Gelöste Aufgaben/StaF: Unterschied zwischen den Versionen

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Version vom 21. Oktober 2024, 13:03 Uhr

Aufgabenstellung

SOME TEXT

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Gesucht ist "SOME EXPLANATION"

Lösung mit Maxima

Lorem Ipsum ....

{\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}}

<math> </math

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@@ Zeile 1: / Zeile 1: @@
 [[Category:Gelöste Aufgaben]]
-[[Category:Dimensionslose Schreibweise]]
 [[Category:A*x=b]]
 [[Category:Lineare Algebra]]
-[[Category:Achsensymmetrie]]
-[[Category:Rotationssymmetrie‎]]
-[[Category:Analytische Lösung]]
 [[Category:Numerische Lösung]]
-[[Category:Anfangswertproblem]]
 [[Category:Randwertproblem]]
-[[Category:Ansys]][[Category:Shell-Element]]
-[[Category:Arbeitsfunktion]]
-[[Category:Potential]]
 [[Category:Prinzip der virtuellen Arbeit‎]]
 [[Category:Prinzip der virtuellen Verrückungen]]
@@ Zeile 68: / Zeile 60: @@
 == Lösung mit Maxima ==
 Lorem Ipsum ....
+::<math>
+\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\\
+& \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}} A E}{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}} A E}{4 {{\ell}_{0}^{3}}}\right)  & \frac{\sqrt{3} {{A}^{2}} E \eta -\sqrt{3} {{\ell}_{0}^{2}} A E}{4 {{\ell}_{0}^{3}}} & \frac{{{A}^{2}} E \eta }{4 {{\ell}_{0}^{2}}}\\
+& -\left( \frac{\sqrt{3} {{A}^{2}} E \eta }{4 {{\ell}_{0}^{2}}}\right)  & 0 & \frac{3 {{A}^{2}} E \eta +{{\ell}_{0}^{2}} A E}{2 {{\ell}_{0}^{3}}}+\frac{2 A E}{{\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}} A E}{4 {{\ell}_{0}^{3}}} & -\left( \frac{3 {{A}^{2}} E \eta +{{\ell}_{0}^{2}} A E}{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}}\\
+& -\left( \frac{{{A}^{2}} E \eta }{2 {{\ell}_{0}^{2}}}\right)  & -\left( \frac{{{A}^{2}} E \eta +3 {{\ell}_{0}^{2}} A E}{4 {{\ell}_{0}^{3}}}\right)  & \frac{\sqrt{3} {{A}^{2}} E \eta -\sqrt{3} {{\ell}_{0}^{2}} A E}{4 {{\ell}_{0}^{3}}} & -\left( \frac{{{A}^{2}} E \eta }{4 {{\ell}_{0}^{2}}}\right)  & \frac{{{A}^{2}} E \eta +3 {{\ell}_{0}^{2}} A E}{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}} A E}{4 {{\ell}_{0}^{3}}}\right)  & -\left( \frac{3 {{A}^{2}} E \eta }{4 {{\ell}_{0}^{2}}}\right) \\
+& 0 & \frac{\sqrt{3} {{A}^{2}} E \eta -\sqrt{3} {{\ell}_{0}^{2}} A E}{4 {{\ell}_{0}^{3}}} & -\left( \frac{3 {{A}^{2}} E \eta +{{\ell}_{0}^{2}} A E}{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}} A E}{4 {{\ell}_{0}^{3}}}\right)  & \frac{3 {{A}^{2}} E \eta +{{\ell}_{0}^{2}} A E}{4 {{\ell}_{0}^{3}}}+\frac{A E}{{\ell_0}} & \frac{\sqrt{3} {{A}^{2}} E \eta }{4 {{\ell}_{0}^{2}}}\\
+& \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}
+\\
+\\
+\\
+\\
+\\
+F\\
+\\
+\end{pmatrix}
+</math>
+<math>
+</math
 ==tmp==

Gelöste Aufgaben/StaF: Unterschied zwischen den Versionen

Version vom 21. Oktober 2024, 13:03 Uhr

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