Thermal deformation due to temperature change

[Prof. R.L. Taylor]

It is necessary to make a mesh with all the geometry to use solid elements.  For thin structures you need several elements in thickness direction to model bending and then numerical issues may occur.

Why not modify the shell element as described before? That’s worked for me.

[Ishihara]

In Table 7.4 of the manual, the THERMAL command does not support SHELL ("-" mark), so I was wondering if it could be used.
Try it by adding "Norm(1:2) = Norm(1:2) - alp(1:2)*d(9)" and making it a shell element.
thank you.

[Prof. R.L. Taylor]

If you modify the shell element by adding the Norm(1:2) statement then you can use the THERmal command for the shell with the T_0 set to the change in temperature you want.   This only works for a uniform change over all the elements in the material set. 

[Ishihara]

I apologize for the delayed response. With the modification method you provided, I was able to analyze the displacement successfully. Thank you very much for your help.
 I have two additional questions. First, does the newly added 'norm(1:2)' refer to the norm of the variables x and y? If so, since I am considering a 3-dimensional hyperbolic surface, shouldn't it be considered with x, y, and z? Second, when applying a temperature change of -85, should I set T_0 in the THERMAL command to 85 instead of -85?

[Ishihara]

I apologize for the follow-up question. Regarding the command you provided, isn't the sign supposed to be positive (+) instead of negative (-)? When plotting the displacement, I expected a thermal contraction for a temperature change of -85 degrees, but it ended up showing thermal expansion instead.

[Prof. R.L. Taylor]

Yes,  you can generated a solid mesh using the BLOCk command

[Ishihara]

Perhaps this is a response to the question on page 1? I am sorry, but the question is on the second page and I would appreciate your response.

[Prof. R.L. Taylor]

yes, you willl used a  minus sign for contraction.

[Ishihara]

Thank you.
However, when I compared the numerical value with other analysis software, the value was different.
Sorry to trouble you, but I would appreciate it if you could tell me the meaning of each term in the added expression "Norm(1:2) = Norm(1:2) - alp(1:2)*d(9)".

[Prof. S. Govindjee]

I assume you are using the linear shell?

In which case norm( ) are the in-plane (membrane) forces per unit edge length == membrane stresses integrated through the thickness of the shell.
d(9) contains the temperature (change) you have specified on the material cards in your input file.  alp( ) contains the thermal expansion coefficients you have specified on the material cards.

Thus the term alp(1:2)*d(9) is giving you a thermal strain, which you will need to subtract from eps(1:2) which are the membrane strains.  If you have those correct, then I think stre3d( ) will properly compute norm(1:2) for you without further adjustment.

Directly subtrating alp(1:2)*d(9) from norm(1:2) seems incorrect unless you have modified alp(1:2) to account for the elastic properties and the shell thickness.

[Ishihara]

Yes, using linear shell elements.

Is the "norm" a force rather than a length?
Also, when subtracting thermal strain from eps(1:2), isn't the right side of the added equation "eps(1:2)-alph(1:2)*d(9)"?

[Prof. R.L. Taylor]

The "norm" variables are the membrane force/length, not stress.   The 'alp' is probably  mis-named as the routine dmat2d multiplies the thermal expansion by the module to produce the force/unit length dimension.

One way to check things is to perform a "patch test" problem to check that all the variables are correctly dimensioned and used.

[Ishihara]

Regarding the previous question, I think that the added formula represents the formula "ΔL = ε-αΔT (ΔL: amount of change in length)" for obtaining thermal deformation.

Therefore, the question was whether the part corresponding to ε in the added formula is not "norm(1:2)" but "eps(1:2)". In other words, "Norm(1:2) = eps(1:2) - alp(1:2)*d(9)".
I apologize if I misunderstood you.

Thank you. I will perform a patch test.

[Prof. R.L. Taylor]

the modification should read

!     Membrane forces
      norm(1) = (dd(1,1)*eps(1) + dd(1,2)*eps(2) + dd(1,4)*eps(3))*thk
      norm(2) = (dd(2,1)*eps(1) + dd(2,2)*eps(2) + dd(2,4)*eps(3))*thk
      norm(3) = (dd(4,1)*eps(1) + dd(4,2)*eps(2) + dd(4,4)*eps(3))*thk
!     Modify in-plane forces by constant temperature change
      norm(1:2) = norm(1:2) - alp(1:2)*d(9)

Looking at this, seems to suggest that there is a missint "thk" on the added term.  A patch test with a thickness not equal to unity (1) should reveal the possible error.

[Ishihara]

I would like to verify with a thickness of 0.5mm.

Does that mean that "*thk" should be added to the right side of the added term?