From: wolf Date: Tue, 29 Jun 2004 13:13:01 +0000 (+0000) Subject: Fix paths to images -- they aren't visible otherwise. X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=12012254e3ac2e39744a740ccb3ca311ba157655;p=dealii-svn.git Fix paths to images -- they aren't visible otherwise. git-svn-id: https://svn.dealii.org/trunk@9480 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-8.data/intro.html b/deal.II/doc/tutorial/chapter-2.step-by-step/step-8.data/intro.html index ed5d996e85..d79d0fbaae 100644 --- a/deal.II/doc/tutorial/chapter-2.step-by-step/step-8.data/intro.html +++ b/deal.II/doc/tutorial/chapter-2.step-by-step/step-8.data/intro.html @@ -30,7 +30,7 @@ absolute value. The elastic equations are the following:
$\displaystyle - \partial_j (c_{ijkl} \partial_k u_l) = @@ -41,17 +41,17 @@ $

where the values $ c_{ijkl}$ are the stiffness coefficients and will usually depend on the space coordinates. In many cases, one knows that the material under consideration is isotropic, in which case by introduction of the two coefficients $ \lambda$ and $ \mu$ the coefficient tensor reduces to $ \varphi_{base(i)}(x)$ describes the space dependence of the shape function, which is taken to be the $ base(i)$-th shape function of the scalar element. Of course, while $ i$ is in the range $ 0,\ldots,N-1$, the functions $ comp(i)$ and $ base(i)$ have the ranges $ 0,1$ (in 2D) and $ 0,\ldots,n-1$, respectively. @@ -304,7 +304,7 @@ the following layout could be used by the library: --> \begin{multline*} \Phi_0(\vec x) = \begin{pmatrix} @@ -329,7 +329,7 @@ comp(0)=0, \quad comp(1)=1, \quad comp(2)=0, \quad comp(3)=1, \quad \ldots <DIV ALIGN= $\displaystyle comp(0)=0, \quad comp(1)=1, \quad comp(2)=0, \quad comp(3)=1, \quad \ldots $

@@ -342,7 +342,7 @@ base(0)=0, \quad base(1)=0, \quad base(2)=1, \quad base(3)=1, \quad \ldots
$\displaystyle base(0)=0, \quad base(1)=0, \quad base(2)=1, \quad base(3)=1, \quad \ldots $

@@ -354,10 +354,10 @@ In all but very rare cases, you will not need to know which shape function --> $ \varphi_{base(i)}$ of the scalar element belongs to a shape function $ \Phi_i$ of the vector element. Let us therefore define \begin{multline*} \sum_{i,j} u_i v_j @@ -504,24 +504,24 @@ f_l, </DIV> We note that here and in the following, the indices <IMG WIDTH= run over spatial directions, i.e. $ 0\le k,l < d$, and that indices $ i,j$ run over degrees of freedoms.

The local stiffness matrix on cell $ K$ therefore has the following entries: $ 0\le i,j < N$. In these formulas, we always take some component of the vector shape functions $ \Phi_i$, which are of course given as follows (see their definition): $ \delta_{nm}$. Due to this, we can delete some of the sums over $ k$ and $ l$:

@@ -610,11 +610,11 @@ the sums over $\displaystyle A^K_{ij}$ $\displaystyle = \sum_{k,l} \Bigl\{ \left( \lambda \partial_l \phi_i \delta_{l,comp(i)}, \partial_k \phi_j \delta_{k,comp(j)} \right)_K$     @@ -622,7 +622,7 @@ the sums over   $\displaystyle \qquad\qquad + \left( \mu \partial_l \phi_i \delta_{k,comp(i)}, ... ..._i \delta_{k,comp(i)}, \partial_k \phi_j \delta_{l,comp(j)} \right)_K \Bigr\}$ @@ -631,7 +631,7 @@ the sums over   $\displaystyle = \left( \lambda \partial_{comp(i)} \phi_i, \partial_{comp(j)} \p... ...j)} + \left( \mu \partial_{comp(j)} \phi_i, \partial_{comp(i)} \phi_j \right)_K$ @@ -640,7 +640,7 @@ the sums over   $\displaystyle = \left( \lambda \partial_{comp(i)} \phi_i, \partial_{comp(j)} \p... ...)} + \left( \mu \partial_{comp(j)} \phi_i, \partial_{comp(i)} \phi_j \right)_K.$ @@ -653,7 +653,7 @@ the sums over Likewise, the contribution of cell $ K$ to the right hand side vector is

@@ -661,11 +661,11 @@ Likewise, the contribution of cell $\displaystyle f^K_j$ $\displaystyle = \sum_l \left( f_l, (\Phi_j)_l \right)_K$     @@ -673,7 +673,7 @@ Likewise, the contribution of cell   $\displaystyle = \sum_l \left( f_l, \phi_j \delta_{l,comp(j)} \right)_K$     @@ -681,7 +681,7 @@ Likewise, the contribution of cell   $\displaystyle = \left( f_{comp(j)}, \phi_j \right)_K.$