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Cell[TextData[{ "From equilibrium:\n", Cell[BoxData[ \(TraditionalForm\`\[PartialD]\_\(x\_1\)\[Sigma]\_11 = 0\)]], " \[Implies] ", Cell[BoxData[ \(TraditionalForm\`\(\(\[Sigma]\_11 = \ C\)\(,\)\)\)]], " b.c.: ", Cell[BoxData[ FormBox[ RowBox[{\(\(\[Sigma]\_11\)(\(-w\)\/2, x\_2, x\_3)\), " ", "=", " ", RowBox[{\(0\ \[Implies] C\), " ", "=", " ", RowBox[{"0", Cell[""]}]}]}], TraditionalForm]]], "\n\[DoubleLongRightArrow]" }], "Subtitle", FontSize->18], Cell[BoxData[ \(\(\[Sigma]\_11 = 0;\)\)], "Input", FontSize->18] }, Open ]], Cell[CellGroupData[{ Cell[" Similarly (from the plane stress condition)", "Subtitle", FontSize->18], Cell[BoxData[ \(\(\[Sigma]\_22 = 0;\)\)], "Input", FontSize->18] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\[PartialD]\_\(x\_3\)\[Sigma]\_33 = 0\)]], " \n\nConstitutive:\n", Cell[BoxData[ \(TraditionalForm\`\[Epsilon]\_33 = \ \(1\/E\)[\[Sigma]\_33 - \[Nu]\ \ \((0 + 0)\)]\)]], "\n\nThen:\n", Cell[BoxData[ \(TraditionalForm\`\[PartialD]\_\(x\_3\)\((E\ \[Epsilon]\_33)\)\ = \ \ \(0\ \[DoubleLongRightArrow]\ \[Epsilon]\_33 = \ \(\[PartialD]\_\(x\_3\)u\_3 \ = c\)\)\)]] }], "Subtitle", FontSize->18], Cell[BoxData[ \(\(u\_3 = c\ x\_3 + d;\)\)], "Input", FontSize->18] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "\tThe bondary conditions are:\n\n", Cell[BoxData[ \(TraditionalForm\`u\_3[L\/2]\ = \ \(c\ L\/2 + d\ = \ 0\)\)]], "\n", Cell[BoxData[ \(TraditionalForm\`u\_3[\(-L\)\/2]\ = \ \(\(-c\)\ L\/2 + d\ = \ \[Delta]\)\)]] }], "Subtitle", FontSize->18], Cell[BoxData[{ \(\(rules\ = \ \ Solve[{c\ L\/2 + d\ \[Equal] 0, \ \(-c\)\ L\/2 + d\ \[Equal] \[Delta]}, {c, d}] // Flatten;\)\), "\[IndentingNewLine]", \(\(sol\ = \ u\_3 /. \ rules;\)\ (*\ this\ auxiliary\ step\ avoids\ infinite\ recursion\ *) \), "\ \[IndentingNewLine]", \(\(u\_3\ = \ sol;\)\)}], "Input", FontSize->18], Cell[BoxData[{ \(\(\[Epsilon]\_33 = \ \[PartialD]\_\(x\_3\)u\_3;\)\), "\ \[IndentingNewLine]", \(\(\(\[Sigma]\_33 = \ EE\ \[Epsilon]\_33;\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(\[Epsilon]\_11 = \ \(\[Epsilon]\_22 = \ \(-\[Nu]\)\ \[Epsilon]\_33\);\ \)\)}], "Input", FontSize->18] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\[Epsilon]\_11 = \ \(\[PartialD]\_\(x\_1\)u\_1\ = \ \ \(-\[Nu]\)\ \[Epsilon]\_33\)\)]], "\n", Cell[BoxData[ \(u\_1 = \ \(\[Epsilon]\_11\) x\_1 + \ d\)]], "\nThe boundary condition is:\n", Cell[BoxData[ \(TraditionalForm\`u\_1\ = \ \(0\ at\ x\_1 = \ 0\)\)]], " \[Implies] d = 0" }], "Subtitle", FontSize->18], Cell[BoxData[ \(\(u\_1 = \ \(\[Epsilon]\_11\) x\_1;\)\)], "Input", FontSize->18] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\[Epsilon]\_22 = \ \(\[PartialD]\_\(x\_2\)u\_2\ = \ \ \(-\[Nu]\)\ \[Epsilon]\_22\)\)]], "\n", Cell[BoxData[ \(u\_2 = \ \(\[Epsilon]\_22\) x\_2 + \ d\)]], "\nThe boundary condition is:\n", Cell[BoxData[ \(TraditionalForm\`u\_2\ = \ \(0\ at\ x\_2 = \ 0\)\)]], " \[Implies] d = 0" }], "Subtitle", FontSize->18], Cell[BoxData[ \(\(u\_2 = \ \(\[Epsilon]\_22\) x\_2;\)\)], "Input", FontSize->18], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{" ", RowBox[{\({u\_1, u\_2, u\_3} // MatrixForm\), "\[IndentingNewLine]", RowBox[{ RowBox[{"(", GridBox[{ {\(\[Epsilon]\_11\), \(\[Epsilon]\_12\), \(\[Epsilon]\_12\)}, {\(\[Epsilon]\_12\), \(\[Epsilon]\_22\), \(\[Epsilon]\_23\)}, {\(\[Epsilon]\_13\), \(\[Epsilon]\_23\), \(\[Epsilon]\_33\)} }], ")"}], "//", "MatrixForm"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"(", GridBox[{ {\(\[Sigma]\_11\), \(\[Sigma]\_12\), \(\[Sigma]\_12\)}, {\(\[Sigma]\_12\), \(\[Sigma]\_22\), \(\[Sigma]\_23\)}, {\(\[Sigma]\_13\), \(\[Sigma]\_23\), \(\[Sigma]\_33\)} }], ")"}], "//", "MatrixForm"}]}]}]], "Input", FontSize->18], Cell[BoxData[ InterpretationBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(\(\[Delta]\ \[Nu]\ x\_1\)\/L\)}, {\(\(\[Delta]\ \[Nu]\ x\_2\)\/L\)}, {\(\[Delta]\/2 - \(\[Delta]\ x\_3\)\/L\)} }], "\[NoBreak]", ")"}], MatrixForm[ { Times[ Power[ L, -1], \[Delta], \[Nu], Subscript[ x, 1]], Times[ Power[ L, -1], \[Delta], \[Nu], Subscript[ x, 2]], Plus[ Times[ Rational[ 1, 2], \[Delta]], Times[ -1, Power[ L, -1], \[Delta], Subscript[ x, 3]]]}]]], "Output", FontSize->18], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(\(\[Delta]\ \[Nu]\)\/L\), "0", "0"}, {"0", \(\(\[Delta]\ \[Nu]\)\/L\), "0"}, {"0", "0", \(-\(\[Delta]\/L\)\)} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output", FontSize->18], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", "0", "0"}, {"0", "0", "0"}, {"0", "0", \(-\(\(EE\ \[Delta]\)\/L\)\)} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output", FontSize->18] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "b) Plane strain conditions:\nThe only things that change are:\n\n", Cell[BoxData[ \(TraditionalForm\`\[Sigma]\_22\)]], "\[NotEqual]0, ", Cell[BoxData[ \(TraditionalForm\`\[Epsilon]\_22 = \ 0\)]], "\n\nUse this in the constitutive equation in compliance form for ", Cell[BoxData[ \(TraditionalForm\`\[Epsilon]\_22\)]], ":\n\n", Cell[BoxData[ \(TraditionalForm\`\[Epsilon]\_\(\(22\)\(\ \)\) = \ \(0\ = \ \(1\/EE\) \ \((\[Sigma]\_22 - \ \[Nu]\ \((\[Sigma]\_11 + \ \[Sigma]\_33)\))\)\)\)]], " \[Implies] ", Cell[BoxData[ \(TraditionalForm\`\[Sigma]\_22 = \ \[Nu]\ \((\ \[Sigma]\_11 + \ \ \[Sigma]\_33)\)\)]], "\n\n", Cell[BoxData[ \(TraditionalForm\`\(\(\[Sigma]\_11 = \ 0\)\(,\)\(\ \)\)\)]], "as before\n\nreplace ", Cell[BoxData[ \(TraditionalForm\`\[Sigma]\_22\)]], "in constitutive equation for ", Cell[BoxData[ \(TraditionalForm\`\(\(\[Epsilon]\_33\)\(:\)\)\)]], "\n\n", Cell[BoxData[ \(TraditionalForm\`\[Epsilon]\_33 = \ \(\(1\/EE\) \((\[Sigma]\_33 - \ \ \[Nu]\ \[Sigma]\_22)\)\ = \ \(\(1\/EE\) \((\[Sigma]\_33 - \ \(\[Nu]\^2\) \ \[Sigma]\_33)\)\ = \ \(\((1 - \[Nu]\^2)\)\/EE\) \[Sigma]\_33\)\)\)]], "\n\nWe note that this gives a stiffer behavior, since the factor in \ parenthesis is smaller than \"1\". \nNote that from here on the solution is \ the same as in a) but with\n", Cell[BoxData[ \(TraditionalForm\`\[Epsilon]\_33\)]], "= ", Cell[BoxData[ \(TraditionalForm\`\(\((1 - \[Nu]\^2)\)\/EE\) \[Sigma]\_33\)]], ", instead of ", Cell[BoxData[ \(TraditionalForm\`\[Epsilon]\_33\)]], "= ", Cell[BoxData[ \(TraditionalForm\`\(1\/EE\) \[Sigma]\_33\)]], "\nSo we can infer the solution by replacing E with ", Cell[BoxData[ \(TraditionalForm\`E\/\(1 - \[Vee]\^2\)\)]], "\n" }], "Subtitle", FontSize->18], Cell[BoxData[{ \(\(\[Sigma]\_\(\(33\)\(\ \ \)\) = \(EE\/\(1 - \[Nu]\^2\)\) \ \[Epsilon]\_33;\)\), "\[IndentingNewLine]", \(\(\[Sigma]\_22 = \ \[Nu]\ \[Sigma]\_33;\)\)}], "Input", FontSize->18], Cell[BoxData[ \(\(\(\ \)\(\[Epsilon]\_11 = \ Simplify[\(-\[Nu]\)\/EE\ \((\[Sigma]\_22 + \[Sigma]\_33)\)]; \ u\_1 = \ \(\[Epsilon]\_11\) x\_1; \[Sigma]\_11 = \ 0;\[IndentingNewLine] \(\(u\_2 = \ 0\)\(;\)\(\ \)\(\(\[Epsilon]\_22 = \ 0\)\(\ \)\)\(;\)\(\ \)\)\)\)\)], "Input", FontSize->18], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{" ", RowBox[{\({u\_1, u\_2, u\_3} // MatrixForm\), "\[IndentingNewLine]", RowBox[{ RowBox[{"(", GridBox[{ {\(\[Epsilon]\_11\), \(\[Epsilon]\_12\), \(\[Epsilon]\_12\)}, {\(\[Epsilon]\_12\), \(\[Epsilon]\_22\), \(\[Epsilon]\_23\)}, {\(\[Epsilon]\_13\), \(\[Epsilon]\_23\), \(\[Epsilon]\_33\)} }], ")"}], "//", "MatrixForm"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"(", GridBox[{ {\(\[Sigma]\_11\), \(\[Sigma]\_12\), \(\[Sigma]\_12\)}, {\(\[Sigma]\_12\), \(\[Sigma]\_22\), \(\[Sigma]\_23\)}, {\(\[Sigma]\_13\), \(\[Sigma]\_23\), \(\[Sigma]\_33\)} }], ")"}], "//", "MatrixForm"}]}]}]], "Input", FontSize->18], Cell[BoxData[ InterpretationBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(\(\[Delta]\ \[Nu]\ x\_1\)\/\(L - L\ \[Nu]\)\)}, {"0"}, {\(\(\[Delta]\ \((L\/2 - x\_3)\)\)\/L\)} }], "\[NoBreak]", ")"}], MatrixForm[ { Times[ \[Delta], \[Nu], Power[ Plus[ L, Times[ -1, L, \[Nu]]], -1], Subscript[ x, 1]], 0, Times[ Power[ L, -1], \[Delta], Plus[ Times[ Rational[ 1, 2], L], Times[ -1, Subscript[ x, 3]]]]}]]], "Output", FontSize->18], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(\(\[Delta]\ \[Nu]\)\/\(L - L\ \[Nu]\)\), "0", "0"}, {"0", "0", "0"}, {"0", "0", \(-\(\[Delta]\/L\)\)} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output", FontSize->18], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", "0", "0"}, {"0", \(-\(\(EE\ \[Delta]\ \[Nu]\)\/\(L\ \((1 - \[Nu]\^2)\)\)\)\), "0"}, {"0", "0", \(-\(\(EE\ \[Delta]\)\/\(L\ \((1 - \[Nu]\^2)\)\)\)\)} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output", FontSize->18] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Question 2: Problem 4.4 from textbook\n\nFor bar:\n", Cell[BoxData[ \(TraditionalForm\`U\_0 = \ \(1\/2\) \[Sigma]\)]], "\[Epsilon] = ", Cell[BoxData[ \(TraditionalForm\`\(1\/2\) E\ \[Epsilon]\^2\)]], "= ", Cell[BoxData[ \(TraditionalForm\`\(1\/2\) E\ \((du\/dx)\)\^2\)]], "\n", Cell[BoxData[ \(TraditionalForm\`U\_bar\)]], " = ", Cell[BoxData[ \(TraditionalForm\`\[Integral]\_V\( U\_0\) dV\)]], "= ", Cell[BoxData[ \(TraditionalForm\`\[Integral]\_0\^L E\)]], "A ", Cell[BoxData[ \(TraditionalForm\`1\/2\ \((du\/dx)\)\^2\)]], "dx\n\nFor spring:\n", Cell[BoxData[ \(TraditionalForm\`U\_spring = \ \(1\/2\) k\ \(u(L)\)\^2\)]], "\n\nU = ", Cell[BoxData[ \(TraditionalForm\`U\_bar + \ U\_spring\)]], "= ", Cell[BoxData[ \(TraditionalForm\`\[Integral]\_0\^L E\)]], "A ", Cell[BoxData[ \(TraditionalForm\`1\/2\ \((du\/dx)\)\^2\)]], "dx + ", Cell[BoxData[ \(TraditionalForm\`\(1\/2\) k\ \(u(L)\)\^2\)]], "\n\nExternal work:\n\n", Cell[BoxData[ \(TraditionalForm\`W\_ext = \ P\ \(u(L)\)\ + \ \[Integral]\_V\( f(x)\)\/A\ \(u(x)\)\ dV\)]], "= P u(L) + ", Cell[BoxData[ \(TraditionalForm\`\(A\/A\) \(\[Integral]\_0\^L\( f(x)\)\ \(u( x)\)\ dx\)\)]], "\n\n", Cell[BoxData[ \(TraditionalForm\`W\_ext\)]], "= P u(L) + ", Cell[BoxData[ \(TraditionalForm\`\(A\/A\) \(\[Integral]\_0\^L\( f(x)\)\ \(u( x)\)\ dx\)\)]], "\n\n" }], "Subtitle", FontSize->18], Cell[TextData[{ "\nQuestion 3: Problem 4.6 from textbook\n\nU = ", Cell[BoxData[ \(TraditionalForm\`\[Integral]\_V\( 1\/2\) \(\[Sigma]\_ij\) \(\[Epsilon]\_ij\) \ \[DifferentialD]V\)]], "\n\nWe consider the contributions from bending :\n", Cell[BoxData[ \(TraditionalForm\`\[Sigma]\_11 = \ \(-\(M(x\_1)\)\)\/I\ x\_3, \ \ \[Epsilon]\_11 = \ \[Sigma]\_11\/E\)]], "= ", Cell[BoxData[ \(TraditionalForm\`\(-\(M(x\_1)\)\)\/EI\ x\_3\)]], "\n", Cell[BoxData[ \(TraditionalForm\`U\^b = \ 