From a6f745f06511067f4d5216404dc852a0c915475d Mon Sep 17 00:00:00 2001 From: Daniel Weschke Date: Tue, 16 Jun 2015 03:46:47 +0200 Subject: [PATCH] =?UTF-8?q?=C3=9Cberarbeitung=20von=20Modellentwicklung=20?= =?UTF-8?q?-=20Computermodell=20und=20Erweiterung=20von=20Modellentwicklun?= =?UTF-8?q?g=20-=20Simulationsmodell?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- datas/Statische_Ergebnisse.dat | 28 ++ ..._WB_Strukturbaum_Kontakte_Verbindungen.png | Bin 0 -> 1136 bytes figures/ANSYS_WB_Strukturbaum_Netz.png | Bin 0 -> 601 bytes figures/Kontakt.png | Bin 0 -> 869357 bytes main.tex | 2 +- sections/Modellentwicklung.tex | 251 +++++++++++------- 6 files changed, 185 insertions(+), 96 deletions(-) create mode 100644 datas/Statische_Ergebnisse.dat create mode 100644 figures/ANSYS_WB_Strukturbaum_Kontakte_Verbindungen.png create mode 100644 figures/ANSYS_WB_Strukturbaum_Netz.png create mode 100644 figures/Kontakt.png diff --git 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zr($4ux*!*i@TaI1lQSE+@XD*@#sbbxf~HlkD!U1aS3Ub1<-S-y+WVVz6Ayo_^TO(# zWrzKOQ#D+=3ydjM_YuShypa z;+JO@KPN#Q;I*pB$M(06I!jtQeRf7hUuEqXkRY}EHKFK;C_VVsBHl{7x4xAh9`E3Z z2|;cJ@d&D!TL5s_s`(f63xpat&le7Ngk0OG(>B87W&B|X7adiDBp3zAYSR~}7*dV$ z!MV!Y#iO&OwbAC9?7JcYTa)ksULDN1E1>y5ai&IQLu>V+_upe9#~&61%5>T0Wj*n2 z1x<}id_fm1uVC!fNFg#;>&u{B5@IMzJ{F80hDD&bU-upLzXy=*#g6aJFy;Xz6&_cy<5I1dS!1bvJVHLx<{=pkEsV?pQNbH1-C!FdPCU-~$`<%|eE&3ybI=3N{=$1B_xyqFseEnq LKmRDWY!&=JCtLw9 literal 0 HcmV?d00001 diff --git a/main.tex b/main.tex index a224905..f3eba6e 100755 --- a/main.tex +++ b/main.tex @@ -10,7 +10,7 @@ % Silbentrennung % ----------------------------------------- \hyphenation{ -WindPACT +ANSYS WindPACT } % wird nach \selectlanguage{ngerman} zurückgesetzt diff --git a/sections/Modellentwicklung.tex b/sections/Modellentwicklung.tex index 07d10aa..e9d80c2 100755 --- a/sections/Modellentwicklung.tex +++ b/sections/Modellentwicklung.tex @@ -139,50 +139,55 @@ Freq. & Beschreibung der Eigenform & FAST & ADAMS \\ \midrule \subsection{Computermodell} Die Forschungsanlage wird als Flächenmodell angenähert. -Ein grundlegendes Computermodell ist durch die Arbeit \cite{Prange14} von \citeauthor{Prange14} validiert. Abbildung \ref{fig:ComputermodellCATIA} links zeigt das übernommene und rechts das durch den nachstehenden Modifikationen angepasste Computermodell. +Ein grundlegendes Computermodell ist durch die Arbeit \cite{Prange14} von \citeauthor{Prange14} entstanden und validiert. +Das dabei verwendete \ac{CAD}-Programm ist \emph{CATIA\,V5} von der Firma \emph{Dassault Systèmes}, mit dem die dreidimensionale Geometrieerzeugung erfolgte. +Alle erforderliche Modifikationen zur Simulation werden ebenfalls mit dem \ac{CAD}-Programm \emph{CATIA\,V5} durchgeführt. +Unter den Modifikationen fallen diverse Schnitte, die in das 3D"=Flächenmodell hinzugefügt werden und damit die nötige Möglichkeit bieten Materialparameter vorgeben zu können. +Die Abbildung \ref{fig:ComputermodellCATIA} links zeigt das übernommene und rechts das durch den nachstehenden Modifikationen angepasste Computermodell. \begin{figure}[H]\centering \includegraphics[height=0.7\textwidth]{Computermodell.png} \includegraphics[height=0.7\textwidth]{Computermodell_neu.png} \caption{Computermodell der Windenergieanlage} \label{fig:ComputermodellCATIA} -\end{figure} \vspace{-1.5em} -Diesem Computermodell -ist für ein hinreichendes mechanisches Modell beziehungsweise \ac{FEM}"=Modell +\end{figure} \vspace{-1.5em} +Für ein hinreichendes mechanisches Modell beziehungsweise \ac{FEM}"=Modell sind %sind für gewünschte \ac{FEM}"=Simulationen Steifigkeiten und Massen zuzuweisen. % weitere Elemente hinzugefügt werden, damit es zu einem hinreichenden mechanisches Modell beziehungsweise \ac{FEM}"=Modell wird. Gemeint sind insbesondere Steifigkeiten - -[REF] Versuche im Forschungsprojekt \ac{WindNumSim} zeigten, dass das Nachbilden der Steifigkeiten für das Rotorblatt nicht trivial sind. -Somit ist es beispielsweise unmöglich, bezogen auf das Computermodell, die Steifigkeit mit einem isotropen Werkstoff nachzuempfinden. +Dabei zeigten anfängliche Versuche im Forschungsprojekt \ac{WindNumSim}, dass das Nachbilden der Steifigkeiten für die Rotorblätter nicht trivial ist. +Somit ist es beispielsweise unmöglich das Verhalten der \ac{WEA} mit ausschließlich isotrope Werkstoffe nachzuempfinden. %% TODO: Referenz zu einer Arbeit Erste Überlegungen die Steifigkeit für das Rotorblatt abzubilden wurden in einem vorangegangenen Masterprojekt~\citep{MP15} durchgeführt. Als Resultat wird eine Modellierung nach \ac{SNL} gewählt, welches ein in \acs{MATLAB} geschriebenes Programm speziell zur Berechnung von Rotorblättern entwickelte. -Dieses Programm -- genannt \acs{NuMAD} -- erstellt ein in \emph{\ac{APDL}} geschriebene Datei. Die Abbildung \ref{fig:LageraufbautenAPDL} zeigt das Ergebnis der Rotorblattmodellierung welche die vorgegebenen Steifigkeiten nachbilden [REF]. +Dieses Programm -- genannt \acs{NuMAD} -- erstellt ein in \emph{\ac{APDL}} geschriebene Datei. Das Ergebnis der Rotorblattmodellierung welche die vorgegebenen Steifigkeiten nachbilden zeigt die Abbildung \ref{fig:LageraufbautenAPDL}. \begin{figure}[H]\centering \includegraphics[width=0.95\textwidth]{Lageraufbauten_iso_ou.png} \caption{Lageraufbauten im Rotorblatt mit Hilfe von Sandias NuMAD-Programm} \label{fig:LageraufbautenAPDL} \end{figure} \vspace{-1.5em} -Zusehen ist, dass das Modell aus vielen kleinen Einzelflächen besteht. +In Abbildung~\ref{fig:LageraufbautenAPDL} ist zusehen, dass das Modell aus vielen kleinen Einzelflächen besteht. +Auf diesen Einzelflächen sind jeweils eigene Materialparameter in Form von unterschiedliche Lagenaufbauten verbunden. +Die hauptsächliche Modifikation besteht darin, das CATIA"=Modell um die gezeigten Einzelflächen zu erweitern. + \subsubsection{Rotorblatt} - +Die Abbildung~\ref{fig:ComputermodellRotorblattCATIA} zeigt das in CATIA bereits modellierte Rotorblatt. \begin{figure}[H]\centering \includegraphics[width=0.95\textwidth]{Computermodell_Rotorblatt.png} \caption{Computermodell -- Rotorblatt} \label{fig:ComputermodellRotorblattCATIA} \end{figure} \vspace{-1.5em} - +Bei der Modellerweiterung für das Rotorblatt werden zuerst zusätzliche Sektionen in das CATIA-Modell geschnitten. +Die Abbildung~\ref{fig:SektionenBatch} zeigt die benötigten Sektionen. \begin{figure}[H]\centering \includegraphics[width=0.95\textwidth]{Sektionen_drauf_cut.png} \caption{Sektionen im Rotorblatt} \label{fig:SektionenBatch} \end{figure} \vspace{-1.5em} - -Bei der Modellerweiterung für das Rotorblatt werden zuerst zusätzliche Sektionen in das CATIA-Modell geschnitten und anschließend Punkte und Linien in Längsrichtung erzeugt. Die Linien werden in radialer Richtung extrudiert und wiederum mit dem CATIA-Modell geschnitten. -Die Informationen werden aus der generierten ANSYS-Einlesedatei \texttt{shell7.src} vom XXX rausgeschrieben, in MATLAB als CATIA-Makro aufbereitet und in CATIA eingelesen und ausgeführt. +Anschließend werden Punkte und Linien in Längsrichtung erzeugt. Die Linien werden in radialer Richtung extrudiert und wiederum mit dem CATIA-Modell geschnitten. +Sämtliche Informationen zum Lagenaufbau werden aus der NuMAD-generierten ANSYS-Einlesedatei \texttt{shell7.src} des Masterprojekts \citep{MP15} rausgeschrieben, in MATLAB als CATIA-Makro aufbereitet und anschließend in CATIA eingelesen und ausgeführt. \paragraph{Sektionen und Punkte}~\\ -Die Informationen zu den Ebenen und der geometrischen Punkte -- beziehungsweise in ANSYS als \emph{Keypoints} bezeichnet -- sind in der Einlesedatei \texttt{shell7.src} von Zeile 8.682 bis 16.406 zu finden. Ein Ausschnitt des Inhalts sind in den folgenden zwei Auszüge dargestellt. Der erste Programmausdruck~\ref{lst:APDL-Punkte-Anfang} stellt den Anfang der \emph{Keypoint}-Erzeugung dar. -\begin{lstlisting}[language=Fortran,firstnumber=8682, caption={APDL shell7.src: Beginn Erstellung von Punkten und Ebenen},label=lst:APDL-Punkte-Anfang] +Die Informationen zu den Sektionsebenen und den geometrischen Punkte für die Längsschnitte -- beziehungsweise in ANSYS als \emph{Keypoints} bezeichnet -- sind in der Einlesedatei \texttt{shell7.src} von Zeile 8.682 bis 16.406 zu finden. Ein Ausschnitt des Inhalts sind in den folgenden zwei Auszüge dargestellt. Der Programmausdruck~\ref{lst:APDL-Punkte-Anfang} stellt den Beginn der \emph{Keypoint}-Erzeugung dar. +\begin{lstlisting}[language=Fortran,firstnumber=8682, caption={APDL shell7.src: Beginn der Erstellung von Punkten und Ebenen},label=lst:APDL-Punkte-Anfang] ! DEFINE KEYPOINTS FOR SECTIONS AND CONNECT KEYPOINTS WITH LINES local,1000,CART,0,0,0, -90,0,-90 @@ -193,7 +198,7 @@ csys,0 k,2,-1.65218,0.365811,0 k,3,-1.66391,0.303277,0 \end{lstlisting} -Der zweite Programmausdruck~\ref{lst:APDL-Punkte-Weitere} zeigt den Wechsel zwischen den Sektionen. +Der Programmausdruck~\ref{lst:APDL-Punkte-Weitere} zeigt den Wechsel zwischen den ersten beiden Sektionen. \begin{lstlisting}[language=Fortran,firstnumber=8882, caption={APDL shell7.src: Weitere Erstellung von Punkten und Ebenen},label=lst:APDL-Punkte-Weitere] k,195,-1.62342,0.474422,0 k,196,-1.64096,0.41326,0 @@ -208,15 +213,14 @@ csys,0 k,1001,-1.64752,0.389762,0.3 k,1002,-1.65218,0.365811,0.3 \end{lstlisting} -Dies Ablauf wird analog für alle 38 Sektionen wiederholt mit welche insgesamt 37.192 \emph{Keypoints} erstellt werden. +Dieser Ablauf wird analog für alle 38 Sektionen wiederholt mit welche insgesamt 37.192 \emph{Keypoints} erstellt werden. -Für das Importieren der Punkte in CATIA sind nur die Zeilen welche mit dem \texttt{k}-Befehl anfangen interessant. Der \texttt{k}-Befehl erstellt die \emph{Keypoints} und erwartet als weitere Parameter den Namen als Zahl und die Koordinaten in den drei Raumrichtungen. -Jene Zeilen mit dem \texttt{k}-Befehl werden als Vorbereitung des CATIA-Makros in eine eigenständige Datei mit dem Namen \texttt{keypoints.txt} gespeichert und in MATLAB eingelesen. +Für das Importieren der Punkte in CATIA sind nur Zeilen welche mit dem \texttt{k}-Befehl anfangen interessant. Der \texttt{k}-Befehl erstellt in ANSYS \emph{Keypoints} und erwartet als weitere Parameter die \emph{Keypoint}"=Bezeichnung als Zahl und die Koordinaten in den drei Raumrichtungen. +Jene Zeilen, mit dem \texttt{k}-Befehl, werden als Vorbereitung des CATIA-Makros in eine eigenständige Datei mit dem Namen \texttt{keypoints.txt} gespeichert und in MATLAB eingelesen. Die Positionen der Ebenen kann beispielsweise von der z-Koordinate der \emph{Keypoints} abgelesen werden. -Hierbei ist zu beachten dass die z-Koordinate bezüglich dem Zusammenbau um \unit{1,5}{m} verschoben wird und folglich den Abstand zur Rotornabe repräsentiert. - -Mit der z-Korrektur liegen die 18 zusätzlichen Ebenen in Bezug auf dem Nabenradius nach der dargestellten MATLAB-Variable \texttt{planeDistances} im Programmausdruck~\ref{lst:MATLAB-Ebenen}. +Hierbei ist zu beachten dass die z-Koordinate bezüglich dem Zusammenbau der Anlage um \unit{1,5}{m} verschoben wird und folglich den Abstand zur Rotornabe repräsentiert. +Die im Programmausdruck~\ref{lst:MATLAB-Ebenen} dargestellte MATLAB-Variable \texttt{planeDistances} listet die 18 zusätzlichen Ebenen mit der z-Korrektur als Bezug zum Nabenradius auf. \begin{lstlisting}[language=Matlab, firstnumber=15, caption={MATLAB Create\_CATIA\_Makro.m: Position der Ebenen},label=lst:MATLAB-Ebenen] planeDistances = [7000, 8333,3, 10500, 13500, 18500, 19950, 22000, 26100, ... 32250, 33500, 38500, 40450, 42500, 43500, 46500, 48650, 56166.7, 58900]; % in mm @@ -241,78 +245,132 @@ part1.Update \end{lstlisting} Dieser Programmausdruck wird für jede zusätzliche Ebene analog durchlaufen und dabei, der in der ersten Zeile angegebene Abstand von 7000, mit den Werten aus der MATLAB-Variable \texttt{planeDistances} ersetzt. -Die zweite Zeile benennt die Ebenen mit den Bezeichnungen von "\texttt{Ebene.1001}"\ bis "\texttt{Ebene.1018}". -Mit den abschließenden Zeilen werden die Ebenen mit dem Modell verknüpft. Zuvor werden noch einige benötigte Variable zur Verfügung gestellt die hier nicht weiter gezeigt werden. Für den interessierten Leser und zur Vollständigkeit ist das gesamte MATLAB-Skript, welches das CATIA-Makro erzeugt, im Anhang als Programmausdruck \ref{lst:MATLAB-CATIA-Makro} angefügt. +Die zweite Zeile benennt die Ebenen mit den Bezeichnungen von \glqq \texttt{Ebene.1001}\grqq\ bis \glqq \texttt{Ebene.1018}\grqq. +Mit den abschließenden Zeilen werden die Ebenen mit dem Modell verknüpft. Zuvor werden noch einige benötigte Variable zur Verfügung gestellt die hier nicht weiter aufgezeigt werden. Für den interessierten Leser und zur Vollständigkeit beziehungsweise zur Reproduzierbarkeit ist das gesamte MATLAB-Skript, welches das CATIA-Makro erzeugt, im Anhang als Programmausdruck \ref{lst:MATLAB-CATIA-Makro} angefügt. + +\paragraph{Längsschnitte}~\\ +~ + + \subsection{Simulationsmodell} % Berechnungsmodell oder Simulationsmodell - -\subsubsection{Netz} - -%\begin{figure}[H]\centering -%\begin{tikzpicture}[] -%\begin{axis}[ -% width=11.0cm, height=5cm, -% title={}, -% enlarge x limits=false, -% enlarge y limits=false, -% scale only axis, -% grid=major, -% tick align = outside, -% axis lines=left, -% xmode=log,log basis x=10, -% xmin=80000, -% xmax=370000, -% ymin=0, -% ymax=1100, -% xlabel={Knotenanzahl}, -% ylabel={\ref{pgfplots:konvergenz:wiege:sigma} Max.\,Spannung $\sigma\ti{Mises}$ in MPa}, -% yticklabel style={ /pgf/number format/.cd,fixed,fixed zerofill,precision=0}, -% ytick={0,200,...,1400}, -% legend style={ -% nodes=right, -% font=\small, -% }, -% legend pos=south west, -%] -% \pgfplotstableread[col sep=semicolon]{data/Konvergenz.csv}\datatable -% \addplot[draw1, mark=x] table[skip first n=1, x index=0,x expr=\thisrowno{0}*1, y index=2] from \datatable; -% \label{pgfplots:konvergenz:wiege:sigma} -%\end{axis} -%\begin{axis}[ -% width=11.0cm, height=5cm, -% enlarge x limits=false, -% enlarge y limits=false, -% scale only axis, -% tick align = outside, -% axis y line*=right, -% xmode=log,log basis x=10, -% xmin=80000, -% xmax=370000, -% ymin=0, -% ymax=22, -% ytick={4,8,...,25}, -% ylabel={\ref{pgfplots:konvergenz:wiege:U} Max.\,Verformung $U$ in mm}, -% axis x line=none, -% legend style={ -% nodes=right, -% font=\small, -% }, -% legend pos=south east, -%] -% \pgfplotstableread[col sep=semicolon]{data/Konvergenz.csv}\datatable -%\addplot[draw2, mark=*,mark size=1] table[skip first n=1, x index=0,x expr=\thisrowno{0}*1, y index=3] from \datatable; -% \label{pgfplots:konvergenz:wiege:U} -%\end{axis} -%\end{tikzpicture}% -%\caption[ -%Konvergenzstudie zur maximalen Vergleichsspannung und der maximalen Verformung -%]{ -%Konvergenzstudie zur maximalen Vergleichsspannung $\sigma\ti{Mises}$~\ref{pgfplots:konvergenz:wiege:sigma} und der maximalen Verformung $U$~\ref{pgfplots:konvergenz:wiege:U} -%}\label{fig:konvergenz:wiege} -%\end{figure} \vspace{-.5em} +In diesem Abschnitt wird der Aufbau des Simulationsmodells näher beschrieben. +Dabei wird auf verwendete Elemente, Netzfeinheit und Randbedingungen sowie vorgegebene Analyseeinstellung eingegangen. +Die Simulation erfolgt mit dem FEM"=Programm \emph{ANSYS} über die \emph{Workbench}-Oberfläche in der 15.