Structures 44(11): 1129-1137.
[5] Sun D., Luo S-N., 2011, Wave propagation and transient response of functionally graded material circularplates under a point impact load, Composites Part B: Engineering 42(4): 657-665.
[6] Zenkour A.M., 2012, Exact relationships between classical and sinusoidal theories for FGM plates, Mechanics of Advanced Materials and Structures 19(7): 551-567.
[7] Abrate S., 2008, Functionally graded plates behave like homogeneous plates, Composites Part B: Engineering 39(1): 151-158.
[8] Ghannadpour S.A.M., Alinia M.M., 2006, Large deflection behavior of functionally graded plates under pressure loads, Composite Structures 75(1-4): 67-71.
[9] Cheng Z.Q., Batra R.C., 2000, Deflection relationship between the homogenous Kirchhoff plate theory and different functionally graded plates theories, Archive of Applied Mechanics 52(1): 143-158.
[10] Menaa R., Tounsi A., Mouaici F., Mechab I., Zidi M., Bedia E.A.A., 2012, Analytical solutions for static shear correction factor of functionally graded rectangular beams, Mechanics of Advanced Materials and Structures 19(8): 641-652.
[11] Saidi A.R., Jomehzadeh E., 2009, On the analytical approach for the bending/stretching of linearly elastic functionally graded rectangular plates with two opposite edges simply supported, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 223(9): 2009-2016.
[12] Nosier A., Fallah F., 2009, Non-linear analysis of functionally graded circular plates under asymmetric transverse loading, International Journal of Non-Linear Mechanics 44(8): 928-942.
[13] Nguyen T-K., Sab K., Bonnet G., 2008, First-order shear deformation plate models for functionally graded materials, Composite Structures 83(1): 25-36.
[14] Liu M., Cheng Y., Liu J., 2015, High-order free vibration analysis of sandwich plates with both functionally graded face sheets and functionally graded flexibl core, Composites Part B: Engineering 72: 97-107.
[15] Reddy J., 2000, Analysis of functionally graded plates, International Journal for Numerical Methods in Engineering 47: 663-684.
[16] Hosseini-Hashemi S., Fadaee M., Atashipour S.R., 2011, Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed- form procedure, Composite Structures 93(2): 722-735.
[17] Qian L.F., Batra R.C., Chen L.M., 2004, Static and dynamic deformations of thick functionally graded elastic plates by using higher-order shear and normal deformable plate theory and meshless local Petrove Galerkin method, Composites Part B: Engineering 35(6-8): 685-697.
[18] Neves A.M.A., Ferreira A.J.M., Carrera E., Cinefra M., Roque C.M.C., Jorge R.M.N., 2013, Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation the ory and a meshless technique, Composites Part B: Engineering 44(1): 657-674.
[19] Wattanasakulpong N., Ungbhakor V., 2014, Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities, Aerospace Science and Technology 32: 111-120.
[20] Wattanasakulpong N., Prusty B.G., Kelly D.W., Hoffman M., 2012, Free vibration analysis of layered functionally graded beams with experimental validation, Materials & Design 36:182-190.
[21] Belabed Z., Houari M.S.A., Tounsi A., Mahmoud S.R., Anwar Beg O., 2014, An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates, Composites Part B: Engineering 60: 274-283.
[22] Mantari J.L., Guedes Soares C., 2013, Finite element formulation of a generalized higher order shear deformation theory for advanced composite plates, Composite Structures 96: 545-553.
[23] Amirpour M., Das R., Saavedra Flores E.I., 2016, Analytical solutions for elastic deformation of functionally Graded thick plates with in-plane stiffness variation using higher order shear deformation theory, Composites Part B: Engineering 94:109-121.
[24] Kim S-E., Thai H-T., Lee J., 2009, Buckling analysis of plates using the two variable refined plate theory, Thin-Walled Structures 47(4): 455-462.
[25] Thai H-T., Choi D-H., 2013, Analytical solutions of refined plate theory for bending, buckling and vibration analyses of thick plates, Applied Mathematical Modelling 37(18-19): 8310-8323.
[26] Tornabene F., 2009, Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution, Computer Methods in Applied Mechanics and Engineering 198(37-40): 2911-2935.