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derivative of stress

Posted May 20, 2014, 12:02 a.m. EDT Structural Mechanics Version 4.3b 5 Replies

Huashun Wen
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Hi,

I have got the stress distribution of a structure, shown in attached Fig. 1. I want to calculate the derivative of stress along y, namely, d(solid.mises,y). But the results I got are zero, shown in Fig. 2. Is there any wrong? Thanks so much.

Huashun

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5 Replies Last Post May 21, 2014, 3:24 a.m. EDT
Henrik Sönnerlind COMSOL Employee

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Posted: 1 decade ago May 20, 2014, 2:08 a.m. EDT
Hi,

Try using d(solid.mises,Y) instead.

The Solid Mechanics interface is formulated on the material frame, so you need to take derivatives with respect to the material coordinates (X,Y,Z) rather than the spatial coordinates (x,y,z).

In addition, it is necessary that at least quadratic shape functions are used, since derivatives of stresses are second derivatives of displacements. Since the default is quadratic shape functions, this should not be a problem. As you are interested in the derivatives of stresses, it could however be a good idea to raise the shape function order to cubic.

Regards,
Henrik
Hi, Try using d(solid.mises,Y) instead. The Solid Mechanics interface is formulated on the material frame, so you need to take derivatives with respect to the material coordinates (X,Y,Z) rather than the spatial coordinates (x,y,z). In addition, it is necessary that at least quadratic shape functions are used, since derivatives of stresses are second derivatives of displacements. Since the default is quadratic shape functions, this should not be a problem. As you are interested in the derivatives of stresses, it could however be a good idea to raise the shape function order to cubic. Regards, Henrik
Huashun Wen
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Posted: 1 decade ago May 20, 2014, 2:39 a.m. EDT
Hi Henrik,

Thanks so much for your helpful answer. I tried d(solid.mises,Y), and it works. Now I got the stress gradient along y axis, shown in attached Fig.3.

I want ask it is possible to calculate summation of stress gradient of the whole surface? Tack.

Huashun
Hi Henrik, Thanks so much for your helpful answer. I tried d(solid.mises,Y), and it works. Now I got the stress gradient along y axis, shown in attached Fig.3. I want ask it is possible to calculate summation of stress gradient of the whole surface? Tack. Huashun

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Pieter Westerik
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Posted: 1 decade ago May 20, 2014, 10:58 a.m. EDT
In the 'Results' node, 'Derived Values' subnode, you can put a surface integral.
In the 'Results' node, 'Derived Values' subnode, you can put a surface integral.
Huashun Wen
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Posted: 1 decade ago May 20, 2014, 2:00 p.m. EDT
Hi Pieter,

Thanks for your answer. For my calculation, surface integral is different from summation. Because the units of summation and integral are N/m3, N/m, respectively. What I want to do is calculate summation of stress gradient for whole surface, in other word, add all individual values of stress gradient. Thanks.

Kind regards,

Huashun
Hi Pieter, Thanks for your answer. For my calculation, surface integral is different from summation. Because the units of summation and integral are N/m3, N/m, respectively. What I want to do is calculate summation of stress gradient for whole surface, in other word, add all individual values of stress gradient. Thanks. Kind regards, Huashun
Pieter Westerik
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Posted: 1 decade ago May 21, 2014, 3:24 a.m. EDT
You can integrate and then divide by the total surface area (or the other way around). Summation I do not know. What points would you choose for the summation?
You can integrate and then divide by the total surface area (or the other way around). Summation I do not know. What points would you choose for the summation?

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