| Original Message (ID '126334') By Julius: |
| Ck[n_] := Table[ck[i], {i, n}]
\[Phi]k[n_] := Table[Sin[(2 i - 1) \[Pi] x/L], {i, 1, n}]
v[n_] := Ck[n].\[Phi]k[n]
\[Theta][n_] := Ck[n].\[Phi]k[n]
\[CapitalPi][n_] := 1/2 \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(L\)]\(\((
\*SubscriptBox[\(EI\), \(z\)]
\*SuperscriptBox[\((
\*SubscriptBox[\(\[PartialD]\), \(x, x\)]v[n])\), \(2\)] +
\*SubscriptBox[\(GI\), \(T\)]
\*SuperscriptBox[\((
\*SubscriptBox[\(\[PartialD]\), \(x\)]\[Theta][n])\), \(2\)] +
\*SubscriptBox[\(EI\), \(\[Omega]\)]
\*SuperscriptBox[\((
\*SubscriptBox[\(\[PartialD]\), \(x, x\)]\[Theta][
n])\), \(2\)])\) \[DifferentialD]x\)\) + 4 \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(L\)]\(\((
\*OverscriptBox[\(\[CapitalMu]\), \(_\)]*\((
\*FractionBox[\(x\), \(L\)] -
\*FractionBox[
SuperscriptBox[\(x\), \(2\)],
SuperscriptBox[\(L\), \(2\)]])\)*\((\[Theta][n] \((
\*SubscriptBox[\(\[PartialD]\), \(x, x\)]v[n])\) +
\*SubscriptBox[\(\[Beta]\), \(z\)]
\*SuperscriptBox[\((
\*SubscriptBox[\(\[PartialD]\), \(x\)]\[Theta][
n])\), \(2\)])\))\) \[DifferentialD]x\)\) + 1/2 \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(L\)]\(\((
\*OverscriptBox[\(\[CapitalMu]\), \(_\)]*\((
\*FractionBox[\(8\),
SuperscriptBox[\(L\), \(2\)]])\)
\*SubscriptBox[\(e\), \(z\)]
\*SuperscriptBox[\((\[Theta][n])\), \(2\)])\) \[DifferentialD]x\)\)
Subscript[k, bb][n_] := 1/2 \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(L\)]\(\((
\*SubscriptBox[\(EI\), \(z\)]
\*SuperscriptBox[\((
\*SubscriptBox[\(\[PartialD]\), \(x, x\)]v[
n])\), \(2\)])\) \[DifferentialD]x\)\)
Subscript[k, cc][n_] := 1/2 \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(L\)]\(\((
\*SubscriptBox[\(GI\), \(T\)]
\*SuperscriptBox[\((
\*SubscriptBox[\(\[PartialD]\), \(x\)]\[Theta][n])\), \(2\)] +
\*SubscriptBox[\(EI\), \(\[Omega]\)]
\*SuperscriptBox[\((
\*SubscriptBox[\(\[PartialD]\), \(x, x\)]\[Theta][
n])\), \(2\)])\) \[DifferentialD]x\)\) + 4 \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(L\)]\(\((
\*OverscriptBox[\(\[CapitalMu]\), \(_\)]*\((
\*FractionBox[\(x\), \(L\)] -
\*FractionBox[
SuperscriptBox[\(x\), \(2\)],
SuperscriptBox[\(L\), \(2\)]])\)*\((
\*SubscriptBox[\(\[Beta]\), \(z\)]
\*SuperscriptBox[\((
\*SubscriptBox[\(\[PartialD]\), \(x\)]\[Theta][
n])\), \(2\)])\))\) \[DifferentialD]x\)\) + 1/2 \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(L\)]\(\((
\*OverscriptBox[\(\[CapitalMu]\), \(_\)]*\((
\*FractionBox[\(8\),
SuperscriptBox[\(L\), \(2\)]])\)
\*SubscriptBox[\(e\), \(z\)]
\*SuperscriptBox[\((\[Theta][n])\), \(2\)])\) \[DifferentialD]x\)\)
Subscript[k, bc][n_] := 4 \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(L\)]\(\((
\*OverscriptBox[\(\[CapitalMu]\), \(_\)]*\((
\*FractionBox[\(x\), \(L\)] -
\*FractionBox[
SuperscriptBox[\(x\), \(2\)],
SuperscriptBox[\(L\), \(2\)]])\)*\((\[Theta][n] \((
\*SubscriptBox[\(\[PartialD]\), \(x, x\)]v[
n])\))\))\) \[DifferentialD]x\)\)
k1[n_] := Sum[\!\(
\*SubscriptBox[\(\[PartialD]\), \(ck[i]\)]\(
\(\*SubscriptBox[\(k\), \(bb\)]\)[n]\)\), {i, n}]
k3[n_] := Sum[\!\(
\*SubscriptBox[\(\[PartialD]\), \(ck[i]\)]\(
\(\*SubscriptBox[\(k\), \(cc\)]\)[n]\)\), {i, n}]
k2[n_] := Sum[(\!\(
\*SubscriptBox[\(\[PartialD]\), \(ck[i]\)]\(
\(\*SubscriptBox[\(k\), \(bc\)]\)[n]\)\)), {i, n}]
m[n_] := ( {
{k1[n], k2[n]/2},
{k2[n]/2, k3[n]}
} )
matrix[n_] := Table[Coefficient[m[n][[i]], ck[n]], {i, n}]
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