On the simple and mixed first-order theories for functionally graded plates resting on elastic foundations

In this article, the bending response of a functionally graded plate resting on elastic foundations and subjected to a transverse mechanical load is investigated. An accurate solution for the functionally graded plate with simply supported edges resting on elastic foundations is presented. The interaction between the plate and the elastic foundations is considered and included in the equilibrium equations. Pasternak’s model is used to describe the two-parameter elastic foundations, and get a special case of Winkler’s model by considering one-parameter of elastic foundation. A relationship between the simple and mixed first-order transverse shear deformation theories is presented. Numerical results for deflections and stresses of functionally graded plates are investigated. Comparisons between the results of the simple and mixed first-order theories are made, and appropriate conclusion is formulated. Additional boundary conditions at the edges of the present plates are investigated.

[1]  A. Zenkour.  A state of stress and displacement of elastic plates using simple and mixed shear deformation theories , 2002 .

[2]  R. D. Mindlin,et al.  Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates , 1951 .

[3]  A. Zenkour.  Maupertuis-Lagrange mixed variational formula for laminated composite structures with a refined higher-order beam theory , 1997 .

[4]  Ashraf M. Zenkour,et al.  Hygro-thermo-mechanical effects on FGM plates resting on elastic foundations , 2010 .

[5]  Maria Kashtalyan,et al.  Three-dimensional elasticity solution for bending of functionally graded rectangular plates , 2004 .

[6]  S. Timoshenko,et al.  THEORY OF PLATES AND SHELLS , 1959 .

[7]  E. Reissner.  ON THE THEORY OF BENDING OF ELASTIC PLATES , 1944 .

[8]  Ashraf M. Zenkour,et al.  The refined sinusoidal theory for FGM plates on elastic foundations , 2009 .

[9]  A. Zenkour.  Buckling and free vibration of elastic plates using simple and mixed shear deformation theories , 2001 .

[10]  J. N. Reddy,et al.  Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates , 1998 .

[11]  Chien Ming Wang,et al.  Canonical exact solutions for Levy-plates on two-parameter foundation using Green's functions , 2000 .

[12]  H. R. Yerli,et al.  THE FIRST ORDER SHEAR DEFORMATION THEORY FOR SYMMETRICALLY LAMINATED COMPOSITE PLATES ON ELASTIC FOUNDATION , 2007 .

[13]  Ashraf M. Zenkour,et al.  MIXED VARIATIONAL FORMULA FOR THE THERMAL BENDING OF LAMINATED PLATES , 1999 .

[14]  S. Vel,et al.  Exact Solution for Thermoelastic Deformations of Functionally Graded Thick Rectangular Plates , 2002 .

[15]  Jamal A. Abdalla,et al.  Development of a discrete Reissner-Mindlin element on Winkler foundation , 2006 .

[16]  Ryszard Buczkowski,et al.  Finite element modelling of thick plates on two‐parameter elastic foundation , 2001 .

[17]  A. Zenkour,et al.  Bending of a fiber-reinforced viscoelastic composite plate resting on elastic foundations , 2011 .

[18]  A. Zenkour.  Exact mixed-classical solutions for the bending analysis of shear deformable rectangular plates , 2003 .

[19]  E. Reissner.  The effect of transverse shear deformation on the bending of elastic plates , 1945 .

[20]  M. Koizumi.  THE CONCEPT OF FGM , 1993 .

[21]  J. Reddy.  Analysis of functionally graded plates , 2000 .

[22]  A. Zenkour,et al.  Hamilton's mixed variational formula for dynamical problems of anisotropic elastic bodies , 1989 .