1\/2\)]], Cell[BoxData[ \(TraditionalForm\`\[Integral]\_V\( 1\/2\) \(\[Sigma]\_11\) \(\[Epsilon]\_11\) \[DifferentialD]V\ \ = \ \(\(1\/2\) \(\[Integral]\_V\ \(x\_3\^2\) \(\(M(x\_1)\)\^2\/EI\^2\) dV\)\ = \ \(1\/2\) \(\[Integral]\_0\%L\(\[Integral]\_A\( \ x\_3\^2\) dA\ \(\(M(x\_1)\)\^2\/EI\^2\) \[DifferentialD]x\_1\)\)\)\)]], "\n\n", Cell[BoxData[ \(TraditionalForm\`U\^b = \(1\/2\) \(\[Integral]\_0\%L\ \ \(\(M(x\_1)\)\^2\/EI\) \(\(\[DifferentialD]x\_1\)\(\ \)\)\)\)]], "\n\nand the contribution from shear:\n\nfrom equilibrium:\n", Cell[BoxData[ \(TraditionalForm\`\[Sigma]\_\(11, 1\) + \ \[Sigma]\_\(31, 3\) = \ 0\)]], "\n", Cell[BoxData[ \(TraditionalForm\`\[Sigma]\_\(31, 3\) = \(M' \((x\_1)\)\)\/I\ \ x\_3\)]], ", also from equilibrium ", Cell[BoxData[ \(TraditionalForm\`M' \((x\_1)\)\)]], "= ", Cell[BoxData[ \(TraditionalForm\`\(\(V\)\((\)\(x\_\(\(1\)\()\)\)\)\)\)]], ", the shear force.\n", Cell[BoxData[ \(TraditionalForm\`\[Sigma]\_31\)]], "= ", Cell[BoxData[ \(TraditionalForm\`\(V(x\_1)\)\/\(2 I\)\ \((x\_3\^2 - \ h\^\(\(2\)\(\ \)\))\)\)]], ", where we have also applied the boundary condition ", Cell[BoxData[ \(TraditionalForm\`\(\(\[Sigma]\_31\)\(=\)\(\ \)\(0\)\(\ \)\)\)]], "\nat ", Cell[BoxData[ \(TraditionalForm\`x\_3 = \ h\)]], " (assume h is half the height of the rectangular beam of dimensions b,2h)\n\ \n", Cell[BoxData[ \(TraditionalForm\`\(\(U\^s\)\(=\)\(\ \)\)\)]], Cell[BoxData[ \(TraditionalForm\`\(1\/2\) \(\[Integral]\_V\((\(\[Sigma]\_13\) \ \[Sigma]\_13\/\(2 G\) + \ \(\[Sigma]\_31\) \[Sigma]\_31\/\(2 G\))\)\ dV\)\ \ = \(\(1\/2\) \(\[Integral]\_V\( \[Sigma]\_13\) \[Sigma]\_13\/G\ dV\)\ = \ \ \(1\/2\) \(\[Integral]\_V\( 1\/G\) \((\(V(x\_1)\)\/\(2 I\)\ \((x\_3\^2 - \ \ h\^\(\(2\)\(\ \)\))\))\)\^2\ dV\)\)\)]], "\n= ", Cell[BoxData[ \(TraditionalForm\`\(1\/2\) \(\[Integral]\_0\%L\(\( V(x\_1)\)\^2\/\(4 G\)\) \(1\/I\^2\) \(\[Integral]\_\(-h\)\%h b\ \(\((x\_3\^2 - \ h\^\(\(2\)\(\ \)\))\)\^2\) \[DifferentialD]x\_\(\(3\)\ \(\ \)\)\ \[DifferentialD]x\_1\)\)\)]], "\nIn this expression:\n" }], "Subtitle", FontSize->18], Cell[CellGroupData[{ Cell[BoxData[{\(Ii\ = \ \[Integral]\_\(-h\)\%h b\ \(x\^2\) \[DifferentialD]x\), "\[IndentingNewLine]", FormBox[\(geomFactor\ = \ \[Integral]\_\(-h\)\%h b\ \(\((x\_3\^2 - \ h\^\(\(2\)\(\ \)\))\)\^2\) \[DifferentialD]x\_\(\(3\)\(\ \ \)\)\), "TraditionalForm"], "\[IndentingNewLine]", \(geomFactor\/Ii\^2\)}], \ "Input", FontSize->18], Cell[BoxData[ \(\(2\ b\ h\^3\)\/3\)], "Output", FontSize->18], Cell[BoxData[ \(\(16\ b\ h\^5\)\/15\)], "Output", FontSize->18], Cell[BoxData[ \(12\/\(5\ b\ h\)\)], "Output", FontSize->18] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "that is:\n", Cell[BoxData[ \(TraditionalForm\`\(\(U\^s\)\(=\)\(\ \)\)\)]], Cell[BoxData[ \(TraditionalForm\`\(1\/2\) \(\[Integral]\_0\%L\(\( V(x\_1)\)\^2\/\(4 G\)\) 12\/\(5\ A\)\ \[DifferentialD]x\_1\)\)]], "\nwhere A = bh is the area of the cross section.\nTherefore:\n", Cell[BoxData[ \(TraditionalForm\`U\^s = \ \(1\/2\) \(\[Integral]\_0\%L\( 12 \( \ V(x\_1)\)\^2\)\/\(20\ GA\)\ \[DifferentialD]x\_1\)\)]], "\n\nFor this specific problem:\n", Cell[BoxData[ FormBox[ RowBox[{ FormBox[\(\(M(x\_1)\)\(\ \)\(=\)\(\ \)\), "TraditionalForm"], \(2\/3\), "P", " ", \(x\_1\), " "}], TraditionalForm]]], " if ", Cell[BoxData[ \(TraditionalForm\`0\ < x\_1 < \ 0.5\ L\)]], "\n\t=", Cell[BoxData[ \(TraditionalForm\`\(\(1\/3\) \(P\)\(\ \)\((1.5 L\ - x\_1)\)\(\ \ \ \)\)\)]], "if ", Cell[BoxData[ \(TraditionalForm\`0.5\ L\ < x\_1 < \ 1.5\ L\)]], "\n\tThis can be conveniently expressed in ", StyleBox["Mathematica", FontSlant->"Italic"], " as:" }], "Subtitle", FontSize->18], Cell[CellGroupData[{ Cell[BoxData[{ \(\(F\_0 = \ 12000;\)\), "\[IndentingNewLine]", \(\(L\ = \ 1;\)\), "\[IndentingNewLine]", \(\(Eb\ = \ 205\ 10\^9;\)\), "\[IndentingNewLine]", \(\(\[Nu]b = \ 0.3;\)\), "\[IndentingNewLine]", \(Gb\ = \ Eb\/\(2\ \((1 + \[Nu]b)\)\)\), "\[IndentingNewLine]", \(\(Ib\ = \ 0.2604\ 10\^\(-6\);\)\), "\[IndentingNewLine]", \(Ab\ = \ 3\/50\ \(10\^4\) Ib; \ (*\ this\ value\ modified\ to\ something\ more\ reasonable\ *) \[IndentingNewLine]M = \ Which[0\ < \ x\ < \ 0.5\ L, \(2\/3\) F\_0\ x, 0.5\ L\ < \ x\ < \ 1.5\ L, \ \(1\/3\) F\_0\ \((1.5\ L\ - \ x)\), True, 0];\), "\[IndentingNewLine]", \(\[PartialD]\_x M\)}], "Input", FontSize->18], Cell[BoxData[ RowBox[{\(General::"spell1"\), \(\(:\)\(\ \)\), "\<\"Possible spelling \ error: new symbol name \\\"\\!\\(\[Nu]b\\)\\\" is 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CellGroupingRules->{"SectionGrouping", 40}, PageBreakBelow->False, CellFrameMargins->{{0, 4}, {8, 4}}, CellFrameColor->RGBColor[0.4, 0, 0.239994], InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, -0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica", "webMathematica"->FormBox[ RowBox[ {"web", AdjustmentBox[ StyleBox[ "Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, CounterIncrements->"Section", CounterAssignments->{{"Subsection", 0}, {"Subsubsection", 0}}, FontFamily->"Helvetica", FontSize->18, FontWeight->"Bold"], Cell[StyleData["Section 1", "Presentation"], CellMargins->{{20, 10}, {6, 30}}, CellFrameMargins->5], Cell[StyleData["Section 1", "Printout"], CellMargins->{{18, 30}, {4, 30}}, CellFrameMargins->4, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Section"], CellFrame->{{0, 0}, {0, 0.25}}, CellMargins->{{18, 10}, {10, 30}}, CellGroupingRules->{"SectionGrouping", 40}, PageBreakBelow->False, CellFrameMargins->4, CellFrameColor->RGBColor[0.4, 0, 0.239994], InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, -0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica", "webMathematica"->FormBox[ RowBox[ {"web", AdjustmentBox[ StyleBox[ "Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, CounterIncrements->"Section", CounterAssignments->{{"Subsection", 0}, {"Subsubsection", 0}}, FontFamily->"Helvetica", FontSize->18, FontWeight->"Bold"], Cell[StyleData["Section", "Presentation"], CellMargins->{{20, 10}, {0, 30}}], Cell[StyleData["Section", "Printout"], CellMargins->{{18, 30}, {0, 30}}, CellFrameMargins->5, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsection"], CellDingbat->"\[FilledSquare]", CellMargins->{{38, 30}, {2, 20}}, CellGroupingRules->{"SectionGrouping", 50}, PageBreakBelow->False, InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, -0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica", "webMathematica"->FormBox[ RowBox[ {"web", AdjustmentBox[ StyleBox[ "Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, CounterIncrements->"Subsection", CounterAssignments->{{"Subsubsection", 0}}, FontFamily->"Times", FontSize->14, FontWeight->"Bold"], Cell[StyleData["Subsection", "Presentation"], CellMargins->{{35, 30}, {0, 20}}], Cell[StyleData["Subsection", "Printout"], CellMargins->{{18, 30}, {0, 10}}, FontSize->12] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubsection"], CellDingbat->"\[FilledSmallSquare]", CellMargins->{{55, 30}, {4, 