Page 209 - Mechanics Analysis Composite Materials
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194 Mechanics and analysis of composite materials
Taking 4 = 0 we can write rotation angle ozaround the z-axis of the global
coordinate frame, i.e.,
(4.147)
Consider now Eqs. (4.I%), (4.144), and (4.147) which form a set of four algebraic
equations with respect to the derivatives of displacement. Omitting the solution
procedure we can write the final output as
Substituting these expressions into Eqs. (4.141) we get
(4.148)
Thus obtained nonlinear equations, Eqs. (4.149, generalize Eqs. (4.69) for the case
of large strains, while Eqs. (4.148) allow us to find the fiber orientation angle after
the deformation.
Equilibrium equations, Eqs. (4.68), retain their form but should be written for the
deformed state, Le.,
(4.149)
where 4, a;, and ~ ' 1 ~are stresses referred to coordinate frame 1'2'' (see Fig. 4.60)
and to the current thickness of the ply.
Consider a problem of uniaxial tension of a *4 angle-ply layer with stress a,. For
this case, y,, = 0, w, = 0, and Eqs. (4.149, (4.146), and (4.148) acquire the form:
