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Theorie Abbildung Kräftegleichgewicht erweitert

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Daniel Weschke
2015-06-20 19:16:44 +02:00
parent 007315c9e7
commit 7ad288e21a
2 changed files with 75 additions and 12 deletions
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19
Preamble/Main.tex
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@@ -734,6 +734,25 @@
small dot/.style={fill=black,circle,scale=0.3},
}
\tikzset{
double -latex/.style args={#1 colored by #2 and #3}{
-latex,line width=#1,#2,
postaction={draw,-latex,#3,line width=(#1)/3,shorten <=(#1)/4,shorten >=4.5*(#1)/3},
},
double round cap-latex/.style args={#1 colored by #2 and #3}{
round cap-latex,line width=#1,#2,
postaction={draw,round cap-latex,#3,line width=(#1)/3,shorten <=(#1)/4,shorten >=4.5*(#1)/3},
},
double round cap-stealth/.style args={#1 colored by #2 and #3}{
round cap-stealth,line width=#1,#2,
postaction={round cap-stealth,draw,,#3,line width=(#1)/3,shorten <=(#1)/3,shorten >=2*(#1)/3},
},
double -stealth/.style args={#1 colored by #2 and #3}{
-stealth,line width=#1,#2,
postaction={-stealth,draw,,#3,line width=(#1)/3,shorten <=(#1)/3,shorten >=2*(#1)/3},
},
}
\newcommand{\FB}[7]{%
\begin{tikzpicture}[auto, node distance=2cm,>=latex']

