Zeile 110:
Zeile 110: <tr><th>Element #4</th></tr>
<tr><th>Element #4</th></tr>
<tr><td>
<tr><td>
<math>
{k_4} = \begin{pmatrix}\frac{{{A}^{2}} E \eta }{{\ell_{0}^{3}}} & 0 & \frac{{{A}^{2}} E \eta }{2 {\ell_{0}^{2}}} & -\left( \frac{{{A}^{2}} E \eta }{{\ell_{0}^{3}}}\right) & 0 & \frac{{{A}^{2}} E \eta }{2 {\ell_{0}^{2}}}\\
{k_4} = \begin{pmatrix}\frac{{{A}^{2}} E \eta }{{\ell_{0}^{3}}} & 0 & \frac{{{A}^{2}} E \eta }{2 {\ell_{0}^{2}}} & -\left( \frac{{{A}^{2}} E \eta }{{\ell_{0}^{3}}}\right) & 0 & \frac{{{A}^{2}} E \eta }{2 {\ell_{0}^{2}}}\\
0 & \frac{A E}{{\ell_0}} & 0 & 0 & -\left( \frac{A E}{{\ell_0}}\right) & 0\\
0 & \frac{A E}{{\ell_0}} & 0 & 0 & -\left( \frac{A E}{{\ell_0}}\right) & 0\\
Zeile 116:
Zeile 117: 0 & -\left( \frac{A E}{{\ell_0}}\right) & 0 & 0 & \frac{A E}{{\ell_0}} & 0\\
0 & -\left( \frac{A E}{{\ell_0}}\right) & 0 & 0 & \frac{A E}{{\ell_0}} & 0\\
\frac{{{A}^{2}} E \eta }{2 {\ell_{0}^{2}}} & 0 & \frac{{{A}^{2}} E \eta }{6 {\ell_0}} & -\left( \frac{{{A}^{2}} E \eta }{2 {\ell_{0}^{2}}}\right) & 0 & \frac{{{A}^{2}} E \eta }{3 {\ell_0}}\end{pmatrix}
\frac{{{A}^{2}} E \eta }{2 {\ell_{0}^{2}}} & 0 & \frac{{{A}^{2}} E \eta }{6 {\ell_0}} & -\left( \frac{{{A}^{2}} E \eta }{2 {\ell_{0}^{2}}}\right) & 0 & \frac{{{A}^{2}} E \eta }{3 {\ell_0}}\end{pmatrix}
</math>
</td></tr>
</td></tr>
</table>
</table>
Version vom 21. Oktober 2024, 18:47 Uhr
Aufgabenstellung SOME TEXT
Caption Gesucht ist "SOME EXPLANATION"
Lösung mit Maxima Lorem Ipsum ....
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{\displaystyle {\begin{pmatrix}{\frac {2{{A}^{2}}E\eta }{3{\ell _{0}}}}&0&-\left({\frac {2{{A}^{2}}E\eta }{{\ell }_{0}^{2}}}\right)&0&{\frac {{{A}^{2}}E\eta }{3{\ell _{0}}}}&0&0&0\\0&{\frac {2{{A}^{2}}E\eta }{3{\ell _{0}}}}&-\left({\frac {{{A}^{2}}E\eta }{4{{\ell }_{0}^{2}}}}\right)&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{{\ell }_{0}^{2}}}}\right)&{\frac {{{A}^{2}}E\eta }{6{\ell _{0}}}}&-\left({\frac {{{A}^{2}}E\eta }{2{{\ell }_{0}^{2}}}}\right)&0&{\frac {{{A}^{2}}E\eta }{6{\ell _{0}}}}\\-\left({\frac {2{{A}^{2}}E\eta }{{\ell }_{0}^{2}}}\right)&-\left({\frac {{{A}^{2}}E\eta }{4{{\ell }_{0}^{2}}}}\right)&{\frac {{{A}^{2}}E\eta +3{{\ell }_{0}^{2}}AE}{2{{\ell }_{0}^{3}}}}+{\frac {8{{A}^{2}}E\eta }{{\ell }_{0}^{3}}}&0&-\left({\frac {2{{A}^{2}}E\eta }{{\ell }_{0}^{2}}}\right)&-\left({\frac {{{A}^{2}}E\eta +3{{\ell }_{0}^{2}}AE}{4{{\ell }_{0}^{3}}}}\right)&{\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{{\ell }_{0}^{2}}AE}{4{{\ell }_{0}^{3}}}}&{\frac {{{A}^{2}}E\eta }{4{{\ell }_{0}^{2}}}}\\0&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{{\ell }_{0}^{2}}}}\right)&0&{\frac {3{{A}^{2}}E\eta +{{\ell }_{0}^{2}}AE}{2{{\ell }_{0}^{3}}}}+{\frac {2AE}{\ell _{0}}}&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta }{2{{\ell }_{0}^{2}}}}\right)&{\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{{\ell }_{0}^{2}}AE}{4{{\ell }_{0}^{3}}}}&-\left({\frac {3{{A}^{2}}E\eta +{{\ell }_{0}^{2}}AE}{4{{\ell }_{0}^{3}}}}\right)&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{{\ell }_{0}^{2}}}}\right)\\{\frac {{{A}^{2}}E\eta }{3{\ell _{0}}}}&{\frac {{{A}^{2}}E\eta }{6{\ell _{0}}}}&-\left({\frac {2{{A}^{2}}E\eta }{{\ell }_{0}^{2}}}\right)&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta }{2{{\ell }_{0}^{2}}}}\right)&{\frac {4{{A}^{2}}E\eta }{3{\ell _{0}}}}&-\left({\frac {{{A}^{2}}E\eta }{4{{\ell }_{0}^{2}}}}\right)&{\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{{\ell }_{0}^{2}}}}&{\frac {{{A}^{2}}E\eta }{6{\ell _{0}}}}\\0&-\left({\frac {{{A}^{2}}E\eta }{2{{\ell }_{0}^{2}}}}\right)&-\left({\frac {{{A}^{2}}E\eta +3{{\ell }_{0}^{2}}AE}{4{{\ell }_{0}^{3}}}}\right)&{\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{{\ell }_{0}^{2}}AE}{4{{\ell }_{0}^{3}}}}&-\left({\frac {{{A}^{2}}E\eta }{4{{\ell }_{0}^{2}}}}\right)&{\frac {{{A}^{2}}E\eta +3{{\ell }_{0}^{2}}AE}{4{{\ell }_{0}^{3}}}}+{\frac {{{A}^{2}}E\eta }{{\ell }_{0}^{3}}}&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{{\ell }_{0}^{2}}AE}{4{{\ell }_{0}^{3}}}}\right)&-\left({\frac {3{{A}^{2}}E\eta }{4{{\ell }_{0}^{2}}}}\right)\\0&0&{\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{{\ell }_{0}^{2}}AE}{4{{\ell }_{0}^{3}}}}&-\left({\frac {3{{A}^{2}}E\eta +{{\ell }_{0}^{2}}AE}{4{{\ell }_{0}^{3}}}}\right)&{\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{{\ell }_{0}^{2}}}}&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{{\ell }_{0}^{2}}AE}{4{{\ell }_{0}^{3}}}}\right)&{\frac {3{{A}^{2}}E\eta +{{\ell }_{0}^{2}}AE}{4{{\ell }_{0}^{3}}}}+{\frac {AE}{\ell _{0}}}&{\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{{\ell }_{0}^{2}}}}\\0&{\frac {{{A}^{2}}E\eta }{6{\ell _{0}}}}&{\frac {{{A}^{2}}E\eta }{4{{\ell }_{0}^{2}}}}&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{{\ell }_{0}^{2}}}}\right)&{\frac {{{A}^{2}}E\eta }{6{\ell _{0}}}}&-\left({\frac {3{{A}^{2}}E\eta }{4{{\ell }_{0}^{2}}}}\right)&{\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{{\ell }_{0}^{2}}}}&{\frac {2{{A}^{2}}E\eta }{3{\ell _{0}}}}\end{pmatrix}}\cdot {\begin{pmatrix}{W_{1,0}}\\{U_{1,0}}\\{{\Phi }_{1,0}}\\{W_{2,0}}\\{U_{2,0}}\\{{\Phi }_{2,0}}\\{W_{3,0}}\\{U_{3,0}}\\{{\Phi }_{3,0}}\\{W_{4,0}}\\{U_{4,0}}\\{{\Phi }_{4,0}}\end{pmatrix}}={\begin{pmatrix}0\\0\\0\\0\\0\\F\\0\\0\end{pmatrix}}}
Hier kommt jetzt irgendein Text.
