## Forum

### Calculation of stress in a composite Beam

1. I want to calculate stress on each ply of a composite beam.
It's a pipe with really thin thickness.
I want to compare my results with VABS.
Please can you give me some informations to run it.

2. Hello Salim,

Greetings.

By "I want to compare my results with VABS.", what model do your results come from?

Best Regards,

Fang

3. Hi Fang,

Sorry, I mean : I want to calculate Stress and Displacement at each ply using beam Theory and compare it with recovery Stress and displacement of VABS.

4. I guess I see.

First of all, please let me split the "beam theory" into 1D global theory and 2D cross-sectional theory. When I want to check the point-wise stress and strain, I do it using both of the 1D global theory and 2D cross-sectional theory by following the steps as:

1. Homogenize the cross section by 2D cross-sectional theory to obtain the beam sectional stiffness (4x4 or 6x6, depends on how slender the beam is). At this step, this theory gives me the beam sectional stiffness when I only have the material properties (Young's modulus and Poisson's ratio) as inputs.

2. Input the beam sectional stiffness into 1D global theory, apply BC and loads, solve the problem, obtain displacements and other results. Please note by "displacement", I mean the displacements of points on the 1D beam reference line.

3. Bring the displacement solution from 1D global theory back to 2D cross-sectional theory, solve the cross-sectional warping field, from which I will obtain the local material strain at each material point in each ply.

4. Calculate the local material stress using strain and Hooke's law.

To my knowledge, there are many 2D cross-sectional theories, among which VABS is a very good candidate.  Traditional cross-sectional integration method (which gives the so-called moment of inertia) is so limited in terms of accuracy, especially when we are dealing with anisotropic materials such as fiber-reinforced composites. And there are many other candidates ...

There are also many 1D global theories. The 1D beam elements are well developed in modern commercial FEA software such as ANSYS and Abaqus. Also, GEBT theory will provide very good displacement field of 1D beam reference line. And there are many other candidates...

After all, speaking of obtaining the local material stress and strain by "beam theory", I will always need a 1D global tool (GEBT, ANSYS, Abaqus, hand-calculation) and 2D cross-sectional tool (VABS, hand-estimation). But if I want to validate the fidelity of VABS, I would compare the stress and strain fields from the 3D FEA of the pipe with the stress and strain fields from using the combination of GEBT and VABS.

Hopefully this would help.

Best Regards,

Fang

5. Thank you for your response

But it's' or exactly what i want.

I want to do tue calculation by my Own way using beam theory to recover stress at each ply. And i don't know how to do this ?

I ´ve built models in abaqus shell 3D and beam and there are some difference.

"But if I want to validate the fidelity of VABS, I would compare the stress and strain fields from the 3D FEA of the pipe with the stress and strain fields from using the combination of GEBT and VABS." Why 3D FEA and not shell analysis or beam analysis please ?

6. Many other beam/shell theories are based on various ad hoc assumptions. Difference between them and VABS are expected. 3D elasticity is the original model (the true model), the results from a converged 3D FEA should be considered as exact numerical solution. Please see https://cdmhub.org/groups/yugroup/blog/2016/10/verification-and-validation-of-beamplateshellmultiscale-theories. ---- Emailed forum response from wenbinyu@purdue.edu
7. Hello Salim,

I agree with Dr. Yu's comment which explains the very reason that I would not validate a beam theory by another beam theory instead of the 3D FEA. A shell or plate model is also an approximation to the 3D FEA.

So far, frankly speaking, I think it is very hard to use analytical beam modeling that can provide me a stress field as a benchmark results to validate the numerical results of composite beams, especially when there are an amount of layers or when the beam sectional geometry is complex.

Attached please find a recently published article, I hope the validation work related to Fig. 22-23 for a composite tube could give some hints.

Best Regards,

Fang

8. Thanks you for all of your responses.
It makes lot of sense.
I Have runned an Analysis in Abaqus 3D (Pipe in 3 points bending analysis).
I have compared results of nodes in  the middle section (under the load ) and results are not the same.
Please can you take a look.
In attachment you will find gebt and vabs files.
I will send you abaqus file in the other message.
Thank you

9. here the abaqus CAE file

10. For the middle section, a beam theory cannot reproduce the correct 3D stress state as the concentrated load creates a singularity even if the theory is as advanced as VABS. However, slightly away from the middle section, we should be able to accurately recover the 3D stresses.