Issue 50

H. Saidi et alii, Frattura ed Integrità Strutturale, 50 (2019) 286-299; DOI: 10.3221/IGF-ESIS.50.24 291 Substituting Eq. (4) into Eq. (6) and the subsequent results into Eqs. (10), the stress resultants are obtained in terms of strains as following compact form: s b s b s s s s s N A B B M B D D k M B D H k                                   , s S A   , (16) in which   , , t x y xy N N N N  ,   , , t b b b b x y xy M M M M  ,   , , t s s s s x y xy M M M M  , (17a)   0 0 0 , , t x y xy      ,   , , t b b b b x y xy k k k k  ,   , , t s s s s x y xy k k k k  , (17b) 11 12 12 22 66 0 0 0 0 A A A A A A            , 11 12 12 22 66 0 0 0 0 B B B B B B            , 11 12 12 22 66 0 0 0 0 D D D D D D            , (17c) 11 12 12 22 66 0 0 0 0 s s s s s s B B B B B B              , 11 12 12 22 66 0 0 0 0 s s s s s s D D D D D D              , 11 12 12 22 66 0 0 0 0 s s s s s s H H H H H H              , (17d)   , t s s xz yz S S S  ,   0 0 , t xz yz     , 44 55 0 0 s s s A A A          , (17e) and stiffness components are given as:   11 11 11 11 11 11 /2 2 2 12 12 12 12 12 12 11 /2 66 66 66 66 66 66 1 1, , , ( ), ( ), ( ) 1 2 s s s h s s s h s s s A B D B D H A B D B D H C z z f z z f z f z dz A B D B D H                                  , (18a)     22 22 22 22 22 22 11 11 11 11 11 11 , , , , , , , , , , s s s s s s A B D B D H A B D B D H  , (18b)   /2 2 44 55 44 /2 ( ) , h s s h A A C g z dz     (18c) A NALYTICAL SOLUTION FOR SIMPLY - SUPPORTED FG PLATES ased on Navier technique, the following expansions of generalized displacements are considered to automatically respect the simply supported boundary conditions: B