In highperformance composite structures, structural components are manufactured mainly from unidirectional fibrereinforced plies, where the ply axes are identified in the principal coordinate system with numbers 1, 2 and 3. Whereas, the laminate axes are identified in the global coordinate system (Cartesian coordinates) with letters x, y and z (Jones, 1999 & Saarela, 1994). The 1axis and zaxis are combined into a single axis (Figure 8).
The Young’s moduli £i, E2, E3 and the shear moduli G12, G23, G13 of the unidirectional ply
determined from experimental tests will become E1, E2 , E3 , G12 , G23 , G13, respectively. In relation to this orientation and for a unidirectional fibrereinforced ply, the ecoefficiency factors related to the engineering constants for the linearelastic mechanical behaviour may be defined in the principal coordinate system as (Attaf, 2008):
E G’ E E
J = —L, J j with —L = – І – (i, j=1,2,3 and i^j) (9)
Ei Gij Vij Vji
where Ei, Ei are classical and sustainable Young’s moduli in idirection (i=1, 2 and 3),
Gij, Gij are classical and sustainable shear moduli in the ij plane (ij=23, 31 and 12),
Ji, Jij are the ecoefficiency factors of Young’s and shear moduli, respectively and, vij is the Poisson’s ratio for transverse strain in the jdirection when stressed in the i
direction. For this value, it is important to note that no attempt was made to investigate the sustainability of Poisson’s ratios. Their influence is beyond the scope of this analysis. According to these assumptions and generalized Hooke’s law, the strainstress ecorelations for an orthotropic material in the principal coordinate system (1,2,3) may be written in compact matrix form as:
6×6 (6 rows by 6 columns). The components Sij = Sji are defined as:
"r—^ II 
S12 = – V12/ 
E1 
S13 = ~V13I E1 
S14 
= 0 
S15 
= 0 
S16 
= 0 

S21 = – У21І 
E2 
S22 = 1E2 
S23 = – V2^l E2 
S24 
= 0 
S25 
= 0 
S26 
= 0 

S31 = – V31 / 
/E3 
S32 = – V321 
^3 
S33 = 1E3 
S34 
= 0 
S35 
= 0 
S36 
= 0 
S41 = 0 
S42 = 0 
S43 = 0 
S44 
=V G23 
S45 
= 0 
S46 
= 0 

Ul. • II 0 
S52 = 0 
О II CO . • LO 
S54 
= 0 
S55 
=V G13 
S56 
= 0 

S61 = 0 
S62 = 0 
О II CO . • 40 чл 
S64 
= 0 
S65 
= 0 
S66 
= V G1 
Also, the ecostiffness matrix of the ply may be obtained by the inverse of the ecocompliance matrix. Thus, we can write:
When using the ecostiffness matrix, the stressstrain relations can be obtained by the inverse of Equation (10). Thus, we obtain:
Since orthotropic fibres have almost the same characteristics along 2 and 3axis, the 23 plane is considered to be a plane of symmetry and the threedimensional 123coordinate system will be reduced to twodimensional 12coordinate system. Thus, Equation (12a) becomes:
where (M12 = {m m2 t12}T, {s}12 = {e1 s2 y12}T are the stress and strain vectors in 12
12
columns).
Using the transformation matrix, Equation (12b) may be written, after some rearrangements, in the global xycoordinate system as:
by 3 columns). The components Qij = Qji (i, j = 1, 2, 6) are functions of the fibre orientation
angle, 0 and the orthotropic elastic ecomoduli of the ply. By letting C=cos 0 and S=sin 0, the ecostiffness components are defined in the global xycoordinate system as:
Q16 = (Q11 – Q12 – 2 Q66 )SC3 + (Q12 – Q22 + 2 Q66 )S3C Q26 = (Q11 – Q12 – 2 Q66)S3C + (Q12 – Q22 + 2 Q66 )SC3 Q66 = (Q11 + Q22 2Q12 2Q66)S2C2 + Q66(S4 + C4)
With these ecological considerations, the constituent equations for laminated composite structures can be derived using the classical lamination theory (Jones, 1999).
1.6 Constitutive ecoequations of laminates
When the environment and health impacts besides quality are taken into consideration in the structural analysis, the constitutive relations for an unsymmetrically иlayered laminated composite plate (к=1,2,..и), and without transverse shear deformations can, after integration through each ply thickness and summation, be written in matrix form as:
(14a)
Or in compacted matrix form:
where N and M are the resultant inplane forces and bending/ torsional moments, respectively. Whereas, є0 and к are the asso ciated strains and curvatures.
The ecocomponents of the submatrices Ay (extensional ecostiffnesses), By (coupling ecostiffnesses) and Dy (bending ecostiffnesses) are expressed as:
bending ecostiffness matrix. Thus,
and Equation (14b) may be written as: