Gelöste Aufgaben/Kw98 - Versionsgeschichte

Mechaniker am 31. März 2021 um 12:30 Uhr

2021-03-31T12:30:37Z

← Nächstältere Version		Version vom 31. März 2021, 12:30 Uhr
Zeile 237:		Zeile 237:
	\|code=		\|code=
	<syntaxhighlight lang="lisp" line start=1>		<syntaxhighlight lang="lisp" line start=1>
	1+1		/* solving */
			D : ratsimp(determinant(AA))$
			[ P, L, U] : ratsimp(get_lu_factors(lu_factor(AA)))$
			cc : ratsimp(linsolve_by_lu(AA,bb)[1])$
			sol : makelist(ICs[i] = cc[i][1],i,1,8)$
	</syntaxhighlight>		</syntaxhighlight>
	}}		}}

Mechaniker am 31. März 2021 um 12:29 Uhr

2021-03-31T12:29:34Z

← Nächstältere Version		Version vom 31. März 2021, 12:29 Uhr
Zeile 174:		Zeile 174:

	::<math>\begin{pmatrix}\frac{{{C}_{1,0}}}{{{\mathit{EI}}_{1}}}=0\\ \frac{{{C}_{1,1}}\cdot {{K}_{A}}}{{{\mathit{EI}}_{1}}}-{{C}_{1,2}}=0\\ \frac{{{\ell}_{1}^{4}}\cdot {{q}_{B}}}{120\cdot {{\mathit{EI}}_{1}}}+\frac{{{\ell}_{1}^{4}}\cdot {{q}_{A}}}{30\cdot {{\mathit{EI}}_{1}}}+\frac{{{\ell}_{1}^{3}}\cdot {{C}_{1,3}}}{6\cdot {{\mathit{EI}}_{1}}}+\frac{{{\ell}_{1}^{2}}\cdot {{C}_{1,2}}}{2\cdot {{\mathit{EI}}_{1}}}+\frac{{{\ell}_{1}}\cdot {{C}_{1,1}}}{{{\mathit{EI}}_{1}}}+\frac{{{C}_{1,0}}}{{{\mathit{EI}}_{1}}}=\frac{{{C}_{2,0}}}{{{\mathit{EI}}_{2}}}\\ \frac{{{\ell}_{1}^{3}}\cdot {{q}_{B}}}{24\cdot {{\mathit{EI}}_{1}}}+\frac{{{\ell}_{1}^{3}}\cdot {{q}_{A}}}{8\cdot {{\mathit{EI}}_{1}}}+\frac{{{\ell}_{1}^{2}}\cdot {{C}_{1,3}}}{2\cdot {{\mathit{EI}}_{1}}}+\frac{{{\ell}_{1}}\cdot {{C}_{1,2}}}{{{\mathit{EI}}_{1}}}+\frac{{{C}_{1,1}}}{{{\mathit{EI}}_{1}}}=\frac{{{C}_{2,1}}}{{{\mathit{EI}}_{2}}}\\ \frac{{{\ell}_{1}}\cdot {{q}_{B}}}{2}-\frac{{{C}_{2,0}}\cdot {{k}_{B}}}{{{\mathit{EI}}_{2}}}+\frac{{{\ell}_{1}}\cdot {{q}_{A}}}{2}-{{C}_{2,3}}+{{C}_{1,3}}=0\\ -{{M}_{B}}+\frac{{{\ell}_{1}^{2}}\cdot {{q}_{B}}}{6}+\frac{{{\ell}_{1}^{2}}\cdot {{q}_{A}}}{3}-{{C}_{2,2}}+{{\ell}_{1}}\cdot {{C}_{1,3}}+{{C}_{1,2}}=0\\ \frac{{{\ell}_{2}^{2}}\cdot {{C}_{2,3}}}{2\cdot {{\mathit{EI}}_{2}}}+\frac{{{\ell}_{2}}\cdot {{C}_{2,2}}}{{{\mathit{EI}}_{2}}}+\frac{{{C}_{2,1}}}{{{\mathit{EI}}_{2}}}=0\\ -\frac{{{\ell}_{2}^{3}}\cdot {{C}_{2,3}}\cdot {{k}_{C}}}{6\cdot {{\mathit{EI}}_{2}}}-\frac{{{\ell}_{2}^{2}}\cdot {{C}_{2,2}}\cdot {{k}_{C}}}{2\cdot {{\mathit{EI}}_{2}}}-\frac{{{\ell}_{2}}\cdot {{C}_{2,1}}\cdot {{k}_{C}}}{{{\mathit{EI}}_{2}}}-\frac{{{C}_{2,0}}\cdot {{k}_{C}}}{{{\mathit{EI}}_{2}}}+{{C}_{2,3}}=0\end{pmatrix}		::<math>\begin{pmatrix}\frac{{{C}_{1,0}}}{{{\mathit{EI}}_{1}}}=0\\ \frac{{{C}_{1,1}}\cdot {{K}_{A}}}{{{\mathit{EI}}_{1}}}-{{C}_{1,2}}=0\\ \frac{{{\ell}_{1}^{4}}\cdot {{q}_{B}}}{120\cdot {{\mathit{EI}}_{1}}}+\frac{{{\ell}_{1}^{4}}\cdot {{q}_{A}}}{30\cdot {{\mathit{EI}}_{1}}}+\frac{{{\ell}_{1}^{3}}\cdot {{C}_{1,3}}}{6\cdot {{\mathit{EI}}_{1}}}+\frac{{{\ell}_{1}^{2}}\cdot {{C}_{1,2}}}{2\cdot {{\mathit{EI}}_{1}}}+\frac{{{\ell}_{1}}\cdot {{C}_{1,1}}}{{{\mathit{EI}}_{1}}}+\frac{{{C}_{1,0}}}{{{\mathit{EI}}_{1}}}=\frac{{{C}_{2,0}}}{{{\mathit{EI}}_{2}}}\\ \frac{{{\ell}_{1}^{3}}\cdot {{q}_{B}}}{24\cdot {{\mathit{EI}}_{1}}}+\frac{{{\ell}_{1}^{3}}\cdot {{q}_{A}}}{8\cdot {{\mathit{EI}}_{1}}}+\frac{{{\ell}_{1}^{2}}\cdot {{C}_{1,3}}}{2\cdot {{\mathit{EI}}_{1}}}+\frac{{{\ell}_{1}}\cdot {{C}_{1,2}}}{{{\mathit{EI}}_{1}}}+\frac{{{C}_{1,1}}}{{{\mathit{EI}}_{1}}}=\frac{{{C}_{2,1}}}{{{\mathit{EI}}_{2}}}\\ \frac{{{\ell}_{1}}\cdot {{q}_{B}}}{2}-\frac{{{C}_{2,0}}\cdot {{k}_{B}}}{{{\mathit{EI}}_{2}}}+\frac{{{\ell}_{1}}\cdot {{q}_{A}}}{2}-{{C}_{2,3}}+{{C}_{1,3}}=0\\ -{{M}_{B}}+\frac{{{\ell}_{1}^{2}}\cdot {{q}_{B}}}{6}+\frac{{{\ell}_{1}^{2}}\cdot {{q}_{A}}}{3}-{{C}_{2,2}}+{{\ell}_{1}}\cdot {{C}_{1,3}}+{{C}_{1,2}}=0\\ \frac{{{\ell}_{2}^{2}}\cdot {{C}_{2,3}}}{2\cdot {{\mathit{EI}}_{2}}}+\frac{{{\ell}_{2}}\cdot {{C}_{2,2}}}{{{\mathit{EI}}_{2}}}+\frac{{{C}_{2,1}}}{{{\mathit{EI}}_{2}}}=0\\ -\frac{{{\ell}_{2}^{3}}\cdot {{C}_{2,3}}\cdot {{k}_{C}}}{6\cdot {{\mathit{EI}}_{2}}}-\frac{{{\ell}_{2}^{2}}\cdot {{C}_{2,2}}\cdot {{k}_{C}}}{2\cdot {{\mathit{EI}}_{2}}}-\frac{{{\ell}_{2}}\cdot {{C}_{2,1}}\cdot {{k}_{C}}}{{{\mathit{EI}}_{2}}}-\frac{{{C}_{2,0}}\cdot {{k}_{C}}}{{{\mathit{EI}}_{2}}}+{{C}_{2,3}}=0\end{pmatrix}
	</math>		</math>.

	für die Integrationskonstanten.		für die Integrationskonstanten.
	\|code=		\|code=
	<syntaxhighlight lang="lisp" line start=1>		<syntaxhighlight lang="lisp" line start=1>
	1+1		/* integration constants */
			ICs : [C[1,0],C[1,1],C[1,2],C[1,3],C[2,0],C[2,1],C[2,2],C[2,3]];
			/* boundary conditions */
			node[A]: [ w[1](0) = 0,
			K[A]*Phi[1](0)+M[1](0) = 0];
			node[B]: [ w[1](l[1]) = w[2](0),
			Phi[1](l[1]) = Phi[2](0),
			-Q[1](l[1]) -k[B]*w[2](0) +Q[2](0) = 0,
			-M[1](l[1]) -M[B]+M[2](0) = 0];
			node[C]: [ Phi[2](l[2]) = 0,
			-Q[2](l[2]) - k[C]*w[2](l[2]) = 0];
			BCs : expand(append(node[A],node[B],node[C]));
	</syntaxhighlight>		</syntaxhighlight>
	}}		}}

Mechaniker am 31. März 2021 um 12:15 Uhr

2021-03-31T12:15:42Z

← Nächstältere Version		Version vom 31. März 2021, 12:15 Uhr
Zeile 1:		Zeile 1:
	[[Category:Gelöste Aufgaben]]		[[Category:Gelöste Aufgaben]]
	~~[[Category:Dimensionslose Schreibweise]]~~
	[[Category:Analytische Lösung]]		[[Category:Analytische Lösung]]
	[[Category:Randwertproblem]]		[[Category:Randwertproblem]]

Mechaniker am 31. März 2021 um 12:13 Uhr

2021-03-31T12:13:21Z

← Nächstältere Version		Version vom 31. März 2021, 12:13 Uhr
Zeile 184:		Zeile 184:
	}}		}}

	==~~tmp==~~		<!-------------------------------------------------------------------------------->
			{{MyCodeBlock\|title=Prepare for Solver
			\|text=
	Das Gleichungssystem wollen wir als		Das Gleichungssystem wollen wir als

	<math>\underline{\underline{A}}\cdot\underline{x}= \underline{b}</math>		::<math>\underline{\underline{A}}\cdot\underline{x}= \underline{b}</math>

	schreiben, also		schreiben, also

	<math>\begin{pmatrix}\frac{1}{{{\mathit{EI}}_{1}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & \frac{{{K}_{A}}}{{{\mathit{EI}}_{1}}} & -1 & 0 & 0 & 0 & 0 & 0\\ \frac{1}{{{\mathit{EI}}_{1}}} & \frac{{{\ell}_{1}}}{{{\mathit{EI}}_{1}}} & \frac{{{\ell}_{1}^{2}}}{2\cdot {{\mathit{EI}}_{1}}} & \frac{{{\ell}_{1}^{3}}}{6\cdot {{\mathit{EI}}_{1}}} & -\frac{1}{{{\mathit{EI}}_{2}}} & 0 & 0 & 0\\ 0 & \frac{1}{{{\mathit{EI}}_{1}}} & \frac{{{\ell}_{1}}}{{{\mathit{EI}}_{1}}} & \frac{{{\ell}_{1}^{2}}}{2\cdot {{\mathit{EI}}_{1}}} & 0 & -\frac{1}{{{\mathit{EI}}_{2}}} & 0 & 0\\ 0 & 0 & 0 & 1 & -\frac{{{k}_{B}}}{{{\mathit{EI}}_{2}}} & 0 & 0 & -1\\ 0 & 0 & 1 & {{\ell}_{1}} & 0 & 0 & -1 & 0\\ 0 & 0 & 0 & 0 & 0 & \frac{1}{{{\mathit{EI}}_{2}}} & \frac{{{\ell}_{2}}}{{{\mathit{EI}}_{2}}} & \frac{{{\ell}_{2}^{2}}}{2\cdot {{\mathit{EI}}_{2}}}\\ 0 & 0 & 0 & 0 & -\frac{{{k}_{C}}}{{{\mathit{EI}}_{2}}} & -\frac{{{\ell}_{2}}\cdot {{k}_{C}}}{{{\mathit{EI}}_{2}}} & -\frac{{{\ell}_{2}^{2}}\cdot {{k}_{C}}}{2\cdot {{\mathit{EI}}_{2}}} & -\frac{{{\ell}_{2}^{3}}\cdot {{k}_{C}}-6\cdot {{\mathit{EI}}_{2}}}{6\cdot {{\mathit{EI}}_{2}}}\end{pmatrix}\cdot\underline{x}=\begin{pmatrix}0\\ 0\\ -\frac{{{\ell}_{1}^{4}}\cdot {{q}_{B}}}{120\cdot {{\mathit{EI}}_{1}}}-\frac{{{\ell}_{1}^{4}}\cdot {{q}_{A}}}{30\cdot {{\mathit{EI}}_{1}}}\\ -\frac{{{\ell}_{1}^{3}}\cdot {{q}_{B}}}{24\cdot {{\mathit{EI}}_{1}}}-\frac{{{\ell}_{1}^{3}}\cdot {{q}_{A}}}{8\cdot {{\mathit{EI}}_{1}}}\\ -\frac{{{\ell}_{1}}\cdot {{q}_{B}}}{2}-\frac{{{\ell}_{1}}\cdot {{q}_{A}}}{2}\\ {{M}_{B}}-\frac{{{\ell}_{1}^{2}}\cdot {{q}_{B}}}{6}-\frac{{{\ell}_{1}^{2}}\cdot {{q}_{A}}}{3}\\ 0\\ 0\end{pmatrix}		::<math>\begin{pmatrix}\frac{1}{{{\mathit{EI}}_{1}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & \frac{{{K}_{A}}}{{{\mathit{EI}}_{1}}} & -1 & 0 & 0 & 0 & 0 & 0\\ \frac{1}{{{\mathit{EI}}_{1}}} & \frac{{{\ell}_{1}}}{{{\mathit{EI}}_{1}}} & \frac{{{\ell}_{1}^{2}}}{2\cdot {{\mathit{EI}}_{1}}} & \frac{{{\ell}_{1}^{3}}}{6\cdot {{\mathit{EI}}_{1}}} & -\frac{1}{{{\mathit{EI}}_{2}}} & 0 & 0 & 0\\ 0 & \frac{1}{{{\mathit{EI}}_{1}}} & \frac{{{\ell}_{1}}}{{{\mathit{EI}}_{1}}} & \frac{{{\ell}_{1}^{2}}}{2\cdot {{\mathit{EI}}_{1}}} & 0 & -\frac{1}{{{\mathit{EI}}_{2}}} & 0 & 0\\ 0 & 0 & 0 & 1 & -\frac{{{k}_{B}}}{{{\mathit{EI}}_{2}}} & 0 & 0 & -1\\ 0 & 0 & 1 & {{\ell}_{1}} & 0 & 0 & -1 & 0\\ 0 & 0 & 0 & 0 & 0 & \frac{1}{{{\mathit{EI}}_{2}}} & \frac{{{\ell}_{2}}}{{{\mathit{EI}}_{2}}} & \frac{{{\ell}_{2}^{2}}}{2\cdot {{\mathit{EI}}_{2}}}\\ 0 & 0 & 0 & 0 & -\frac{{{k}_{C}}}{{{\mathit{EI}}_{2}}} & -\frac{{{\ell}_{2}}\cdot {{k}_{C}}}{{{\mathit{EI}}_{2}}} & -\frac{{{\ell}_{2}^{2}}\cdot {{k}_{C}}}{2\cdot {{\mathit{EI}}_{2}}} & -\frac{{{\ell}_{2}^{3}}\cdot {{k}_{C}}-6\cdot {{\mathit{EI}}_{2}}}{6\cdot {{\mathit{EI}}_{2}}}\end{pmatrix}\cdot\underline{x}=\begin{pmatrix}0\\ 0\\ -\frac{{{\ell}_{1}^{4}}\cdot {{q}_{B}}}{120\cdot {{\mathit{EI}}_{1}}}-\frac{{{\ell}_{1}^{4}}\cdot {{q}_{A}}}{30\cdot {{\mathit{EI}}_{1}}}\\ -\frac{{{\ell}_{1}^{3}}\cdot {{q}_{B}}}{24\cdot {{\mathit{EI}}_{1}}}-\frac{{{\ell}_{1}^{3}}\cdot {{q}_{A}}}{8\cdot {{\mathit{EI}}_{1}}}\\ -\frac{{{\ell}_{1}}\cdot {{q}_{B}}}{2}-\frac{{{\ell}_{1}}\cdot {{q}_{A}}}{2}\\ {{M}_{B}}-\frac{{{\ell}_{1}^{2}}\cdot {{q}_{B}}}{6}-\frac{{{\ell}_{1}^{2}}\cdot {{q}_{A}}}{3}\\ 0\\ 0\end{pmatrix}
	</math>		</math>

	Die Matrix-Elemente sind für die Koeffizientenmatrix		Die Matrix-Elemente sind für die Koeffizientenmatrix

	<math>\begin{array}{l} a_{1,1} = 1/EI_{1}\\ a_{2,2} = K_{A}/EI_{1}\\ a_{2,3} = -1\\ a_{3,1} = 1/EI_{1}\\ a_{3,2} = \ell_{1}/EI_{1}\\ a_{3,3} = \ell_{1}^2/(2\cdot EI_{1})\\ a_{3,4} = \ell_{1}^3/(6\cdot EI_{1})\\ a_{3,5} = -1/EI_{2}\\ a_{4,2} = 1/EI_{1}\\ a_{4,3} = \ell_{1}/EI_{1}\\ a_{4,4} = \ell_{1}^2/(2\cdot EI_{1})\\ a_{4,6} = -1/EI_{2}\\ a_{5,4} = 1\\ a_{5,5} = -k_{B}/EI_{2}\\ a_{5,8} = -1\\ a_{6,3} = 1\\ a_{6,4} = \ell_{1}\\ a_{6,7} = -1\\ a_{7,6} = 1/EI_{2}\\ a_{7,7} = \ell_{2}/EI_{2}\\ a_{7,8} = \ell_{2}^2/(2\cdot EI_{2})\\ a_{8,5} = -k_{C}/EI_{2}\\ a_{8,6} = -(\ell_{2}\cdot k_{C})/EI_{2}\\ a_{8,7} = -(\ell_{2}^2\cdot k_{C})/(2\cdot EI_{2})\\ a_{8,8} = -(\ell_{2}^3\cdot k_{C}-6\cdot EI_{2})/(6\cdot EI_{2})\\ \end{array}</math>		::<math>\begin{array}{l} a_{1,1} = 1/EI_{1}\\ a_{2,2} = K_{A}/EI_{1}\\ a_{2,3} = -1\\ a_{3,1} = 1/EI_{1}\\ a_{3,2} = \ell_{1}/EI_{1}\\ a_{3,3} = \ell_{1}^2/(2\cdot EI_{1})\\ a_{3,4} = \ell_{1}^3/(6\cdot EI_{1})\\ a_{3,5} = -1/EI_{2}\\ a_{4,2} = 1/EI_{1}\\ a_{4,3} = \ell_{1}/EI_{1}\\ a_{4,4} = \ell_{1}^2/(2\cdot EI_{1})\\ a_{4,6} = -1/EI_{2}\\ a_{5,4} = 1\\ a_{5,5} = -k_{B}/EI_{2}\\ a_{5,8} = -1\\ a_{6,3} = 1\\ a_{6,4} = \ell_{1}\\ a_{6,7} = -1\\ a_{7,6} = 1/EI_{2}\\ a_{7,7} = \ell_{2}/EI_{2}\\ a_{7,8} = \ell_{2}^2/(2\cdot EI_{2})\\ a_{8,5} = -k_{C}/EI_{2}\\ a_{8,6} = -(\ell_{2}\cdot k_{C})/EI_{2}\\ a_{8,7} = -(\ell_{2}^2\cdot k_{C})/(2\cdot EI_{2})\\ a_{8,8} = -(\ell_{2}^3\cdot k_{C}-6\cdot EI_{2})/(6\cdot EI_{2})\\ \end{array}</math>

	und für die rechte Seite		und für die rechte Seite

	<math>\begin{array}{l} b_{1} = 0\\ b_{2} = 0\\ b_{3} = (-(\ell_{1}^4\cdot q_{B})/(120\cdot EI_{1}))-(\ell_{1}^4\cdot q_{A})/(30\cdot EI_{1})\\ b_{4} = (-(\ell_{1}^3\cdot q_{B})/(24\cdot EI_{1}))-(\ell_{1}^3\cdot q_{A})/(8\cdot EI_{1})\\ b_{5} = (-(\ell_{1}\cdot q_{B})/2)-(\ell_{1}\cdot q_{A})/2\\ b_{6} = M_{B}-(\ell_{1}^2\cdot q_{B})/6-(\ell_{1}^2\cdot q_{A})/3\\ b_{7} = 0\\ b_{8} = 0 \end{array}</math>~~<!-------------------------------------------------------------------------------->~~		::<math>\begin{array}{l} b_{1} = 0\\ b_{2} = 0\\ b_{3} = (-(\ell_{1}^4\cdot q_{B})/(120\cdot EI_{1}))-(\ell_{1}^4\cdot q_{A})/(30\cdot EI_{1})\\ b_{4} = (-(\ell_{1}^3\cdot q_{B})/(24\cdot EI_{1}))-(\ell_{1}^3\cdot q_{A})/(8\cdot EI_{1})\\ b_{5} = (-(\ell_{1}\cdot q_{B})/2)-(\ell_{1}\cdot q_{A})/2\\ b_{6} = M_{B}-(\ell_{1}^2\cdot q_{B})/6-(\ell_{1}^2\cdot q_{A})/3\\ b_{7} = 0\\ b_{8} = 0 \end{array}</math>.


	~~{{MyCodeBlock\|title=Prepare for Solver~~
	~~\|text=Text~~
	\|code=		\|code=
	<syntaxhighlight lang="lisp" line start=1>		<syntaxhighlight lang="lisp" line start=1>
	1+1		/* augmented coeff matrix */
			ACM: augcoefmatrix(BCs,ICs);
			AA : submatrix(ACM,9);
			bb : - col(ACM,9);

			for i: 1 thru 8 do
			print(simplode(["b[",i,"] = ", string(bb[i][1])]))$
			for i: 1 thru 8 do
			for j: 1 thru 8 do
			if not AA[i][j] = 0 then
			print(simplode(["A[",i,",",j,"] = ", string(AA[i][j])]))$
	</syntaxhighlight>		</syntaxhighlight>
	}}		}}

	==~~tmp==~~		<!-------------------------------------------------------------------------------->
			{{MyCodeBlock\|title=Solving
			\|text=
	Das Lösen des Gleichungssystems liefert		Das Lösen des Gleichungssystems liefert

	<math>\begin{array}{l} {{C}_{1,0}}=0,\\{{C}_{1,1}}=246.1 \; N {{m}^{2}},\\{{C}_{1,2}}=703.2\; N m,\\{{C}_{1,3}}=-2404.3\; N,\\{{C}_{2,0}}=127.6 \; N m^3,\\{{C}_{2,1}}=224.7\; N m^2,\\{{C}_{2,2}}=-979.8 \; N m,\\{{C}_{2,3}}=2101.8 N \end{array}</math>~~<!-------------------------------------------------------------------------------->~~		::<math>\begin{array}{l} {{C}_{1,0}}=0,\\{{C}_{1,1}}=246.1 \; N {{m}^{2}},\\{{C}_{1,2}}=703.2\; N m,\\{{C}_{1,3}}=-2404.3\; N,\\{{C}_{2,0}}=127.6 \; N m^3,\\{{C}_{2,1}}=224.7\; N m^2,\\{{C}_{2,2}}=-979.8 \; N m,\\{{C}_{2,3}}=2101.8 N \end{array}</math>.

	~~{{MyCodeBlock\|title=Solving~~
	~~\|text=Text~~
	\|code=		\|code=
	<syntaxhighlight lang="lisp" line start=1>		<syntaxhighlight lang="lisp" line start=1>
Zeile 226:		Zeile 231:
	}}		}}

	=~~=tmp=~~=		<!-------------------------------------------------------------------------------->
			{{MyCodeBlock\|title=Post-Processing
			\|text=
	Und die Ergebnisse können wir uns anschauen ...		Und die Ergebnisse können wir uns anschauen ...

Zeile 241:		Zeile 248:
	[[Datei:Kw98-24.png\|mini\|Querkraft ''Q(x)''\|alternativtext=\|ohne]]		[[Datei:Kw98-24.png\|mini\|Querkraft ''Q(x)''\|alternativtext=\|ohne]]

			====... für die Lager-Reaktionskräfte:====
			::<math>\begin{array}{l} {{A}_{z}}=2404.3 N,\\{{M}_{A}}=703.2 Nm,\\{{B}_{z}}=743.9 N,\\{{C}_{z}}=2101.8 N,\\{{M}_{C}}=-123.7 Nm\end{array}</math>

	~~<!-------------------------------------------------------------------------------->~~
	~~{{MyCodeBlock\|title=Post-Processing~~
	~~\|text=Text~~
	\|code=		\|code=
	<syntaxhighlight lang="lisp" line start=1>		<syntaxhighlight lang="lisp" line start=1>
	1+1		/* bearing forces and moments */
			reactForces: [A[z]=Q[1](0),
			M[A] = K[A]*Phi[1](0),
			B[z] = k[B]*w[2](0),
			C[z] = k[C]*w[2](l[2]),
			M[C] = M[2](l[2])];

			expand(subst(params,subst(sol, reactForces)));

			/* plot displacements */

			fcts: [[ w [1](x), w [2](x-l[1])],
			[Phi[1](x),Phi[2](x-l[1])],
			[ M [1](x), M [2](x-l[1])],
			[ Q [1](x), Q [2](x-l[1])]];
			facts: [EI[1]/(l[1]^4q[A]),EI[1]/(l[1]^3q[A]),1/(l[1]^2q[A]),1/(l[1]^1q[A])];
			subst(M[B]/l[1]^2,q[A],facts);
			textlabels : ["w(x)/(M[B]l^2/EI[1])→", "w'(x)/(M[B]l/EI[1])→", "M(x)/M[B]→", "Q(x)/(M[B]/l[1]→"];
			for i: 1 thru 4 do(
			f : expand(subst(simple,subst(xil[1],x,facts[i][subst(sol, fcts[i][1]),
			subst(sol, fcts[i][2])]))),
			f1 : f[1], f2 : f[2],
			toplot : [if xi<=1 then f1 else 0,
			if xi < 1 then 0 else f2],
			plot2d(toplot,[xi,0,1+subst(simple,l[2]/l[1])], [legend, "sec. I", "sec. II"],
			[gnuplot_preamble, "set yrange [] reverse"] ,
			[xlabel, "x/l[1] ->"],
			[ylabel, textlabels[i]]))$
	</syntaxhighlight>		</syntaxhighlight>
	}}		}}

Mechaniker am 31. März 2021 um 12:09 Uhr

2021-03-31T12:09:42Z

Änderungen zeigen

Mechaniker: /* Aufgabenstellung */

2021-03-31T12:05:20Z

Aufgabenstellung

Änderungen zeigen

Mechaniker: /* tmp */

2021-03-31T11:46:37Z

tmp

← Nächstältere Version		Version vom 31. März 2021, 11:46 Uhr
Zeile 65:		Zeile 65:
	====Aus Rand "A"====		====Aus Rand "A"====
	<table class="wikitable" style="background-color:white;">		<table class="wikitable" style="background-color:white;">
	<tr><td>[[Datei:~~Kw50~~-11A.png\|rahmenlos\|alternativtext=\|150px]]		<tr><td>[[Datei:Kw98-11A.png\|rahmenlos\|alternativtext=\|150px]]
	</td><td>''Geometrische Randbedingungen''		</td><td>''Geometrische Randbedingungen''

Zeile 79:		Zeile 79:
	====Aus Übergang "B"====		====Aus Übergang "B"====
	<table class="wikitable" style="background-color:white;">		<table class="wikitable" style="background-color:white;">
	<tr><td>[[Datei:~~Kw50~~-11B.png\|rahmenlos\|alternativtext=\|180px]]		<tr><td>[[Datei:Kw98-11B.png\|rahmenlos\|alternativtext=\|180px]]
	</td><td>''Geometrische Randbedingungen''		</td><td>''Geometrische Randbedingungen''
	# <math>w_1(\ell_1)=w_2(\ell_1)</math>		# <math>w_1(\ell_1)=w_2(\ell_1)</math>
Zeile 93:		Zeile 93:
	====Aus Rand "C"====		====Aus Rand "C"====
	<table class="wikitable" style="background-color:white;">		<table class="wikitable" style="background-color:white;">
	<tr><td>[[Datei:~~Kw50~~-11C.png\|rahmenlos\|alternativtext=\|170px]]		<tr><td>[[Datei:Kw98-11C.png\|rahmenlos\|alternativtext=\|170px]]
	</td><td>''Geometrische Randbedingungen''		</td><td>''Geometrische Randbedingungen''
	# <math>w_2(\ell)=0</math>		# <math>w_2(\ell)=0</math>

Mechaniker am 31. März 2021 um 11:45 Uhr

2021-03-31T11:45:42Z

Änderungen zeigen

Mechaniker: /* Aufgabenstellung */

2021-03-31T11:40:05Z

Aufgabenstellung

← Nächstältere Version		Version vom 31. März 2021, 11:40 Uhr
Zeile 84:		Zeile 84:
	</table>		</table>



			[[Datei:Kw98-11A.png\|rahmenlos]][[Datei:Kw98-11AB.png\|rahmenlos]][[Datei:Kw98-11B.png\|rahmenlos]][[Datei:Kw98-11BC.png\|rahmenlos]][[Datei:Kw98-11C.png\|rahmenlos]][[Datei:Kw98-21.png\|rahmenlos]][[Datei:Kw98-22.png\|rahmenlos]][[Datei:Kw98-23.png\|rahmenlos]][[Datei:Kw98-24.png\|rahmenlos]]

	<hr/>		<hr/>

Mechaniker am 31. März 2021 um 11:03 Uhr

2021-03-31T11:03:46Z

← Nächstältere Version		Version vom 31. März 2021, 11:03 Uhr
Zeile 1:		Zeile 1:
	j		[[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]]
			[[Category:Prinzip vom Minimum der Potentiellen Energie]]
			[[Category:Formänderungsenergie]]
			[[Category:Axiom]]
			[[Category:Biege-Belastung]][[Category:Membranspannung]]
			[[Category:Computer]]
			[[Category:Stab]][[Category:Dehnstab]]
			[[Category:Euler-Bernoulli-Balken]]
			[[Category:Timoshenko-Balken]]
			[[Category:Feder-Masse-System‎]]
			[[Category:Draft]]
			[[Category:Dynamik‎]][[Category:D’Alembertsches Prinzip]]
			[[Category:Eigenvektor]][[Category:Eigenwert]][[Category:Eigenwertproblem‎]]
			[[Category:Englisch]]
			[[Category:Fehlerquadratsumme]]
			[[Category:Finite-Elemente-Methode‎]][[Category:Rayleigh-Ritz-Prinzip]][[Category:Finite-Differenzen-Methode]]
			[[Category:Floquet-Theorem]]
			[[Category:Freischneiden]]
			[[Category:Fundamentalmatrix]]
			[[Category:Geometrische Zwangsbedingung]]
			[[Category:Haften und Reiben]]
			[[Category:Hauptspannung]]
			[[Category:Innovation]]
			[[Category:Kennlinie]]
			[[Category:Knotenpunktverfahren]]
			[[Category:Koordinaten‎]]
			[[Category:Lagrange-Multiplikator]]
			[[Category:Lernvideo]]
			[[Category:Mathieusche Differentialgleichung]]
			[[Category:Matlab‎]]
			[[Category:Maxima‎]]
			[[Category:Mechatronik]]
			[[Category:Modalanalyse]]
			[[Category:Newtonverfahren]][[Category:Runge-Kutta-Verfahren‎]]
			[[Category:Nichtlineare Schwingungen]][[Category:Parametererregte Schwingungen]]
			[[Category:Schwingungen von Kontinua‎]]
			[[Category:Smartphone]]
			[[Category:Stabilität]]
			[[Category:Stabwerk]]
			[[Category:Starrer Körper]]
			[[Category:Statik]]
			[[Category:Stick-Slip-Effekt]]
			[[Category:Totzeit]]

			==Aufgabenstellung==
			SOME TEXT

			<onlyinclude>
			[[Datei:Screenshot 20210111-063733~2.png\|100px\|left\|mini\|Caption]]
			Gesucht ist "SOME EXPLANATION"
			</onlyinclude>

			== Lösung mit Maxima ==
			Lorem Ipsum ....

			==tmp==
			<!-------------------------------------------------------------------------------->
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			<table class="wikitable" style="background-color:white; float: left; margin-right:14px;
			">
			<tr><th></th><th></th></tr>
			<tr><td></td><td></td></tr>
			</table>


			<hr/>
			'''Links'''
			* ...

			'''Literature'''
			* ...