10}}, CellGroupingRules->{"SectionGrouping", 60}, PageBreakBelow->False, InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, -0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica", "webMathematica"->FormBox[ RowBox[ {"web", AdjustmentBox[ StyleBox[ "Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, CounterIncrements->"Subsubsection", FontFamily->"Times", FontSize->12, FontWeight->"Bold"], Cell[StyleData["Subsubsection", "Presentation"], CellMargins->{{31, 30}, {0, 12}}], Cell[StyleData["Subsubsection", "Printout"], CellMargins->{{18, 30}, {0, 12}}, FontSize->10] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Styles for Body Text", "Section"], Cell[CellGroupData[{ Cell[StyleData["Text"], CellMargins->{{55, 10}, {6, 6}}, InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, -0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica", "webMathematica"->FormBox[ RowBox[ {"web", AdjustmentBox[ StyleBox[ "Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, TextJustification->1, Hyphenation->True, LineSpacing->{1, 2}, FontFamily->"Times"], Cell[StyleData["Text", "Presentation"], CellMargins->{{20, 10}, {6, 6}}, TextAlignment->Left, TextJustification->0, LineSpacing->{1.3, 0}, FontSize->14], Cell[StyleData["Text", "Printout"], CellMargins->{{18, 4}, {4, 4}}, LineSpacing->{1, 3}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Commentary"], CellMargins->{{55, 10}, {2, 6}}, TextJustification->1, Hyphenation->True, LineSpacing->{1, 2}, FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 0.4]], Cell[StyleData["Commentary", "Presentation"], CellMargins->{{60, 30}, {2, 6}}, TextJustification->1, LineSpacing->{1.3, 0}, FontSize->12], Cell[StyleData["Commentary", "Printout"], CellMargins->{{18, 30}, {3, 0}}, LineSpacing->{1, 3}, FontFamily->"Times", FontSize->10] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Styles for Input/Output", "Section"], Cell["\<\ The cells in this section define styles used for input and output \ to the kernel. Be careful when modifying, renaming, or removing these \ styles, because the front end associates special meanings with these style \ names.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Input"], CellFrame->{{1, 1}, {0, 1}}, CellMargins->{{55, 10}, {0, 0}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelPositioning->Automatic, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, LinebreakAdjustments->{0.85, 2, 10, 0, 1}, FontSize->12, FontWeight->"Bold", Background->GrayLevel[0.966674]], Cell[StyleData["Input", "Presentation"], CellMargins->{{60, 10}, {0, 10}}, Background->GrayLevel[0.850004]], Cell[StyleData["Input", "Printout"], CellMargins->{{55, 10}, {0, 10}}, LinebreakAdjustments->{0.85, 2, 10, 1, 1}, FontSize->10, Background->GrayLevel[0.850004]] }, Open ]], Cell[StyleData["InlineInput"], Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, DefaultFormatType->DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, CounterIncrements->"Input", FontWeight->"Bold"], Cell[CellGroupData[{ Cell[StyleData["Output"], CellFrame->{{1, 1}, {1, 0}}, CellMargins->{{55, 10}, {15, 0}}, CellEditDuplicate->True, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", FormatType->InputForm, FontSize->12, Background->GrayLevel[0.850004]], Cell[StyleData["Output", "Presentation"], CellMargins->{{60, Inherited}, {10, 0}}], Cell[StyleData["Output", "Printout"], CellMargins->{{55, Inherited}, {10, 0}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["InputOnly"], CellFrame->1, CellMargins->{{55, 