Diff of /trunk/doc/user/heatedblock.tex

revision 1745 by lgraham, Thu Aug 14 03:35:46 2008 UTC revision 1746 by lgraham, Wed Sep 3 01:24:16 2008 UTC
# Line 75  $r$ and $q$ are each \RankOne. Line 75  $r$ and $q$ are each \RankOne.
75  We can easily identify the coefficients in~\eqn{LINEARPDE.SYSTEM.1 TUTORIAL}:  We can easily identify the coefficients in~\eqn{LINEARPDE.SYSTEM.1 TUTORIAL}:
76  \begin{eqnarray}\label{LINEARPDE ELASTIC COEFFICIENTS}  \begin{eqnarray}\label{LINEARPDE ELASTIC COEFFICIENTS}
77  A\hackscore{ijkl}=\lambda \delta\hackscore{ij} \delta\hackscore{kl} + \mu (  A\hackscore{ijkl}=\lambda \delta\hackscore{ij} \delta\hackscore{kl} + \mu (
78  +\delta\hackscore{ik} \delta\hackscore{jl}  \delta\hackscore{ik} \delta\hackscore{jl}
79  \delta\hackscore{il} \delta\hackscore{jk}) \\  + \delta\hackscore{il} \delta\hackscore{jk}) \\
80  X\hackscore{ij}=(\lambda+\frac{2}{3} \mu) \;  \alpha \; (T-T\hackscore{ref})\delta\hackscore{ij} \\  X\hackscore{ij}=(\lambda+\frac{2}{3} \mu) \;  \alpha \; (T-T\hackscore{ref})\delta\hackscore{ij} \\
81  \end{eqnarray}  \end{eqnarray}
82  The characteristic function $q$ defining the locations and components where constraints are set is given by:  The characteristic function $q$ defining the locations and components where constraints are set is given by:
# Line 104  The \LinearPDE class is notified of this Line 104  The \LinearPDE class is notified of this
104  After we have solved the Lame equation we want to analyse the actual stress distribution. Typically the von--Mises stress\index{von--Mises stress} defined by  After we have solved the Lame equation we want to analyse the actual stress distribution. Typically the von--Mises stress\index{von--Mises stress} defined by
105
106  \sigma\hackscore{mises} = \sqrt{  \sigma\hackscore{mises} = \sqrt{
107  \frac{1}{6} ((\sigma\hackscore{00}-\sigma\hackscore{11})^2+  \frac{1}{6} ((\sigma\hackscore{00}-\sigma\hackscore{11})^2
108                 (\sigma\hackscore{11}-\sigma\hackscore{22})^2              + (\sigma\hackscore{11}-\sigma\hackscore{22})^2
109                 (\sigma\hackscore{22}-\sigma\hackscore{00})^2)              + (\sigma\hackscore{22}-\sigma\hackscore{00})^2)
110  +  \sigma\hackscore{01}^2+\sigma\hackscore{12}^2+\sigma\hackscore{20}^2}  +  \sigma\hackscore{01}^2+\sigma\hackscore{12}^2+\sigma\hackscore{20}^2}
111
112  is used to detect material damage. Here we want to calculate the von--Mises and write the stress to a file for visualization.  is used to detect material damage. Here we want to calculate the von--Mises and write the stress to a file for visualization.

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