From 42811253b1b82d025d8550856aa0ae9fedf6ae3b Mon Sep 17 00:00:00 2001 From: bangerth Date: Sat, 23 Apr 2011 00:52:09 +0000 Subject: [PATCH] Add a note on the equations. git-svn-id: https://svn.dealii.org/trunk@23630 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-8/doc/intro.dox | 15 ++++++++++++++- 1 file changed, 14 insertions(+), 1 deletion(-) diff --git a/deal.II/examples/step-8/doc/intro.dox b/deal.II/examples/step-8/doc/intro.dox index 87d8a0c0cf..0e454a55d0 100644 --- a/deal.II/examples/step-8/doc/intro.dox +++ b/deal.II/examples/step-8/doc/intro.dox @@ -83,8 +83,21 @@ or also writing the first term a sum over components: \right)_\Omega. @f] +@note As written, the equations above are generally considered to be the right +description for the displacement of three-dimensional objects if the +displacement is small and we can assume that Hooke's law is valid. In +that case, the indices $i,j,k,l$ above all run over the set $\{1,2,3\}$ (or, +in the C++ source, over $\{0,1,2\}$). However, as is, the program runs in 2d, +and while the equations above also make mathematical sense in that case, they +would only describe a truly two-dimensional solid. In particular, they are not +the appropriate description of an $x-y$ cross-section of a body infinite in +the $z$ direction, as many other two-dimensional equations are. For a +description of such cases, see for example the wikipedia article on antiplane shear. -How do we now assemble the matrix for such an equation? A very long answer +But let's get back to the original problem. +How do we assemble the matrix for such an equation? A very long answer with a number of different alternatives is given in the documentation of the @ref vector_valued module. Historically, the solution shown below was the only one available in the early years of the library. It turns out to also be the -- 2.39.5