10}, {15, 0}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelPositioning->Automatic, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, LinebreakAdjustments->{0.85, 2, 10, 0, 1}, FontSize->12, FontWeight->"Bold", Background->GrayLevel[0.966674]], Cell[StyleData["InputOnly", "Presentation"], CellMargins->{{60, Inherited}, {10, 10}}], Cell[StyleData["InputOnly", "Printout"], CellMargins->{{55, Inherited}, {10, 10}}, LinebreakAdjustments->{0.85, 2, 10, 1, 1}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Message"], CellFrame->{{1, 1}, {0, 0}}, CellDingbat->"\[LongDash]", CellMargins->{{55, 10}, {0, 0}}, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, FormatType->InputForm, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->10, FontSlant->"Oblique", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[StyleData["Message", "Presentation"], CellMargins->{{60, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}], Cell[StyleData["Message", "Printout"], CellMargins->{{55, Inherited}, {0, 0}}, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Print"], CellMargins->{{55, 26}, {1, 6}}, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, TextAlignment->Left, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, FormatType->InputForm, StyleMenuListing->None, Background->GrayLevel[0.700008]], Cell[StyleData["Print", "Presentation"], CellMargins->{{60, Inherited}, {10, 2}}], Cell[StyleData["Print", "Printout"], CellMargins->{{54, Inherited}, {2, 6}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Graphics"], CellFrame->{{1, 1}, {0, 0}}, CellMargins->{{55, 10}, {0, 0}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, FormatType->InputForm, ImageMargins->{{35, Inherited}, {Inherited, 0}}, StyleMenuListing->None, Background->GrayLevel[0.850004]], Cell[StyleData["Graphics", "Presentation"], CellMargins->{{60, Inherited}, {0, 0}}, ImageMargins->{{10, 10}, {10, 10}}], Cell[StyleData["Graphics", "Printout"], CellMargins->{{55, Inherited}, {0, 0}}, ImageSize->{0.0625, 0.0625}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->10, FontSlant->"Oblique", FontColor->RGBColor[0.6, 0, 0.6]], Cell[StyleData["CellLabel", "Presentation"], CellMargins->{{18, Inherited}, {Inherited, Inherited}}], Cell[StyleData["CellLabel", "Printout"], CellMargins->{{0, Inherited}, {Inherited, Inherited}}, FontSize->8] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Unique Styles", "Section"], Cell[CellGroupData[{ Cell[StyleData["Author"], CellMargins->{{20, 30}, {45, 5}}, CellGroupingRules->{"TitleGrouping", 20}, PageBreakBelow->False, CellFrameMargins->{{0, 4}, {8, 4}}, LineSpacing->{1, 0}, CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}}, FontFamily->"Helvetica", FontSize->14, FontSlant->"Italic"], Cell[StyleData["Author", "Presentation"], CellMargins->{{20, 30}, {45, 10}}], Cell[StyleData["Author", "Printout"], CellMargins->{{18, 30}, {45, 5}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Abstract"], CellFrame->False, CellMargins->{{18, 140}, {4, 30}}, Hyphenation->True, LineSpacing->{0.9, 0}, FontFamily->"Times", FontSize->12], Cell[StyleData["Abstract", "Presentation"], CellFrame->True, CellMargins->{{20, 10}, {Inherited, 30}}], Cell[StyleData["Abstract", "Printout"], LineSpacing->{1, 2}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Caption"], CellMargins->{{55, 10}, {5, 3}}, PageBreakAbove->False, Hyphenation->True, FontFamily->"Helvetica", FontSize->9], Cell[StyleData["Caption", "Presentation"], CellMargins->{{60, 