Issue 50

H. Saidi et alii, Frattura ed Integrità Strutturale, 50 (2019) 286-299; DOI: 10.3221/IGF-ESIS.50.24 288 where the subscripts m and c denote the metallic and ceramic components, respectively; and p is the power law exponent. The value of k equal to zero indicates a fully ceramic plate, whereas infinite p represents a fully metallic plate. Since the influences of the variation of Poisson's ratio  on the behavior of FG plates are very small [37], it is supposed to be constant for convenience. is the factor of the distribution of the porosity according to the thickness of the plate [41]. K INEMATICS AND STRAINS n this investigation, further simplifying supposition are made to the conventional higher shear deformation theory (HSDT) so that the number of unknowns is reduced. The displacement field of the conventional HSDT is expressed by Saidi et al [40]. 0 0 ( , , , ) ( , , ) ( ) ( , , ) x w u x y z t u x y t z f z x y t x       (2a) 0 0 ( , , , ) ( , , ) ( ) ( , , ) y w v x y z t v x y t z f z x y t y       (2b) 0 ( , , , ) ( , , ) w x y z t w x y t  (2c) where the shape function ( ) f z is chosen according to Mahi et al [42]: 3 2 2 4 ( ) tanh 2 2 3cosh (1) z z h f z h h               (3) Clearly, the displacement field in Eq. (2) considers only four unknowns ( 0 u , 0 v , 0 w and  ). The nonzero strains associated with the displacement field in Eq. (2) are: 0 0 0 ( ) b s x x x x b s y y y y b s xy xy xy xy k k z k f z k k k                                                          , 0 0 ( ) yz yz xz xz g z                      (4) where 0 0 0 0 0 0 0 x y xy u x v x u v y x                                            , 2 0 2 2 0 2 2 0 2 b x b y b xy w x k w k y k w x y                                             , 2 2 2 2 2 2 s x s y s xy x k k y k x y                                                  , 0 0 yz xz y x                               (5a) and ( ) ( ) df z g z dz   (5b) I