Issue 50

K. Meftah et alii, Frattura ed Integrità Strutturale, 50 (2019) 276-285; DOI: 10.3221/IGF-ESIS.50.23 280 T T a a a D d d A D     (20) By substituting the expression of the plastic multiplier d  into Eq. (15), the elasto-plastic tangent modulus is derived as: T T a a a a ep D D D D A D    (21) The incremental stress-strain relationship is given as:   0 0 ep f f f s s s D d d d d D                          (22) For Mindlin plate, yield function F is assumed to be function of f  but not of the transverse shear stresses s  , the direct stresses associated with flexure only hence s D always remain elastic [1, 16, 17]. F INITE ELEMENT FORMULATION he Mindlin-Reissner theory takes the shear deformation into account by decoupling the rotation of the plate cross- section from the slope of the deformed mid-surface and the displacement field requires C 0 continuity only. Then the displacement fields (the transverse displacement w and two rotations  x ,  y ) are described by the same order of shape functions as follows:   1 0 0 0 0 0 0 i i n x i xi i y i yi w N w d N N                                       (23) The bending and shear strain-displacement relationships are given as: 1 . n f fi i i B d      ; 1 . n s si i i B d      (24) with 0 0 0 0 0 i i fi i i N x N B y N N y x                                ; 0 0 i i si i i N N x B N N y                (25) The tangential stiffness matrix can be written as follows:         T T T f ep f s s A K B D B B D B dA                (26) T