高阶板壳理论中的 抛物拉伸和立方翘曲的 整体局部坐标转换
位移表达式为：file:///C:\Documents and Settings\Administrator\Application Data\Tencent\Users\549489120\QQ\WinTemp\RichOle\~DC_U]AOFL@NTZ34](GT]M6.jpg自由度是（K是复合材料层合板的层号，可以不用管）其中，Z 的二次和三次项的系数自由度物理意义是parabolic stretching(抛物拉伸）和cubic warping（立方翘曲）那么将坐标从局部转换成整体时，是如下这样吗？就是说将U1,U2,U3都看做x方向，V1,V2,V3都看做y方向来转换？
另外是不是将局部坐标系三个方向都取做跟整体坐标系平行，就不必再进行坐标转换了，因为除本身自由度外和其他自由度方向的夹角都为90度，余弦为零，转换矩阵为单位矩阵？谢谢！
file:///C:\Documents and Settings\Administrator\Application Data\Tencent\Users\549489120\QQ\WinTemp\RichOle\~DC_U]AOFL@NTZ34](GT]M6.jpg
pingnuaa 发表于 2012-7-14 16:56 static/image/common/back.gif
,当自由度只有u,v,w,和转角时，可以如图所示进行整体局部坐标转换。所以问题里有自由度很多时，
我猜想根据 ...
是不是把U1,U2,U3,都看做是和U0同向，V1,V2,V3看做和V0同向等等 进行转换？
=> You are right! But the you cannnot ignore W3 in your above equation. W3 maybe zero in local coodinate system but not in glocal coordinate.
把局部坐标设成和整体平行，根据以上的原理向整体刚度矩阵组长时是不是就可以不用进行转换了？
=> Yes There is not enough information for us to tell something. You might need to attach the paper you are reading.
Intuitively, z looks like the coordinate along the shell thickness direction. U1, U2, U3, V1, V2, V3, W1, W2 seem like the rotation. I just don't understand why you don't have W3. tonnyw 发表于 2012-7-13 10:34 static/image/common/back.gif
There is not enough information for us to tell something. You might need to attach the paper you are ...
我的主要问题就是：如果将局部坐标系三个方向都取做跟整体坐标系平行，无论多少自由度，和自由度什么意义都不必再进行坐标转换了？（因为除本身自由度外和其他自由度方向的夹角都为90度，余弦为零，转换矩阵为单位矩阵？） Do you understand Chinese? If not I will describe it in English. Thank you tonnyw 发表于 2012-7-13 10:34 static/image/common/back.gif
There is not enough information for us to tell something. You might need to attach the paper you are ...
版主只需要看第一个就可以，第二个应该是一个道理，但是更为复杂难懂，是复合材料方面的，如果有时间能帮忙看一下更好。感谢您的热情解答!Wish to be good friends！
I thought you meant shell element. Now I got what you mean.
Let us do it step-by-step way. Can you show me how you got the transformation matrix between the local and global coordinate? ,当自由度只有u,v,w,和转角时，可以如图所示进行整体局部坐标转换。所以问题里有自由度很多时，
我猜想根据这个公式
是不是把U1,U2,U3,都看做是和U0同向，V1,V2,V3看做和V0同向等等 进行转换？
以上是第一个问题
另外最主要的还是那个问题：把局部坐标设成和整体平行，根据以上的原理向整体刚度矩阵组长时是不是就可以不用进行转换了？
Many thanks!
tonnyw 发表于 2012-7-14 02:15 static/image/common/back.gif
I thought you meant shell element. Now I got what you mean.
Let us do it step-by-step way. Can you...
If you can tell me exactly whether it is right to think this way, I will be very appreciate it! My guess is that for plate usually it is flat. I would suggest you transform the global coordinates into the local coordinates instead of transforming the local dofs. into global ones. Like I said the first step is to define your local coordinate system which can be done as follows:
1. Calculate the unit vectors along the two edges sharing the same node;
2. Take the cross product of the two vectors and you will have the vector normal to plate;
3. Take the cross product between the normal vector and the unit vector along one edge. You will have the local orthogonal coordinate system.
Then you know the transformation matrix between the global coordinate system and the local one. Therefore, you can transform the global coordinate into local one.
BTW, I know Chinese well.
hillyuan 发表于 2012-7-15 13:28 static/image/common/back.gif
是不是把U1,U2,U3,都看做是和U0同向，V1,V2,V3看做和V0同向等等 进行转换？
=> You are right! But the y ...
非常感谢！但是还不明白Why W3 maybe zero in local coodinate system but not in glocal coordinate?此公式是在局部坐标系下的吧，那位什么整体坐标里还要有W3呢？
tonnyw 发表于 2012-7-15 12:40 static/image/common/back.gif
My guess is that for plate usually it is flat. I would suggest you transform the global coordinates...
终于遇到有限元高人解答，敢接涕零！ hillyuan 发表于 2012-7-15 13:28 static/image/common/back.gif
是不是把U1,U2,U3,都看做是和U0同向，V1,V2,V3看做和V0同向等等 进行转换？
=> You are right! But the y ...
终于遇到有限元高人解答，敢接涕零！ hillyuan 发表于 2012-7-15 13:28 static/image/common/back.gif
是不是把U1,U2,U3,都看做是和U0同向，V1,V2,V3看做和V0同向等等 进行转换？
=> You are right! But the y ...
非常感谢！但是还不明白Why W3 maybe zero in local coodinate system but not in glocal coordinate?
2012-7-15 15:37:33 上传下载附件 (19.96 KB)
此公式是在局部坐标系下的吧，那位什么整体坐标里还要有W3呢？
本帖最后由 hillyuan 于 2012-8-2 09:28 编辑
pingnuaa 发表于 2012-8-1 19:50 http://forum.simwe.com/static/image/common/back.gif
非常感谢！但是还不明白Why W3 maybe zero in local coodinate system but not in glocal coordinate?
...
一个指向于X轴的2维矢量，它在Y轴上的分量为零。当这坐标系旋转30度，它在新坐标系下的Y分量还为零吗？
hillyuan 发表于 2012-8-2 09:26 static/image/common/back.gif
一个指向于X轴的2维矢量，它在Y轴上的分量为零。当这坐标系旋转30度，它在新坐标系下的Y分量还为零吗？
...
可能您的研究方向不涉猎复合材料板壳理论吧？这里我说的高阶理论意思是将每一层的u,v,w在厚度方向z进行级数展开，即：
将其中的U0，U1。。。做为自由度，即，这些都是将u，v,w 展开的级数项而已，有的理论只将w写作w=w0，并没有w1,w2等 z 的二次三次项。将他们进行插值，即：。。。。。。 所以我的意思是，局部坐标系里没有w3, 整体坐标系里也没有w3。不知道我有没有表述清楚？
非常感谢您的耐心解答。如果您能抽空看下refined...那篇文章就更好了。。。万分感谢！祝笑口常开！
hillyuan 发表于 2012-8-2 09:26 static/image/common/back.gif
一个指向于X轴的2维矢量，它在Y轴上的分量为零。当这坐标系旋转30度，它在新坐标系下的Y分量还为零吗？
...
不只高人是否知晓啊？Thank you
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