Commit 9e029e5a authored by Turnhout, M.C. van's avatar Turnhout, M.C. van
Browse files

fix some typesetting

parent 89823b9d
......@@ -303,10 +303,10 @@ The output arguments \kwo{Me} and \kwo{Ce} are empty: these are not used, but th
The matrices $\mat{B}$ and $\mat{H}$ are calculated with:
\begin{align}
\mat{B} &= \begin{bmatrix} \pderiv{N_1}{x}& 0& \pderiv{N_2}{x} &0 & \dots & \pderiv{N_n}{x} &0 \\[1em]
0 & \pderiv{N_1}{y}& 0& \pderiv{N_2}{y} &0 & \dots & \pderiv{N_n}{y} \\[1em]
0 & \pderiv{N_1}{y}& 0& \pderiv{N_2}{y} & \dots &0 & \pderiv{N_n}{y} \\[1em]
\pderiv{N_1}{y}& \pderiv{N_1}{x}& \pderiv{N_2}{y}& \pderiv{N_2}{x} & \dots & \pderiv{N_n}{y}& \pderiv{N_n}{x}\\[1em] 0 & 0 & 0 & 0 & \dots & 0 & 0\end{bmatrix}\label{matb1}\quad \text{(plane strain, plane stress)}\\[1em]
\mat{B} &= \begin{bmatrix} \pderiv{N_1}{x}& 0& \pderiv{N_2}{x} &0 & \dots & \pderiv{N_n}{x} &0 \\[1em]
0 & \pderiv{N_1}{y}& 0& \pderiv{N_2}{y} &0 & \dots & \pderiv{N_n}{y} \\[1em]
0 & \pderiv{N_1}{y}& 0& \pderiv{N_2}{y} & \dots &0& \pderiv{N_n}{y} \\[1em]
\pderiv{N_1}{y}& \pderiv{N_1}{x}& \pderiv{N_2}{y}& \pderiv{N_2}{x} & \dots & \pderiv{N_n}{y}& \pderiv{N_n}{x}\\[1em] \frac{N_1}{x} & 0 & \frac{N_2}{x} & 0 & \dots & \frac{N_n}{x} & 0\end{bmatrix}\quad \text{(axi-symmetric)}\label{matb2}
\end{align}
and
......@@ -319,7 +319,6 @@ The matrices $\mat{B}$ and $\mat{H}$ are calculated with:
\begin{itemize}
\item the theory behind this element is described in chapter 18 of the book `Biomechanics: Concepts and Computation' \cite{Oomens2018}.
\item the plane strain and plane stress $\mat{H}$ matrices are the subject of exercise 18.1 in the book `Biomechanics: Concepts and Computation' \cite{Oomens2018}.
\item
\item each node has two degrees of freedom.
\item this element is used in \kwc{demo\_2ds\_axi\_cyl.m}, \kwc{demo\_2ds\_bar\_bending.m} and \\\kwc{demo\_2ds\_bar\_shear.m}.
\end{itemize}
......
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