\,Version. -%\begin{figure}[H] +\subsubsection{Materialparameter} +~ + +\subsubsection{Elemente} +Infolge der Flächenmodellierung der \ac{WEA} ist das Simulationsmodell mit Schalenelemente modelliert. +Auf ein Modell mit Volumenelementen wurde verzichtet, da anzunehmen ist dass die Schalenelemente hier gleiche Ergebnisse liefern und andererseits die Rechenzeit erheblich reduzieren. +Weiterhin würden für eine hinreichende Volumenmodellierung Informationen, insbesondere in Dickenrichtung beziehungsweise dem Innenaufbau der Anlage, fehlen, wobei viele Annahmen getroffen werden müssten. +Es fanden bereits für die Flächenmodellierung unterschiedliche Interpolationen und Annahmen statt. +So stehen für die Rotorblätter Modellinformationen nur in gewissen Abständen zur Verfügung. + +Bei den Schalenelementen handelt es sich zum großen Teil um Viereckselemente und vereinzelt um Dreieckselemente, beide mit linearen Verschiebungsansätzen. Die ausreichende Netzfeinheit wird durch eine Konvergenzstudie belegt. + + +\vspace{.5em} +\textsf{\textbf{Kontakte}} +\hfill | {\small ANSYS Workbench Strukturbaum: }% +\raisebox{-.35em}{% +\includegraphics[width=4cm]{ANSYS_WB_Strukturbaum_Kontakte_Verbindungen.png} +}\\\nopagebreak +% +Die Kopplung von Rotorblatt zu Spinner, Spinner zu Gondel und Gondel zu Turm erfolgt mit Kontaktelementen. +Dazu sind jeweils die stirnseitigen Flächen miteinander verbunden. +Dies hat zur Folge, dass die Elemente an der Stelle der Kopplung einen Verbund eingehen. +Dabei ist der \emph{Kontaktkörper} stets die bodenabgewandte Struktur und der \emph{Zielkörper} die bodenzugewandte Struktur. +Eingebaute Kontaktpartner sind in Abbildung \ref{fig:Kontakte} dargestellt. +\begin{figure}[H]\centering +\includegraphics[width=0.85\textwidth]{Kontakt.png} +\caption{Kontaktelemente} +\label{fig:Kontakte} +\end{figure} \vspace{-1.5em} + +\vspace{.5em} +\textsf{\textbf{Netz}} +\hfill | {\small ANSYS Workbench Strukturbaum: }% +\raisebox{-.35em}{% +\includegraphics[width=1.4cm]{ANSYS_WB_Strukturbaum_Netz.png} +}\\\nopagebreak +% +In der Abbildung~\ref{fig:konvergenz:statik} ist die Konvergenzanalyse zur maximalen Vergleichspannung~\(\sigma\ti{Mises}\) und der maximalen Verformung~\(U\) zu einer statischen Analyse dargestellt, worin die Anlage dem Eigengewicht ausgesetzt ist. +Die Abbildung~\ref{fig:konvergenz:modal} zeigt hingegen die Konvergenzanalyse zu den Eigenfrequenzen der Anlage. +Bei der Netzwahl wurde die globale Elementkantengröße zuerst von \unit{1000}{mm} bis auf \unit{100}{mm} herabgesetzt. +Anschließend wurde die in ANSYS verfügbare Einstellung \emph{Relevanz} immer weiter hoch gesetzt. +Diese Funktion verfeinert das Netz mit internen ANSYS-Regeln. +Einzelne Elemente erreichten dabei Elementkantengrößen im Bereich von \unit{70}{mm}. +Den Spannungs- und Verformungswerten beziehungsweise den Eigenfrequenzwerten werden die Anzahl von Freiheitsgrade gegenübergestellt, dessen Intervall von etwa 40.000 bis 3.000.000 läuft. +% +\begin{figure}[H]\centering +\begin{tikzpicture}[] +\begin{axis}[ + width=11.0cm, height=5cm, + title={}, + enlarge x limits=false, + enlarge y limits=false, + scale only axis, + grid=major, + tick align = outside, + axis lines=left, + xmode=log,log basis x=10, + xmin=40000, + xmax=2600000, + ymin=0, + ymax=1100, + xlabel={Anzahl der Freiheitsgrade}, + ylabel={\ref{pgfplots:konvergenz:sigma} Max.