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{\displaystyle SomeText}
Title Text
Element-Steigigkeitsmatrizen mit globalen Koordinaten Element #1
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{\displaystyle {k_{1}}={\begin{pmatrix}{\frac {8{{A}^{2}}E\eta }{\ell _{0}^{3}}}&0&{\frac {2{{A}^{2}}E\eta }{\ell _{0}^{2}}}&-\left({\frac {8{{A}^{2}}E\eta }{\ell _{0}^{3}}}\right)&0&{\frac {2{{A}^{2}}E\eta }{\ell _{0}^{2}}}\\0&{\frac {2AE}{\ell _{0}}}&0&0&-\left({\frac {2AE}{\ell _{0}}}\right)&0\\{\frac {2{{A}^{2}}E\eta }{\ell _{0}^{2}}}&0&{\frac {2{{A}^{2}}E\eta }{3{\ell _{0}}}}&-\left({\frac {2{{A}^{2}}E\eta }{\ell _{0}^{2}}}\right)&0&{\frac {{{A}^{2}}E\eta }{3{\ell _{0}}}}\\-\left({\frac {8{{A}^{2}}E\eta }{\ell _{0}^{3}}}\right)&0&-\left({\frac {2{{A}^{2}}E\eta }{\ell _{0}^{2}}}\right)&{\frac {8{{A}^{2}}E\eta }{\ell _{0}^{3}}}&0&-\left({\frac {2{{A}^{2}}E\eta }{\ell _{0}^{2}}}\right)\\0&-\left({\frac {2AE}{\ell _{0}}}\right)&0&0&{\frac {2AE}{\ell _{0}}}&0\\{\frac {2{{A}^{2}}E\eta }{\ell _{0}^{2}}}&0&{\frac {{{A}^{2}}E\eta }{3{\ell _{0}}}}&-\left({\frac {2{{A}^{2}}E\eta }{\ell _{0}^{2}}}\right)&0&{\frac {2{{A}^{2}}E\eta }{3{\ell _{0}}}}\end{pmatrix}}}
Element #2
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{\displaystyle {k_{2}}={\begin{pmatrix}{\frac {{{A}^{2}}E\eta +3{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}&{\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}&{\frac {{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}&-\left({\frac {{{A}^{2}}E\eta +3{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}\right)&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}\right)&{\frac {{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}\\{\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}&{\frac {3{{A}^{2}}E\eta +{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}&{\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}\right)&-\left({\frac {3{{A}^{2}}E\eta +{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}\right)&{\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}\\{\frac {{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}&{\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}&{\frac {{{A}^{2}}E\eta }{3{\ell _{0}}}}&-\left({\frac {{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}\right)&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}\right)&{\frac {{{A}^{2}}E\eta }{6{\ell _{0}}}}\\-\left({\frac {{{A}^{2}}E\eta +3{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}\right)&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}\right)&-\left({\frac {{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}\right)&{\frac {{{A}^{2}}E\eta +3{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}&{\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}&-\left({\frac {{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}\right)\\-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}\right)&-\left({\frac {3{{A}^{2}}E\eta +{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}\right)&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}\right)&{\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}&{\frac {3{{A}^{2}}E\eta +{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}\right)\\{\frac {{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}&{\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}&{\frac {{{A}^{2}}E\eta }{6{\ell _{0}}}}&-\left({\frac {{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}\right)&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}\right)&{\frac {{{A}^{2}}E\eta }{3{\ell _{0}}}}\end{pmatrix}}}
