Thermal load on shells:

[Luciano Jacinto]

Dear NextFEM admin:
Thanks for your fast support in this forum.
According to NextFEM manual, the program supports uniform gradient on planar elements, but it’s not clear how to add it to the model.
Attached is a first tentative to add it on a beam modeled with shells but does not work. Can you help me?
The material is ‘C25/30’ (E = 31.476 GPa, alphaT = 10^-5) and the uniform temperature is DT = -25ºC.
The expected tension in the beam is then:
sxx = alphaT * DT * E = 1e-5 * 31.476e6 * 25 = 7869 kN/m2.
Thanks in advance.

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[NextFEM Admin]

Dear Luciano,
in shell elements, the uniform thermal distorsion by temperature is applied in both plane directions, hence you cannot expect such value – maybe a monodimensional element is more suitable in this case.

[Luciano Jacinto]

Many thanks for your help. Ok, it makes sense that for shell elements NextFEM applies uniform temperature gradient simultaneously in both local directions. Ok, in my example, a monodimensional element would be more suitable, but this was simply to test NextFEM regarding uniform temperature gradients in shells.

So, continuing with my test, I corrected the model freeing displacements in the z-direction, and, after the analysis, the model behaves as expected, except for stresses in x-direction. NextFEM gives sxx = 11805 kN/m2, but I expected sxx = 7869 kN/m2. I would expect a closer result.

Once more, many thanks for your fast response.

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[NextFEM Admin]

Hello,
you cannot expect the beam-like behaviour from thermal distorsion in shell elements – the stress is higher since the therma distorsion is applied in both directions and plane directions in shape functions of the shells are tied together, hence you’ll have an additional quota of restrained isotropic stress.

ps.
to same the model in the same folder where .py script is, you can use:
# Save the model, including analysis results
dir=os.path.abspath(os.path.dirname(__file__))
print(“Model saved in ” + dir + “\\” + model_name)
nf.saveModel(dir + “\\” + model_name)

# Call the app and open the file just created
nf.startDesigner(“\”” + dir + “\\” + model_name + “\””)

[Luciano Jacinto]

I understood your response. So, I run again the model with a zero Poisson coefficient (turning strains in both directions independent from each other) and got the same high result (sxx = 11805 kN/m2). So, the question seems a bit more complicated. I’m not an expert on FEM, but, perhaps it has to do with the shape functions, as you said. Thanks for your time spent on this.

[NextFEM Admin]

It is not a matter of Poisson’s ratio, it will only affects mixed terms of the Jacobian and shear modulus – it’s the same Young modulus valid for stresses in both direction.
To have a numerical proof of what I’m saying, please try releasing x boundary condition on node 2 – you’ll see in results the gradient with a lower sxx around node 2.

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