Composite Laminates: How to reduce the flexural integrity

[kaizen.moto]

Dear all,

Iam trying to figure out how to reduce or simplified the flexural rigidity (D) of composite orthotropic laminates consists of many plies into a single layer isotropic model.

I know that for an isotropic case, D = Et^3/12(1-v^2).

However, for the case of, say, 3 plies orthotropic laminates:

Ply1 has D1x and D1y
Ply2 has D2x and D2y
Ply3 has D3x and D3y

My question is that how to reduce or transform the above D1x, D1y, D2x, D2y, D3x and D3y into a single D that behave as an isotropic model. In another word, I wanted to treat the orthotropic laminates into an isotropic case by using 'smear' method.

Any help is very much appreciated.

 

[Achy47]

Reducing the flexural rigidity (D) of composite orthotropic laminates into a single layer isotropic model can be achieved through the use of the Rule of Mixtures. This method involves calculating the effective properties of the composite laminate by taking weighted averages of the individual ply properties based on their volume fractions.

In the case of flexural rigidity, the effective value (Deff) can be calculated using the following equation:

Deff = Σ(ViDi) / ΣVi

Where Vi and Di represent the volume fraction and flexural rigidity of each individual ply, respectively. This equation assumes that the plies are perfectly bonded and have the same thickness.

In your case, for a 3-ply orthotropic laminate, the effective flexural rigidity can be calculated as follows:

Deff = (V1D1x + V2D2x + V3D3x) / (V1 + V2 + V3)

Similarly, the effective flexural rigidity in the y-direction can be calculated using the same equation, but with the corresponding ply properties.

This method of using the Rule of Mixtures can help in simplifying the flexural rigidity of composite orthotropic laminates into a single layer isotropic model. However, it is important to note that this approach is an approximation and may not accurately capture the behavior of the composite laminate under all loading conditions. Further analysis and testing may be required to validate the results.
I hope this helps. Best of luck with your research.