Page 244 - Mechanics Analysis Composite Materials

Chapter 5. Mechanics of laminates 229

Substituting stresses in Eqs. (5.4) into these equations we arrive at constitutive
equations that link stress resultants and couples with the correspondinggeneralized
strains, i.e.,

These equations include membrane stiffness coefficients

-e
which specify the layer stiffness under in-plane deformation (Figs. 5.3a and b),
bending stiffness coefficients

which are associated with the layer bending and twisting (Figs. 5.3~and d), and
membrane-bending coupling coefficients

F
c,, = c,,,= 1A,,~&
-e
through which in-plane stress resultants are linked with bending deformations and
stress couples are linked with in-plane strains.
Coefficientswith subscripts 11, 12, 22, and 44compose the basic set of the layer
stiffnesses associated with in-plane extension, contraction, and shear (BII,Bl2, B22,
BM),bending and twisting (DII,012,022, OM),and coupling effects(CI~,C12, C22,
CM).For an anisotropic layer there exist also coupling between extension (a) and
shear (b) in Fig. 5.3 (coefficientsB14, B24), extension (a) and twisting (d) in Fig. 5.3
(coefficientsc14,Ct4), bending (c) and twisting (d) in Fig. 5.3 (coefficientsD14,D24).
Forces and moments N and M specified by Eqs. (5.5) are resultants and couples
of in-plane stresses a,, cy,and zXy(see Fig. 5.1). However, there exist also transverse
shear stresses z, and z, which should be expressed in terms of the corresponding
shear strains. Unfortunately, we cannot apply for this purpose the direct approach