Issue 41

M.F. Funari et alii, Frattura ed Integrità Strutturale, 41 (2017) 524-535; DOI: 10.3221/IGF-ESIS.41.63

0 T U W      

(1)

where T  is the virtual work of the inertial forces, U 

is the work of the internal forces and the tractions across the

interfaces and W  is the work of the external forces. According to the first-order transverse shear deformable laminate theory and multilayered approach, the variational form of the governing equations can be expressed by means of the following expressions:     1 2 0 1 2 l LN l l l l l l l l T U U dx, U U                 

 





1 0

l



L

L N

1



N 

l

i







0 

0 

i T dX ,   i

l l l    U N T M dx    l l l 



(2)





1

1

l

i





L

L

N 

N 

l

l

0 

0 

W f U h dX p U dx       

l

l l

l

l









1

1

l

l





where the subscripts l=1,..,N and i=1,..,N-1 indicate the numbering of the layers ( N ) and the interfaces ( N-1 ),   N,T ,M are the generalized stresses defined as a function of the classical extensional   A , bending   D , bending–extensional coupling   D and the shear stiffness   H variables,   i t n T T T   is the cohesive interfaces traction vector ,   i t n      is the cohesive interface displacement jump vector,  and 0  are the mass and polar mass per unit length of the layer and l f  and l p  ,with   1 2 0 l f f f   and   1 2 l p p p m   , are the per unit volume and area forces acting on the l -th layer, respectively.  , ,    with   1 1 U ,    2 U , ' '   '    ,x  represent the generalized strains, 

Figure 1 : Layered structure: geometry, interfaces and TSL

526