(* Content-type: application/vnd.wolfram.cdf.text *) (*** Wolfram CDF File ***) (* http://www.wolfram.com/cdf *) (* CreatedBy='Mathematica 10.4' *) (*************************************************************************) (* *) (* The Mathematica License under which this file was created prohibits *) (* restricting third parties in receipt of this file from republishing *) (* or redistributing it by any means, including but not limited to *) (* rights management or terms of use, without the express consent of *) (* Wolfram Research, Inc. For additional information concerning CDF *) (* licensing and redistribution see: *) (* *) (* www.wolfram.com/cdf/adopting-cdf/licensing-options.html *) (* *) (*************************************************************************) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 1064, 20] NotebookDataLength[ 32459, 714] NotebookOptionsPosition[ 33027, 710] NotebookOutlinePosition[ 33463, 729] CellTagsIndexPosition[ 33420, 726] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`azim$$ = 0.86, $CellContext`centrKS$$ = False, $CellContext`elev$$ = 0.75, $CellContext`showNap$$ = False, $CellContext`showRes$$ = False, $CellContext`sxx$$ = 0, $CellContext`sxy$$ = 0, $CellContext`sxz$$ = 0, $CellContext`syy$$ = 0, $CellContext`syz$$ = 0, $CellContext`szz$$ = 0, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`azim$$], 0.86, "Smer vektorja normale: Azimut, merjen v x-y ravnini, od x osi \ [rad]"}, Rational[-1, 2] Pi, Rational[1, 2] Pi, 0.05}, {{ Hold[$CellContext`elev$$], 0.75, "Elevacija [rad]"}, Rational[-1, 2] Pi, Rational[1, 2] Pi, 0.05}, {{ Hold[$CellContext`sxx$$], 0, "\!\(\*SubscriptBox[\(\[Sigma]\), \(xx\)]\)"}, -100, 100}, {{ Hold[$CellContext`sxy$$], 0, "\!\(\*SubscriptBox[\(\[Tau]\), \(xy\)]\)"}, -100, 100}, {{ Hold[$CellContext`syy$$], 0, "\!\(\*SubscriptBox[\(\[Sigma]\), \(yy\)]\)"}, -100, 100}, {{ Hold[$CellContext`syz$$], 0, "\!\(\*SubscriptBox[\(\[Tau]\), \(yz\)]\)"}, -100, 100}, {{ Hold[$CellContext`szz$$], 0, "\!\(\*SubscriptBox[\(\[Sigma]\), \(zz\)]\)"}, -100, 100}, {{ Hold[$CellContext`sxz$$], 0, "\!\(\*SubscriptBox[\(\[Tau]\), \(xz\)]\)"}, -100, 100}, {{ Hold[$CellContext`centrKS$$], False, ""}, {True, False}}, {{ Hold[$CellContext`showNap$$], False, ""}, {True, False}}, {{ Hold[$CellContext`showRes$$], False, ""}, {True, False}}, { Hold[ Grid[{{ Style[" Komponente napetostnega tenzorja", 11], Spacer[20], Style[" Napetostni tenzor", 11], Spacer[20], Style[" Normala in napetostni vektor", 11]}, { Grid[{{ Manipulate`Place[1], Manipulate`Place[2]}, { Manipulate`Place[3], Manipulate`Place[4]}, { Manipulate`Place[5], Manipulate`Place[6]}}], Spacer[20], Style[ Row[{ Text[ Style[ TraditionalForm[ HoldForm[{{ Subscript[$CellContext`\[Sigma], $CellContext`x], Subscript[$CellContext`\[Tau], $CellContext`yx], Subscript[$CellContext`\[Tau], $CellContext`zx]}, { Subscript[$CellContext`\[Tau], $CellContext`xy], Subscript[$CellContext`\[Sigma], $CellContext`y], Subscript[$CellContext`\[Tau], $CellContext`zy]}, { Subscript[$CellContext`\[Tau], $CellContext`xz], Subscript[$CellContext`\[Tau], $CellContext`yz], Subscript[$CellContext`\[Sigma], $CellContext`z]}}]]]], " = ", Dynamic[ TraditionalForm[{{$CellContext`sxx$$, $CellContext`sxy$$, \ $CellContext`sxz$$}, {$CellContext`sxy$$, $CellContext`syy$$, \ $CellContext`syz$$}, {$CellContext`sxz$$, $CellContext`syz$$, \ $CellContext`szz$$}}]]}], 11], Spacer[20], Grid[{{ Style[ Row[{ Text[ Style[ TraditionalForm[ HoldForm[{ Subscript[$CellContext`n, $CellContext`x], Subscript[$CellContext`n, $CellContext`y], Subscript[$CellContext`n, $CellContext`z]}]]]], " = ", Dynamic[ NumberForm[{$CellContext`a, $CellContext`b, $CellContext`c}, \ {4, 3}]]}], 11]}, { Style[ Row[{ Text[ Style[ TraditionalForm[ HoldForm[{ Subscript[$CellContext`p, $CellContext`x], Subscript[$CellContext`p, $CellContext`y], Subscript[$CellContext`p, $CellContext`z]}]]]], " = ", Dynamic[ NumberForm[$CellContext`p, {3, 0}]]}], 11]}, { Style[ Row[{ Text[ Style[ TraditionalForm[ HoldForm[{ Subscript[$CellContext`\[Sigma], $CellContext`norm], Subscript[$CellContext`\[Tau], $CellContext`norm]}]]]], " = ", Dynamic[ NumberForm[{$CellContext`sNorm, $CellContext`tNorm}, {3, 0}]]}], 11]}}], Spacer[10], Grid[{{ Row[{ Text[ Style[" Koord. sist. v centru", 12]], Manipulate`Place[7]}]}, { Row[{ Text[ Style[" Prika\[ZHacek]i napetosti", 12]], Manipulate`Place[8]}]}, { Row[{ Text[ Style[ "Na\[SHacek]tej re\[SHacek]itve za \ \!\(\*SubscriptBox[\(\[Tau]\), \(norm\)]\)=0", 12]], Manipulate`Place[9]}]}}]}}, Alignment -> Left, Spacings -> {1, 0.4}, Frame -> True, FrameStyle -> Directive[ Thickness[0.005], GrayLevel[0.5]]]], Manipulate`Dump`ThisIsNotAControl}}, Typeset`size$$ = {1003., {297., 303.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`azim$951249$$ = 0, $CellContext`elev$951250$$ = 0, $CellContext`sxx$951251$$ = 0, $CellContext`sxy$951252$$ = 0, $CellContext`syy$951253$$ = 0, $CellContext`syz$951254$$ = 0, $CellContext`szz$951255$$ = 0, $CellContext`sxz$951256$$ = 0, $CellContext`centrKS$951257$$ = False, $CellContext`showNap$951258$$ = False, $CellContext`showRes$951259$$ = False}, DynamicBox[Manipulate`ManipulateBoxes[ 2, StandardForm, "Variables" :> {$CellContext`azim$$ = 0.86, $CellContext`centrKS$$ = False, $CellContext`elev$$ = 0.75, $CellContext`showNap$$ = False, $CellContext`showRes$$ = False, $CellContext`sxx$$ = 0, $CellContext`sxy$$ = 0, $CellContext`sxz$$ = 0, $CellContext`syy$$ = 0, $CellContext`syz$$ = 0, $CellContext`szz$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`azim$$, $CellContext`azim$951249$$, 0], Hold[$CellContext`elev$$, $CellContext`elev$951250$$, 0], Hold[$CellContext`sxx$$, $CellContext`sxx$951251$$, 0], Hold[$CellContext`sxy$$, $CellContext`sxy$951252$$, 0], Hold[$CellContext`syy$$, $CellContext`syy$951253$$, 0], Hold[$CellContext`syz$$, $CellContext`syz$951254$$, 