Element #3
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{\displaystyle {k_{3}}={\begin{pmatrix}{\frac {{{A}^{2}}E\eta +3{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}\right)&{\frac {{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}&-\left({\frac {{{A}^{2}}E\eta +3{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}\right)&{\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}&{\frac {{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}\\-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}\right)&{\frac {3{{A}^{2}}E\eta +{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}\right)&{\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}&-\left({\frac {3{{A}^{2}}E\eta +{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}\right)&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}\right)\\{\frac {{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}\right)&{\frac {{{A}^{2}}E\eta }{3{\ell _{0}}}}&-\left({\frac {{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}\right)&{\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}&{\frac {{{A}^{2}}E\eta }{6{\ell _{0}}}}\\-\left({\frac {{{A}^{2}}E\eta +3{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}\right)&{\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}&-\left({\frac {{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}\right)&{\frac {{{A}^{2}}E\eta +3{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}\right)&-\left({\frac {{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}\right)\\{\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}&-\left({\frac {3{{A}^{2}}E\eta +{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}\right)&{\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta -{\sqrt {3}}{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}\right)&{\frac {3{{A}^{2}}E\eta +{\ell _{0}^{2}}AE}{4{\ell _{0}^{3}}}}&{\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}\\{\frac {{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}&-\left({\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}\right)&{\frac {{{A}^{2}}E\eta }{6{\ell _{0}}}}&-\left({\frac {{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}\right)&{\frac {{\sqrt {3}}{{A}^{2}}E\eta }{4{\ell _{0}^{2}}}}&{\frac {{{A}^{2}}E\eta }{3{\ell _{0}}}}\end{pmatrix}}}
Element #4
k
4
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{\displaystyle {k_{4}}={\begin{pmatrix}{\frac {{{A}^{2}}E\eta }{\ell _{0}^{3}}}&0&{\frac {{{A}^{2}}E\eta }{2{\ell _{0}^{2}}}}&-\left({\frac {{{A}^{2}}E\eta }{\ell _{0}^{3}}}\right)&0&{\frac {{{A}^{2}}E\eta }{2{\ell _{0}^{2}}}}\\0&{\frac {AE}{\ell _{0}}}&0&0&-\left({\frac {AE}{\ell _{0}}}\right)&0\\{\frac {{{A}^{2}}E\eta }{2{\ell _{0}^{2}}}}&0&{\frac {{{A}^{2}}E\eta }{3{\ell _{0}}}}&-\left({\frac {{{A}^{2}}E\eta }{2{\ell _{0}^{2}}}}\right)&0&{\frac {{{A}^{2}}E\eta }{6{\ell _{0}}}}\\-\left({\frac {{{A}^{2}}E\eta }{\ell _{0}^{3}}}\right)&0&-\left({\frac {{{A}^{2}}E\eta }{2{\ell _{0}^{2}}}}\right)&{\frac {{{A}^{2}}E\eta }{\ell _{0}^{3}}}&0&-\left({\frac {{{A}^{2}}E\eta }{2{\ell _{0}^{2}}}}\right)\\0&-\left({\frac {AE}{\ell _{0}}}\right)&0&0&{\frac {AE}{\ell _{0}}}&0\\{\frac {{{A}^{2}}E\eta }{2{\ell _{0}^{2}}}}&0&{\frac {{{A}^{2}}E\eta }{6{\ell _{0}}}}&-\left({\frac {{{A}^{2}}E\eta }{2{\ell _{0}^{2}}}}\right)&0&{\frac {{{A}^{2}}E\eta }{3{\ell _{0}}}}\end{pmatrix}}}
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