Issue 48

Y. Khalfi et alii, Frattura ed Integrità Strutturale, 48 (2019) 208-221; DOI: 10.3221/IGF-ESIS.48.22 210 ( , ) ( , ) ( , )   b s w x y w x y w x y (1c) where u 0 and v 0 are the mid-plane displacements of the plate in the x and y direction, respectively; w b and w s are the bending and shear components of transverse displacement, respectively. Figure 1 : Coordinate system and geometry for rectangular composite plate on Pasternak elastic foundation. This displacement field verifies the nullity of traction boundary conditions on the top and bottom faces of the plate, and leads to a quadratic variation of transverse shear deformations (and therefore stresses) across the thickness. Thus, it is not necessary to use shear correction factors. The nonlinear deformation-displacement equations of Von Karman are as follows: 0 0 0 ( ) , ( ) b s x x x s x yz yz b s y y y y s xz yz b s xy xy xy xy k k z k f z k g z k k                                                                                         (2) where 2 2 2 0 0 2 2 1 , , 2                     b s b s b s x x x u w w w w k k x x x x x (3a) 2 2 2 0 0 2 2 1 , , 2                       b s b s b s y x x v w w w w k k y y y y y (3b) 0 0 0                               b s b s xy u v w w w w y x x x y y 2 2 2 2 2 , 2         b s b s xy xy w w k k y y (3c)   / sinh( ) , , ( ) cosh( / ) 1               s s s s yz xz h z z w w h f z y x h ( ) ( ) 1 ( ), ( ) f z g z f z f z z        (3d) The linear constitutive relations of a composite plate can be written as