\,Spannung $\sigma\ti{Mises}$ in MPa}, + yticklabel style={ /pgf/number format/.cd,fixed,fixed zerofill,precision=0}, + ytick={0,200,...,1400}, + legend style={ + nodes=right, + font=\small, + }, + legend pos=south west, +] + \pgfplotstableread{datas/Statische_Ergebnisse.dat}\datatable + \addplot[draw1, mark=x] table[skip first n=1, x index=1,x expr=\thisrowno{1}*1, y index=3] from \datatable; + \label{pgfplots:konvergenz:sigma} +\end{axis} +\begin{axis}[ + width=11.0cm, height=5cm, + enlarge x limits=false, + enlarge y limits=false, + scale only axis, + tick align = outside, + axis y line*=right, + xmode=log,log basis x=10, + xmin=40000, + xmax=2600000, + ymin=0, + ymax=550, + ytick={100,200,...,500}, + ylabel={\ref{pgfplots:konvergenz:u} Max.\,Verformung $U$ in mm}, + axis x line=none, + legend style={ + nodes=right, + font=\small, + }, + legend pos=south east, +] + \pgfplotstableread{datas/Statische_Ergebnisse.dat}\datatable +\addplot[draw2, mark=*,mark size=1] table[skip first n=1, x index=1,x expr=\thisrowno{1}*1, y index=2] from \datatable; + \label{pgfplots:konvergenz:u} +\end{axis} +\end{tikzpicture}% +\caption[ +Konvergenzstudie zur maximalen Vergleichsspannung und der maximalen Verformung +]{ +Konvergenzstudie zur maximalen Vergleichsspannung $\sigma\ti{Mises}$~\ref{pgfplots:konvergenz:sigma} und der maximalen Verformung $U$~\ref{pgfplots:konvergenz:u} +}\label{fig:konvergenz:statik} +\end{figure} \vspace{-.5em} +% +Wie sich in Abbildung~\ref{fig:konvergenz:statik} zeigt, ist sowohl für die Verformung als auch für die Spannung +die Konvergenz erreicht. +% \begin{figure}[H]\centering %!htb \begin{tikzpicture}[] \begin{axis}[ @@ -328,8 +386,8 @@ Mit den abschließenden Zeilen werden die Ebenen mit dem Modell verknüpft. Zuvo xmin=40000, xmax=3100000, ymin=0, - ymax=3.6, - xlabel={Freiheitsgrade}, + ymax=3.65, + xlabel={Anzahl der Freiheitsgrade}, ylabel={Eigenfrequenzen $f_i$ in Hz}, yticklabel style={ /pgf/number format/.cd,fixed,fixed zerofill,precision=1}, ytick={0,.5,...,3.5}, @@ -362,11 +420,14 @@ Mit den abschließenden Zeilen werden die Ebenen mit dem Modell verknüpft. Zuvo Konvergenzstudie zur Eigenfrequenz der Windenergieanlage ]{ Konvergenzstudie zur Eigenfrequenz der Windenergieanlage -}\label{fig:konvergenz:wiege} +}\label{fig:konvergenz:modal} \end{figure} \vspace{-.5em} %\vspace{-1.5em} +% +In Abbildung~\ref{fig:konvergenz:modal} ist die Konvergenz zu den Eigenfrequenzen zu erkennen, die sich gegenüber der Konvergenz zur Spannung und Verformung deutlich früher einstellt. \subsubsection{Randbedingungen} +~ \subsubsection{Analyseparameter} - +~

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