0], Hold[$CellContext`szz$$, $CellContext`szz$951255$$, 0], Hold[$CellContext`sxz$$, $CellContext`sxz$951256$$, 0], Hold[$CellContext`centrKS$$, $CellContext`centrKS$951257$$, False], Hold[$CellContext`showNap$$, $CellContext`showNap$951258$$, False], Hold[$CellContext`showRes$$, $CellContext`showRes$951259$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ($CellContext`dL = 2.; $CellContext`dNorm = 6; $CellContext`dNap = 30.; $CellContext`a = Cos[$CellContext`elev$$] Cos[$CellContext`azim$$]; $CellContext`b = Cos[$CellContext`elev$$] Sin[$CellContext`azim$$]; $CellContext`c = Sin[$CellContext`elev$$]; $CellContext`norm = {$CellContext`a, \ $CellContext`b, $CellContext`c}; $CellContext`v1 = {(-$CellContext`dL) Sign[$CellContext`a], (-$CellContext`dL) Sign[$CellContext`b], (-$CellContext`dL) Sign[$CellContext`c]}; $CellContext`v2 = {($CellContext`b \ $CellContext`dL Sign[$CellContext`b] + $CellContext`c $CellContext`dL Sign[$CellContext`c])/ If[$CellContext`a != 0, $CellContext`a, 10^(-3)], (-$CellContext`dL) Sign[$CellContext`b], (-$CellContext`dL) Sign[$CellContext`c]}; $CellContext`v3 = {(-$CellContext`dL) Sign[$CellContext`a], ($CellContext`c $CellContext`dL Sign[$CellContext`c] + $CellContext`a $CellContext`dL Sign[$CellContext`a])/ If[$CellContext`b != 0, $CellContext`b, 10^(-3)], (-$CellContext`dL) Sign[$CellContext`c]}; $CellContext`v4 = {(-$CellContext`dL) Sign[$CellContext`a], (-$CellContext`dL) Sign[$CellContext`b], ($CellContext`a $CellContext`dL Sign[$CellContext`a] + $CellContext`b $CellContext`dL Sign[$CellContext`b])/ If[$CellContext`c != 0, $CellContext`c, 10^(-3)]}; $CellContext`tezX = ($CellContext`v1 + $CellContext`v3 + \ $CellContext`v4)/ 3; $CellContext`tezY = ($CellContext`v1 + $CellContext`v2 + \ $CellContext`v4)/ 3; $CellContext`tezZ = ($CellContext`v1 + $CellContext`v2 + \ $CellContext`v3)/3; If[Abs[ Part[$CellContext`tezX, 1]] > $CellContext`dL, Part[$CellContext`tezX, 1] = Sign[ Part[$CellContext`tezX, 1]] $CellContext`dL, {}]; If[Abs[ Part[$CellContext`tezX, 2]] > $CellContext`dL, Part[$CellContext`tezX, 2] = Sign[ Part[$CellContext`tezX, 2]] $CellContext`dL, {}]; If[Abs[ Part[$CellContext`tezX, 3]] > $CellContext`dL, Part[$CellContext`tezX, 3] = Sign[ Part[$CellContext`tezX, 3]] $CellContext`dL, {}]; If[Abs[ Part[$CellContext`tezY, 1]] > $CellContext`dL, Part[$CellContext`tezY, 1] = Sign[ Part[$CellContext`tezY, 1]] $CellContext`dL, {}]; If[Abs[ Part[$CellContext`tezY, 2]] > $CellContext`dL, Part[$CellContext`tezY, 2] = Sign[ Part[$CellContext`tezY, 2]] $CellContext`dL, {}]; If[Abs[ Part[$CellContext`tezY, 3]] > $CellContext`dL, Part[$CellContext`tezY, 3] = Sign[ Part[$CellContext`tezY, 3]] $CellContext`dL, {}]; If[Abs[ Part[$CellContext`tezZ, 1]] > $CellContext`dL, Part[$CellContext`tezZ, 1] = Sign[ Part[$CellContext`tezZ, 1]] $CellContext`dL, {}]; If[Abs[ Part[$CellContext`tezZ, 2]] > $CellContext`dL, Part[$CellContext`tezZ, 2] = Sign[ Part[$CellContext`tezZ, 