Compute the stress rate at the blue point. This stress rate is expressed in terms of the laminar coordinate system.
The rate constitutive relation of the material is given by
The map between the notations for a composite beam are shown in Figure 14.
Since the problem is a 2-D one, based on the figure, the reduced constitutive equation is
The laminar -direction maps to the composite -direction and the laminar -directions maps to the composite -direction. Hence the constitutive equation can be written as
Rearranging,
Plugging in the values, we get
The Maple script for this calculation is shown below.
> #
> # Compute stress rate
> #
> # Set up the rate of deformation in Voigt notation
> #
> DLamVoigt := linalg[matrix](3,1,[Dlam[1,1],Dlam[2,2],Dlam[1,2]]);
> #
> # Set up stiffness matrix (Voigt notation)
> #
> CLamVoigt := linalg[matrix](3,3,[C33,C13,0,
>C13,C11,0,
>0,0,C44]);
> #
> # Compute stress rate (Voigt notation)
> #
> DDtSigLamVoigt := evalm(CLamVoigt&*DLamVoigt);