Talk:Stiffness matrix

Example

The "example" on this page is just a random matrix with no explanation at all. It should be explained with further diagrams, or deleted. Napalm Llama (talk) 15:48, 12 October 2009 (UTC)

article rewrite

I have rewritten this article to add more information and have a clearer exposition; the old version was a bit of a hodge-podge. Compsonheir (talk) 03:22, 13 August 2012 (UTC)

Could use a simpler example first

like the one with a linear arrangement of springs and masses used in Strang's Introduction to Applied Mathematics. 86.127.138.234 (talk) 03:19, 22 February 2015 (UTC)

Yes !!! The present article explains the maths of stiffness matrices to those who already have higher maths - it is not at all accessible to most Wikipedia readers with a good general education - please can someone re-write it.

Stiffness matrix for other problems

The equation should describe a relation between the solution variable $u$ and the right-hand side $f$. In the form after an edit made earlier,

$-\sum _{k,l}{\frac {\partial }{\partial x_{k}}}\left(a^{kl}{\frac {\partial u}{\partial x_{l}}}\right){\frac {\partial }{\partial x_{l}}}=f$

The left-hand side is a differential operator, while the right-hand side is a function. There is no way they can be equal to each other. Also, the original edit comment doesn't make sense. There is already a differential operator ${\frac {\partial }{\partial x_{l}}}$ in the ${\frac {\partial u}{\partial x_{l}}}$ part. There is no reason why $\partial x_{l}$ should appear twice. Therefore, I am reverting a previous edit to restore it to the correct form before that edit. -- 61.18.56.229 (talk) 09:47, 7 September 2021 (UTC)

Please also note that in the special case $a^{kl}=\delta _{kl}$, $-\sum _{k,l}{\frac {\partial }{\partial x_{k}}}\left(a^{kl}{\frac {\partial u}{\partial x_{l}}}\right)$ is simply $-\nabla ^{2}u$ in the first section of this article. -- 61.18.56.229 (talk) 09:54, 7 September 2021 (UTC)