2]] $CellContext`dL, {}]; If[Abs[ Part[$CellContext`tezZ, 3]] > $CellContext`dL, Part[$CellContext`tezZ, 3] = Sign[ Part[$CellContext`tezZ, 3]] $CellContext`dL, {}]; $CellContext`sij = \ {{$CellContext`sxx$$, $CellContext`sxy$$, $CellContext`sxz$$}, \ {$CellContext`sxy$$, $CellContext`syy$$, $CellContext`syz$$}, \ {$CellContext`sxz$$, $CellContext`syz$$, $CellContext`szz$$}}; $CellContext`p = Dot[$CellContext`sij, $CellContext`norm]; $CellContext`sNorm = Dot[$CellContext`p, $CellContext`norm]; $CellContext`tNormVekt = \ $CellContext`p - $CellContext`sNorm $CellContext`norm; $CellContext`tNorm = Sqrt[ Dot[$CellContext`tNormVekt, $CellContext`tNormVekt]]; \ $CellContext`sumSig = $CellContext`sxx$$ + $CellContext`syy$$ + \ $CellContext`szz$$ + $CellContext`sxy$$ + $CellContext`sxz$$ + \ $CellContext`syz$$; If[Abs[$CellContext`sumSigOld - $CellContext`sumSig] > 3., {$CellContext`napVdata = {{0., 0.}}, $CellContext`sumSigOld = $CellContext`sumSig, \ $CellContext`sGlav1 = Eigenvalues[$CellContext`sij]; $CellContext`sGlav = Sort[$CellContext`sGlav1, Greater]; $CellContext`plRanX1 = Part[$CellContext`sGlav, 3] - 10; $CellContext`plRanX2 = Part[$CellContext`sGlav, 1] + 10; $CellContext`plRanY2 = (Part[$CellContext`sGlav, 1] - Part[$CellContext`sGlav, 3])/2. + 10; $CellContext`sVekt = Eigenvectors[$CellContext`sij]; $CellContext`ele1 = ArcSin[ Part[$CellContext`sVekt, 1, 3]]; $CellContext`ele2 = ArcSin[ Part[$CellContext`sVekt, 2, 3]]; $CellContext`ele3 = ArcSin[ Part[$CellContext`sVekt, 3, 3]]; $CellContext`az = ArcCos[Part[$CellContext`sVekt, 1, 1]/Cos[$CellContext`ele1]]; If[Part[$CellContext`sVekt, 1, 2] > 0, $CellContext`azi1 = $CellContext`az, $CellContext`azi1 = \ -$CellContext`az]; $CellContext`az = ArcCos[Part[$CellContext`sVekt, 2, 1]/Cos[$CellContext`ele2]]; If[Part[$CellContext`sVekt, 2, 2] > 0, $CellContext`azi2 = $CellContext`az, $CellContext`azi2 = \ -$CellContext`az]; $CellContext`az = ArcCos[Part[$CellContext`sVekt, 3, 1]/Cos[$CellContext`ele3]]; If[Part[$CellContext`sVekt, 3, 2] > 0, $CellContext`azi3 = $CellContext`az, $CellContext`azi3 = \ -$CellContext`az]; If[$CellContext`azi1 > Pi/2, {$CellContext`azi1 = $CellContext`azi1 - Pi/ 2, $CellContext`ele1 = -$CellContext`ele1}, {}]; If[$CellContext`azi1 < (-Pi)/ 2, {$CellContext`azi1 = $CellContext`azi1 + Pi/2, $CellContext`ele1 = -$CellContext`ele1}, {}]; If[$CellContext`azi2 > Pi/2, {$CellContext`azi2 = $CellContext`azi2 - Pi/ 2, $CellContext`ele2 = -$CellContext`ele2}, {}]; If[$CellContext`azi2 < (-Pi)/ 2, {$CellContext`azi2 = $CellContext`azi2 + Pi/2, $CellContext`ele2 = -$CellContext`ele2}, {}]; If[$CellContext`azi3 > Pi/2, {$CellContext`azi3 = $CellContext`azi3 - Pi/ 2, $CellContext`ele3 = -$CellContext`ele3}, {}]; If[$CellContext`azi3 < (-Pi)/ 2, {$CellContext`azi3 = $CellContext`azi3 + Pi/2, $CellContext`ele3 = -$CellContext`ele3}, {}]; Null}, {}]; If[ Or[ Abs[$CellContext`elevOld - $CellContext`elev$$] > 0.05, Abs[$CellContext`azimOld - $CellContext`azim$$] > 0.05], {$CellContext`napVdata = Append[$CellContext`napVdata, {$CellContext`sNorm, \ $CellContext`tNorm}], $CellContext`azimOld = $CellContext`azim$$, \ $CellContext`elevOld = $CellContext`elev$$}, {}]; Row[{ Column[{ ListPlot[$CellContext`napVdata, AxesLabel -> { "\!