65}, {6, 4}}, FontSize->10], Cell[StyleData["Caption", "Printout"], CellMargins->{{55, 55}, {5, 4}}, LineSpacing->{1, 2}, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Reference"], CellMargins->{{24, 40}, {6, 6}}, TextJustification->1, Hyphenation->True, LineSpacing->{1, 0}, FontFamily->"Times"], Cell[StyleData["Reference", "Presentation"], CellMargins->{{20, 40}, {Inherited, 6}}, TextJustification->0, LineSpacing->{1, 4}, FontSize->12], Cell[StyleData["Reference", "Printout"], CellMargins->{{18, 4}, {4, 4}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["PictureGroup"], CellFrame->{{1, 1}, {0, 0}}, CellMargins->{{55, Inherited}, {0, 0}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, ShowCellLabel->False, ImageMargins->{{35, Inherited}, {Inherited, 0}}, StyleMenuListing->None, Background->GrayLevel[0.850004]], Cell[StyleData["PictureGroup", "Presentation"], CellMargins->{{60, Inherited}, {0, 0}}, ImageMargins->{{10, 10}, {10, 10}}], Cell[StyleData["PictureGroup", "Printout"], CellMargins->{{55, Inherited}, {0, 0}}, ImageSize->{0.0625, 0.0625}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext \ ButtonBoxes. The \"Hyperlink\" style is for links within the same Notebook, \ or between Notebooks.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Presentation"], FontSize->16], Cell[StyleData["Hyperlink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["\<\ The following styles are for linking automatically to the on-line \ help system.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Presentation"], FontSize->16], Cell[StyleData["MainBookLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["AddOnsLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["AddOnsLink", "Presentation"], FontSize->16], Cell[StyleData["AddOnsLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Presentation"], FontSize->16], Cell[StyleData["RefGuideLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["GettingStartedLink", "Presentation"], FontSize->16], Cell[StyleData["GettingStartedLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Presentation"], FontSize->16], Cell[StyleData["OtherInformationLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Palette Styles", "Section"], Cell["\<\ The cells below define styles that define standard \ ButtonFunctions, for use in palette buttons.\ \>", "Text"], Cell[StyleData["Paste"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, After]}]&)}], Cell[StyleData["Evaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["EvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionMove[ FrontEnd`InputNotebook[ ], All, Cell, 1], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}] }, Closed]], Cell[CellGroupData[{ Cell["Formulas and Programming", "Section"], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], CellMargins->{{55, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", ScriptLevel->0, SingleLetterItalics->True, StyleMenuListing->None, UnderoverscriptBoxOptions->{LimitsPositioning->True}], Cell[StyleData["DisplayFormula", "Presentation"], CellMargins->{{60, 10}, {Inherited, 6}}, LineSpacing->{1, 5}], Cell[StyleData["DisplayFormula", "Printout"], CellMargins->{{18, 4}, {4, 4}}] }, Open ]], Cell[CellGroupData[{ Cell[StyleData["ChemicalFormula"], CellMargins->{{55, 10}, {Inherited, 0}}, CellHorizontalScrolling->True, 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