From: bangerth Date: Wed, 6 Sep 2006 01:49:41 +0000 (+0000) Subject: Add a few spaces to formulas where necessary X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=86d7c50260892891a5a00fdbf1dfa82b2471f410;p=dealii-svn.git Add a few spaces to formulas where necessary git-svn-id: https://svn.dealii.org/trunk@13837 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-18/doc/intro.dox b/deal.II/examples/step-18/doc/intro.dox index cfd60cad0d..8d44637c0b 100644 --- a/deal.II/examples/step-18/doc/intro.dox +++ b/deal.II/examples/step-18/doc/intro.dox @@ -78,7 +78,8 @@ much larger than $\tau$. In that case, the dynamic nature of the change is unimportant: we can consider the body to always be in static equilibrium, i.e. we can assume that at all times the body satisfies @f{eqnarray*} - - \textrm{div}\ ( C \varepsilon(\mathbf{u})) &=& \mathbf{f} + - \textrm{div}\ ( C \varepsilon(\mathbf{u})) &=& \mathbf{f}(\mathbf{x},t) + \qquad \textrm{in}\ \Omega, \\ \mathbf{u}(\mathbf{x},t) &=& \mathbf{d}(\mathbf{x},t) @@ -102,7 +103,8 @@ large deformations is a little more complicated. To do so, let us first introduce a tensorial stress variable $\sigma$, and write the differential equations in terms of the stress: @f{eqnarray*} - - \textrm{div}\ \sigma &=& \mathbf{f} + - \textrm{div}\ \sigma &=& \mathbf{f}(\mathbf{x},t) + \qquad \textrm{in}\ \Omega(t), \\ \mathbf{u}(\mathbf{x},t) &=& \mathbf{d}(\mathbf{x},t) @@ -147,6 +149,7 @@ This way, if we want to solve for the displacement increment, we have to solve the following system: @f{eqnarray*} - \textrm{div}\ C \varepsilon(\Delta\mathbf{u}^n) &=& \mathbf{f} + \textrm{div}\ \sigma^{n-1} + \qquad \textrm{in}\ \Omega(t_{n-1}), \\ \Delta \mathbf{u}^n(\mathbf{x},t) &=& \mathbf{d}(\mathbf{x},t_n) - \mathbf{d}(\mathbf{x},t_{n-1})