\(\*SubscriptBox[\(\[Sigma]\), \(norm\)]\)", "\!\(\*SubscriptBox[\(\[Tau]\), \(norm\)]\)"}, ImageSize -> {300, 250}, AspectRatio -> 0.5, PlotRange -> {{$CellContext`plRanX1, $CellContext`plRanX2}, { 0, $CellContext`plRanY2}}], If[$CellContext`showRes$$, Graphics[ Text[ StringJoin[ "Trije vektorji normal, \n pri katerih \!\(\*SubscriptBox[\(\ \[Tau]\), \(norm\)]\)=0: \n azimut, elevacija \n ", ToString[ NumberForm[$CellContext`azi1, {4, 2}]], " ", ToString[ NumberForm[$CellContext`ele1, {4, 2}]], "\n ", ToString[ NumberForm[$CellContext`azi2, {4, 2}]], " ", ToString[ NumberForm[$CellContext`ele2, {4, 2}]], "\n ", ToString[ NumberForm[$CellContext`azi3, {4, 2}]], " ", ToString[ NumberForm[$CellContext`ele3, {4, 2}]]], Center], ImageSize -> {300, 150}], Graphics[ Text[" "], ImageSize -> {300, 150}]]}, Frame -> None], Show[ Graphics3D[ Polygon[{$CellContext`v1, $CellContext`v2, $CellContext`v3}], PlotRange -> {{-6, 6}, {-6, 6}, {-6, 6}}, ViewPoint -> {6, 1, 2}, Boxed -> True, SphericalRegion -> True, ImageSize -> {700, 600}, ImageMargins -> 0], Graphics3D[ Polygon[{$CellContext`v1, $CellContext`v2, $CellContext`v4}]], Graphics3D[ Polygon[{$CellContext`v3, $CellContext`v1, $CellContext`v4}]], Graphics3D[ Polygon[{$CellContext`v2, $CellContext`v3, $CellContext`v4}]], Graphics3D[{Blue, Arrowheads[0.06], Arrow[ Tube[{{0, 0, 0}, $CellContext`dNorm {$CellContext`a, $CellContext`b, \ $CellContext`c}}, 0.015]], Text[ Style[ "normala", Medium, Bold], $CellContext`dNorm {$CellContext`a + 0.04, $CellContext`b + 0.04, $CellContext`c + 0.04}]}], If[$CellContext`centrKS$$, { Graphics3D[{Gray, Arrowheads[0.04], Arrow[ Tube[{{0, 0, 0}, {2.3, 0, 0}}, 0.015]], Text[ Style["X", Medium, Bold], {2.6, 0, 0}]}], Graphics3D[{Gray, Arrowheads[0.04], Arrow[ Tube[{{0, 0, 0}, {0, 2.3, 0}}, 0.015]], Text[ Style["Y", Medium, Bold], {0, 2.6, 0}]}], Graphics3D[{Gray, Arrowheads[0.04], Arrow[ Tube[{{0, 0, 0}, {0, 0, 2.3}}, 0.025]], Text[ Style["Z", Medium, Bold], {0, 0, 2.6}]}]}, { Graphics3D[{Gray, Arrowheads[0.04], Arrow[ Tube[{{(-2) $CellContext`dL, (-2) $CellContext`dL, (-2) \ $CellContext`dL}, {(-2) $CellContext`dL + 2.3, (-2) $CellContext`dL, (-2) $CellContext`dL}}, 0.015]], Text[ Style[ "X", Medium, Bold], {(-2) $CellContext`dL + 2.6, (-2) $CellContext`dL, (-2) $CellContext`dL}]}], Graphics3D[{Gray, Arrowheads[0.04], Arrow[ Tube[{{(-2) $CellContext`dL, (-2) $CellContext`dL, (-2) \ $CellContext`dL}, {(-2) $CellContext`dL, (-2) $CellContext`dL + 2.3, (-2) $CellContext`dL}}, 0.015]], Text[ Style[ "Y", Medium, Bold], {(-2) $CellContext`dL, (-2) $CellContext`dL + 2.6, (-2) $CellContext`dL}]}], Graphics3D[{Gray, Arrowheads[0.04], Arrow[ Tube[{{(-2) $CellContext`dL, (-2) $CellContext`dL, (-2) \ $CellContext`dL}, {(-2) $CellContext`dL, (-2) $CellContext`dL, (-2) \ $CellContext`dL + 2.3}}, 0.025]], Text[ Style[ "Z", Medium, Bold], {(-2) $CellContext`dL, (-2) $CellContext`dL, (-2) \ $CellContext`dL + 2.6}]}]}], If[$CellContext`showNap$$, { If[$CellContext`sxx$$ > 0., Graphics3D[{Black, Arrowheads[0.02], Arrow[{$CellContext`tezX, $CellContext`tezX - \ {$CellContext`sxx$$ (Sign[$CellContext`a]/$CellContext`dNap), 0, 0}}]}], Graphics3D[{Black, Arrowheads[0.02], Arrow[{$CellContext`tezX + {$CellContext`sxx$$ ( Sign[$CellContext`a]/$CellContext`dNap), 0, 0}, $CellContext`tezX}]}]], Graphics3D[{Black, Arrowheads[0.02], Arrow[{$CellContext`tezX, $CellContext`tezX - { 0, $CellContext`sxy$$ ( Sign[$CellContext`a]/$CellContext`dNap), 0}}]}], Graphics3D[{Black, Arrowheads[0.02], Arrow[{$CellContext`tezX, $CellContext`tezX - { 0, 0, $CellContext`sxz$$ ( Sign[$CellContext`a]/$CellContext`dNap)}}]}], If[$CellContext`syy$$ > 0., Graphics3D[{Black, Arrowheads[0.02], Arrow[{$CellContext`tezY, $CellContext`tezY - { 0, $CellContext`syy$$ ( Sign[$CellContext`b]/$CellContext`dNap), 0}}]}], Graphics3D[{Black, Arrowheads[0.02], Arrow[{$CellContext`tezY + { 0, $CellContext`syy$$ ( Sign[$CellContext`b]/$CellContext`dNap), 0}, $CellContext`tezY}]}]], Graphics3D[{Black, Arrowheads[0.02], Arrow[{$CellContext`tezY, $CellContext`tezY - \ {$CellContext`sxy$$ (Sign[$CellContext`b]/$CellContext`dNap), 0, 0}}]}], Graphics3D[{Black, Arrowheads[0.02], Arrow[{$CellContext`tezY, $CellContext`tezY - { 0, 0, $CellContext`syz$$ ( Sign[$CellContext`b]/$CellContext`dNap)}}]}], If[$CellContext`szz$$ > 0., Graphics3D[{Black, Arrowheads[0.02], Arrow[{$CellContext`tezZ, $CellContext`tezZ - { 0, 0, $CellContext`szz$$ ( Sign[$CellContext`c]/$CellContext`dNap)}}]}], Graphics3D[{Black, Arrowheads[0.02], Arrow[{$CellContext`tezZ + { 0, 0, $CellContext`szz$$ ( Sign[$CellContext`c]/$CellContext`dNap)}, \ $CellContext`tezZ}]}]], Graphics3D[{Black, Arrowheads[0.02], Arrow[{$CellContext`tezZ, $CellContext`tezZ - \ {$CellContext`sxz$$ (Sign[$CellContext`c]/$CellContext`dNap), 0, 0}}]}], Graphics3D[{Black, Arrowheads[0.02], Arrow[{$CellContext`tezZ, $CellContext`tezZ - { 0, $CellContext`syz$$ ( Sign[$CellContext`c]/$CellContext`dNap), 0}}]}], If[$CellContext`sNorm > 0, { Graphics3D[{Red, Arrowheads[0.03], Arrow[ Tube[{{0, 0, 0}, $CellContext`p/$CellContext`dNap}, 0.04]], Text[ Style["p", Larger, Bold], $CellContext`p/( 0.97 $CellContext`dNap)]}], Graphics3D[{Red, Arrowheads[0.02], Arrow[ Tube[{{0, 0, 0}, $CellContext`sNorm \ ($CellContext`norm/$CellContext`dNap)}, 0.04]], Text[ Style[ "\!\(\*SubscriptBox[\(\[Sigma]\), \(norm\)]\)", Larger, Bold], $CellContext`sNorm ($CellContext`norm/( 0.97 $CellContext`dNap))]}], Graphics3D[{Red, Arrowheads[0.02], Arrow[ Tube[{{0, 0, 0}, $CellContext`tNormVekt/$CellContext`dNap}, 0.04]], Text[ Style[ "\!