68
sections/Theorie.tex
View File

@@ -85,7 +85,7 @@ Zur näherungsweisen Verarbeitung der Differentialgleichung wird hier das Variat
%
\begin{figure}[H]\centering
\begin{tikzpicture}[scale=2.7]
\begin{tikzpicture}[scale=2.5]
{
\fill[color=black!5] (0,0,1) -- (1,0,1) -- (1,1,1) -- (0,1,1) -- cycle;
\fill[color=black!15] (0,1,1) -- (1,1,1) -- (1,1,0) -- (0,1,0) -- cycle;
@@ -119,22 +119,66 @@ Zur näherungsweisen Verarbeitung der Differentialgleichung wird hier das Variat
\draw[->] (.5,1,.5) -- (.5,1.4,.5) node[right] {$\sigma\ti{yy}$};
% Koordinatensystem
\draw[->] (-1,0,0) -- (-.7,0,0) node[right] {$x$};
\draw[->] (-1,0,0) -- (-1,.3,0) node[above] {$y$};
\draw[->] (-1,0,0) -- (-1,0,.3) node[below left] {$z$};
\draw[->] (-.9,0,0) -- (-.6,0,0) node[right] {$x$};
\draw[->] (-.9,0,0) -- (-.9,.3,0) node[above] {$y$};
\draw[->] (-.9,0,0) -- (-.9,0,.3) node[below left] {$z$};
}
\end{tikzpicture}
\hspace{2em}
\raisebox{0.9em}{
\begin{tikzpicture}[scale=2]
\hspace{.5em}
%\raisebox{0.9em}{
%\begin{tikzpicture}[scale=2]
%{
% \fill[color=black!5] (0,0,0) -- (1,0,0) -- (1,1,0) -- (0,1,0) -- cycle;
% \draw[color=black!50] (0,0,0) -- node[below, color=black] {$\dif{x}$} (1,0,0) -- (1,1,0) -- node[above, color=black] {Vergleich mit 1D} (0,1,0) -- cycle;
% \draw[<-] (-0.5,0.5,0) -- (0,0.5,0) node[above left] {$\sigma(x)$};
% \draw[->] (1,0.5,0) node[above right] {$\sigma(x+\dif{x})$} -- (1.5,0.5,0);
%}
%\end{tikzpicture}
%}
\begin{tikzpicture}[scale=2.5]
{
\fill[color=black!5] (0,0,0) -- (1,0,0) -- (1,1,0) -- (0,1,0) -- cycle;
\draw[color=black!50] (0,0,0) -- node[below, color=black] {$\dif{x}$} (1,0,0) -- (1,1,0) -- node[above, color=black] {Vergleich mit 1D} (0,1,0) -- cycle;
\draw[<-] (-0.5,0.5,0) -- (0,0.5,0) node[above left] {$\sigma(x)$};
\draw[->] (1,0.5,0) node[above right] {$\sigma(x+\dif{x})$} -- (1.5,0.5,0);
\fill[color=black!25] (1,0,1) -- (1,0,0) -- (1,1,0) -- (1,1,1) -- cycle;
\fill[color=black!15] (0,1,1) -- (1,1,1) -- (1,1,0) -- (0,1,0) -- cycle;
\fill[color=black!5] (0,0,1) -- (1,0,1) -- (1,1,1) -- (0,1,1) -- cycle;
\draw[color=black!50] (0,0,1) -- (1,0,1);
\draw[color=black!50] (0,0,1) -- (0,1,1);
\draw[color=black!50] (1,0,1) -- (1,0,0);
\draw[color=black!50] (0,1,1) -- (0,1,0);
\draw[color=black!50] (1,0,0) -- (1,1,0);
\draw[color=black!50] (0,1,0) -- (1,1,0);
\draw[color=black!50] (0,1,1) -- (1,1,1);
\draw[color=black!50] (1,0,1) -- (1,1,1);
\draw[color=black!50] (1,1,1) -- (1,1,0);
\draw[color=black!50, dashed] (0,0,0) -- (1,0,0);
\draw[color=black!50, dashed] (0,0,0) -- (0,1,0);
\draw[color=black!50, dashed] (0,0,0) -- (0,0,1);
% X-Ebene
\fill[color=black!35] (1,.45,.55) -- (1,.45,.45) -- (1,.55,.45) -- (1,.55,.55) -- cycle;
\fill[color=black!15] (0,.45,.55) -- (0,.45,.45) -- (0,.55,.45) -- (0,.55,.55) -- cycle;
\draw[->] (1,.5,.5) -- (1.4,.5,.5) node[right] {$\displaystyle\sigma\ti{xx}+\frac{\partial\sigma\ti{xx}}{\partial x}\dif x$};
\draw[->] (0,.5,.5) -- (-.4,.5,.5) node[left] {$\sigma\ti{xx}$};
% Y-Ebene
\fill[color=black!25] (.45,1,.55) -- (.55,1,.55) -- (.55,1,.45) -- (.45,1,.45) -- cycle;
\fill[color=black!15] (.45,0,.55) -- (.55,0,.55) -- (.55,0,.45) -- (.45,0,.45) -- cycle;
\draw[->] (.5,1,.5) -- (.9,1,.5) node[above right=-10pt] {$\displaystyle\tau\ti{yx}+\frac{\partial\tau\ti{yx}}{\partial y}\dif y$};
\draw[->,dashed] (.5,0,.5) -- (.1,0,.5) node[below] {$\tau\ti{yx}$};
% Z-Ebene
\fill[color=black!12] (.45,.45,1) -- (.55,.45,1) -- (.55,.55,1) -- (.45,.55,1) -- cycle;
\fill[color=black!12] (.45,.45,0) -- (.55,.45,0) -- (.55,.55,0) -- (.45,.55,0) -- cycle;
\draw[->] (.5,.5,1) -- (.9,.5,1) node[below right=-10pt] {$\displaystyle\tau\ti{zx}+\frac{\partial\tau\ti{zx}}{\partial z}\dif z$};
\draw[->,dashed] (.5,.5,0) -- (.1,.5,0) node[above right] {$\tau\ti{zx}$};
% fx
\draw[double -latex=2pt colored by black!80 and white] (.5,.5,.5) node[right] {$f\ti{x}$} -- (.1,.5,.5);
}
\end{tikzpicture}
}
\caption{Kräfte an einem infinitesimalen Volumenelement}
\label{pgfplots:Kraeftegleichgewicht}
\end{figure} \vspace{-1.5em}