tensor

 Dear Ravi

 Maybe you can refer to the wikipedia, http://en.wikipedia.org/wiki/Tensor

Help this will help you.

Weixu

Gosh, is it just me or is there really a mistake at the above Wiki page? Refer to the figure at the above page, and then to the description just below it.

The figure labels the stress components acting in reference to the face \vec{e_1} as: \sigma_{11}, \sigma_{12} and \sigma_{13}.

Therefore, the force acting on the face \vec{e_1} (i.e. \vec{T}^{\vec{e}_1}) should be given by the vector sum of the aforementiond three stresses, after multiplication by the infinitesimal area of the face \vec{e_1}.

In other words, after simplifying the notation,
T1 = s11 + s12 + s13 
T2 = s21 + s22 + s23
T3 = s31 + s32 + s33

As the above listing plainly shows, in order that the three traction vectors together represent the stress tensor, these traction vectors themselves should form a column matrix---not a row matrix as written by the Wiki author (refer to the first equality in the legend to the figure).

Here, I first thought that the Wiki author just forgot to add the transpose symbol on that matrix containing the T's. Ok.

But, next, the author also adds that "[stress tensor's] columns are the forces acting on the \vec{e_1}, \vec{e_2}, and \vec{e_3} faces of the cube." Here, for the reason given above, the statement should have read "rows" in place of "columns"

I am perplexed. ... If I am making a mistake, let me know.

--Ajit

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[E&OE]

Thanks Ajit. 

There are some problems in the wikipedia. Hope someone can contact the authors and correct the problems.

All the readers should be careful with wikipedia.  But I think the introduction of tensor is helpful for beginners.

There is a nice pdf on tensor, google search on tensor brings this up!

www.grc.nasa.gov/WWW/k-12/Numbers/.../Tensors_TM2002211716.pdf

Regards,

Sandip Haldar