\(\*SubscriptBox[\(\[Tau]\), \(norm\)]\)", Larger, Bold], $CellContext`tNormVekt/(0.97 $CellContext`dNap)]}], Graphics3D[{Red, Line[{$CellContext`sNorm \ ($CellContext`norm/$CellContext`dNap), $CellContext`p/$CellContext`dNap, \ $CellContext`tNormVekt/$CellContext`dNap}]}]}, { Graphics3D[{Red, Arrowheads[0.03], Arrow[ Tube[{(-$CellContext`p)/$CellContext`dNap, {0, 0, 0}}, 0.04]], Text[ Style["p", Larger, Bold], (-$CellContext`p)/( 0.97 $CellContext`dNap)]}], Graphics3D[{Red, Arrowheads[0.02], Arrow[ Tube[{(-$CellContext`sNorm) \ ($CellContext`norm/$CellContext`dNap), {0, 0, 0}}, 0.04]], Text[ Style[ "\!\(\*SubscriptBox[\(\[Sigma]\), \(norm\)]\)", Larger, Bold], (-$CellContext`sNorm) ($CellContext`norm/( 0.97 $CellContext`dNap))]}], Graphics3D[{Red, Arrowheads[0.02], Arrow[ Tube[{(-$CellContext`tNormVekt)/$CellContext`dNap, {0, 0, 0}}, 0.04]], Text[ Style[ "\!\(\*SubscriptBox[\(\[Tau]\), \(norm\)]\)", Larger, Bold], (-$CellContext`tNormVekt)/( 0.97 $CellContext`dNap)]}], Graphics3D[{Red, Line[{(-$CellContext`sNorm) \ ($CellContext`norm/$CellContext`dNap), (-$CellContext`p)/$CellContext`dNap, \ (-$CellContext`tNormVekt)/$CellContext`dNap}]}]}]}, {}]]}]), "Specifications" :> {{{$CellContext`azim$$, 0.86, "Smer vektorja normale: Azimut, merjen v x-y ravnini, od x osi \ [rad]"}, Rational[-1, 2] Pi, Rational[1, 2] Pi, 0.05, ImageSize -> Medium, ControlPlacement -> Up, Appearance -> "Labeled"}, {{$CellContext`elev$$, 0.75, "Elevacija [rad]"}, Rational[-1, 2] Pi, Rational[1, 2] Pi, 0.05, ImageSize -> Medium, ControlPlacement -> Up, Appearance -> "Labeled"}, {{$CellContext`sxx$$, 0, "\!\(\*SubscriptBox[\(\[Sigma]\), \(xx\)]\)"}, -100, 100, ImageSize -> Tiny, ControlPlacement -> 1}, {{$CellContext`sxy$$, 0, "\!\(\*SubscriptBox[\(\[Tau]\), \(xy\)]\)"}, -100, 100, ImageSize -> Tiny, ControlPlacement -> 2}, {{$CellContext`syy$$, 0, "\!\(\*SubscriptBox[\(\[Sigma]\), \(yy\)]\)"}, -100, 100, ImageSize -> Tiny, ControlPlacement -> 3}, {{$CellContext`syz$$, 0, "\!\(\*SubscriptBox[\(\[Tau]\), \(yz\)]\)"}, -100, 100, ImageSize -> Tiny, ControlPlacement -> 4}, {{$CellContext`szz$$, 0, "\!\(\*SubscriptBox[\(\[Sigma]\), \(zz\)]\)"}, -100, 100, ImageSize -> Tiny, ControlPlacement -> 5}, {{$CellContext`sxz$$, 0, "\!\(\*SubscriptBox[\(\[Tau]\), \(xz\)]\)"}, -100, 100, ImageSize -> Tiny, ControlPlacement -> 6}, {{$CellContext`centrKS$$, False, ""}, { True, False}, ControlPlacement -> 7}, {{$CellContext`showNap$$, False, ""}, {True, False}, ControlPlacement -> 8}, {{$CellContext`showRes$$, False, ""}, { True, False}, ControlPlacement -> 9}, Grid[{{ Style[" Komponente napetostnega tenzorja", 11], Spacer[20], Style[" Napetostni tenzor", 11], Spacer[20], Style[" Normala in napetostni vektor", 11]}, { Grid[{{ Manipulate`Place[1], Manipulate`Place[2]}, { Manipulate`Place[3], Manipulate`Place[4]}, { Manipulate`Place[5], Manipulate`Place[6]}}], Spacer[20], Style[ Row[{ Text[ Style[ TraditionalForm[ HoldForm[{{ Subscript[$CellContext`\[Sigma], $CellContext`x], Subscript[$CellContext`\[Tau], $CellContext`yx], Subscript[$CellContext`\[Tau], $CellContext`zx]}, { Subscript[$CellContext`\[Tau], $CellContext`xy], Subscript[$CellContext`\[Sigma], $CellContext`y], Subscript[$CellContext`\[Tau], $CellContext`zy]}, { Subscript[$CellContext`\[Tau], $CellContext`xz], Subscript[$CellContext`\[Tau], $CellContext`yz], Subscript[$CellContext`\[Sigma], $CellContext`z]}}]]]], " = ", Dynamic[ TraditionalForm[{{$CellContext`sxx$$, $CellContext`sxy$$, \ $CellContext`sxz$$}, {$CellContext`sxy$$, $CellContext`syy$$, \ $CellContext`syz$$}, {$CellContext`sxz$$, $CellContext`syz$$, \ $CellContext`szz$$}}]]}], 11], Spacer[20], Grid[{{ Style[ Row[{ Text[ Style[ TraditionalForm[ HoldForm[{ Subscript[$CellContext`n, $CellContext`x], Subscript[$CellContext`n, $CellContext`y], Subscript[$CellContext`n, $CellContext`z]}]]]], " = ", Dynamic[ NumberForm[{$CellContext`a, $CellContext`b, \ $CellContext`c}, {4, 3}]]}], 11]}, { Style[ Row[{ Text[ Style[ TraditionalForm[ HoldForm[{ Subscript[$CellContext`p, $CellContext`x], Subscript[$CellContext`p, $CellContext`y], Subscript[$CellContext`p, $CellContext`z]}]]]], " = ", Dynamic[ NumberForm[$CellContext`p, {3, 0}]]}], 11]}, { Style[ Row[{ Text[ Style[ TraditionalForm[ HoldForm[{ Subscript[$CellContext`\[Sigma], $CellContext`norm], Subscript[$CellContext`\[Tau], $CellContext`norm]}]]]], " = ", Dynamic[ NumberForm[{$CellContext`sNorm, $CellContext`tNorm}, {3, 0}]]}], 11]}}], Spacer[10], Grid[{{ Row[{ Text[ Style[" Koord. sist. v centru", 12]], Manipulate`Place[7]}]}, { Row[{ Text[ Style[" Prika\[ZHacek]i napetosti", 12]], Manipulate`Place[8]}]}, { Row[{ Text[ Style[ "Na\[SHacek]tej re\[SHacek]itve za \!\(\*SubscriptBox[\(\ \[Tau]\), \(norm\)]\)=0", 12]], Manipulate`Place[9]}]}}]}}, Alignment -> Left, Spacings -> {1, 0.4}, Frame -> True, FrameStyle -> Directive[ Thickness[0.005], GrayLevel[0.5]]]}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{1054., {398., 405.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>(($CellContext`napVdata = {{0., 0.}}; $CellContext`sGlav = {{0., 0., 0.}}; $CellContext`sumSigOld = 0.; $CellContext`azimOld = 0.86; $CellContext`elevOld = 0.75; {$CellContext`plRanX1, $CellContext`plRanX2, \ $CellContext`plRanY2} = {-1, 1, 1}; {$CellContext`sxx$$, $CellContext`syy$$, $CellContext`szz$$, \ $CellContext`sxy$$, $CellContext`syz$$, $CellContext`sxz$$} = {0, 0, 0, 0, 0, 0}; Null); Typeset`initDone$$ = True), SynchronousInitialization->True, UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$}, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output"] }, WindowSize->{1280, 677}, Visible->True, ScrollingOptions->{"VerticalScrollRange"->Fit}, ShowCellBracket->Automatic, CellContext->Notebook, TrackCellChangeTimes->False, FrontEndVersion->"10.4 for Microsoft Windows (64-bit) (April 11, 2016)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[1464, 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