关于六面体单元面中心应力的计算

woshimaidi

请教各位：
   本人在做有限元边界破坏方面的工作，即裂纹发生在六面体之间的公共面上。现在需要知道某一时刻该公共面中心的应力值。请问该应力值怎么计算才比较精确呢？
   注：六面体采用单点高斯积分进行计算的。
   现在有个思路是：通过高斯积分点的应力外推到节点应力，再通过面的四个节点应力进行平均得到面中心的应力值。 但是单点高斯应力怎么外推得到八个节点的应力呢？好像只有采用八点高斯积分才能外推得到八个节点的应力吧？

woshimaidi

怎么没人回复啊？

hillyuan

   sigma{gauss}= N*sigma(node)  => NT * sigma{gauss} = NT*N*sigma{node}  => sigma{node} = transverse[NT*N]*NT*sigma{gauss}

woshimaidi

hillyuan 发表于 2012-2-15 11:08
sigma{gauss}= N*sigma(node)  => NT * sigma{gauss} = NT*N*sigma{node}  => sigma{node} = transverse ...

这是八个高斯点外推八个节点的公式吧？

fanxiaochen

可以看一下 有限单元法(王勖成) 书中的第五章 中的分片应力磨平 或许有借鉴作用

hillyuan

woshimaidi 发表于 2012-2-15 15:44
这是八个高斯点外推八个节点的公式吧？

It is general form for any type of element

woshimaidi

hillyuan 发表于 2012-2-16 10:12
It is general form for any type of element

对于单个高斯积分点来说，NT*N是不可逆的。

caoer

gauss积分点的话，只有插值了。可以不通过节点。直接考虑高斯点插值到单元外侧面上。
方法是可行的，过程是艰辛的。
牵扯的细节太多，这个课题最好找导师多指导。

tonnyw

Why do you need to use reduced integration for Hex. element? Is it really necessary?

Since you only have one integration point for each element, extrapolation doesn't make sense.
How about calculating the stress at the four nodes directly? Then you can use linear interpolation to get the stress at the center of the surface. Since you know the [B] matrix and displacement {U}, it should be easy to get the stress and strain.

woshimaidi

tonnyw 发表于 2012-2-20 13:52
Why do you need to use reduced integration for Hex. element? Is it really necessary?

Since you only ...

Since the complete integration takes too much computational time, I choose the reduced integration.
As for your suggestion, it is an approach which I am considering, while the precision of the stress computed this way still remains to be proved. Thank you again for your help.

woshimaidi

caoer 发表于 2012-2-20 09:55
gauss积分点的话，只有插值了。可以不通过节点。直接考虑高斯点插值到单元外侧面上。
方法是可行的，过程是 ...

谢谢您的指导，这确实是一个方法，但是不知道在大变形情况下，该方法是否可行？

tonnyw

woshimaidi 发表于 2012-2-20 15:20
Since the complete integration takes too much computational time, I choose the reduced integration ...

Here is thing I don't understand. You want accuracy. But you are still using one Gauss integration point simply because you want to save the computational time. I thought you were trying to avoid some kind of locking. Eight-noded brick element is not computationally expensive.
I suggest you use mixed formulation for the large deformation analysis.

caoer

如果是大变形，问题就不是一般的复杂了。很可能最后结不了题。
lz慎重。