hill za novi materijal
DESCRIPTION
gxfgsfgTRANSCRIPT
In[159]:=
sigma0 = 118.4;sigma15 = 130.05;sigma30 = 128.43;sigma45 = 130.35;sigma60 = 131.24;sigma75 = 131.3;sigma90 = 133.64;sigmab = 126.02;
data = {{0, sigma0}, {Pi / 12, sigma15}, {Pi / 6, sigma30}, {Pi / 4, sigma45},{Pi / 3, sigma60}, {(5 * Pi) / 12, sigma75}, {Pi / 2, sigma90}};
In[168]:= G0 =1
21 -
sigma02
sigma902+sigma02
sigmab2
H0 =1
21 -
sigma02
sigma902-sigma02
sigmab2
F0 = -1
21 -
sigma02
sigma902-sigma02
sigmab2
L45 = 2 ×sigma02
sigma452-1
2×sigma02
sigmab2
L30 = -1 +1
0.375×
sigma02
sigma302+ 0.333 ×
sigma02
sigma902- 0.5 ×
sigma02
sigmab2
L60 = 0.333 +1
0.375×
sigma02
sigma602-
sigma02
sigma902- 0.5 ×
sigma02
sigmab2
Out[168]= 0.548897
Out[169]= -0.333826
Out[170]= 0.333826
Out[171]= 1.20874
Out[172]= 1.08643
Out[173]= 1.27711
In[174]:= y1[x_] :=
sigma0
(Cos[x])4 × (H1 + G1) + (Sin[x])4 × (H1 + F1) + 2 × (Cos[x])2 × (Sin[x])2 × (L1 - H1)
In[175]:= H1 = H0F1 = F0L1 = L45G1 = G0
Out[175]= -0.333826
Out[176]= 0.333826
Out[177]= 1.20874
Out[178]= 0.548897
In[179]:= Plot[{y1[x]}, {x, 0, Pi / 2}]
Out[179]=
0.5 1.0 1.5
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In[180]:=
H2 = H0F2 = F0L2 = L30G2 = G0
Out[180]= -0.333826
Out[181]= 0.333826
Out[182]= 1.08643
Out[183]= 0.548897
In[184]:= y2[x_] := sigma0
√
(Cos[x])4 × (H2 + G2) + (Sin[x])4 × (H2 + F2) + 2 × (Cos[x])2 × (Sin[x])2 × (L2 - H2)
2 Hill za novi materijal.nb
In[185]:= Plot[{y2[x]}, {x, 0, Pi / 2}]
Out[185]=
0.5 1.0 1.5
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450
In[186]:= y3[x_] := sigma0
√
(Cos[x])4 × (H3 + G3) + (Sin[x])4 × (H3 + F3) + 2 × (Cos[x])2 × (Sin[x])2 × (L3 - H3)
In[187]:= H3 = H0F3 = F0L3 = L60G3 = G0
Out[187]= -0.333826
Out[188]= 0.333826
Out[189]= 1.27711
Out[190]= 0.548897
In[191]:= Plot[{y3[x]}, {x, 0, Pi / 2}]
Out[191]=
Hill za novi materijal.nb 3
In[192]:= Show[Plot[{y1[x], y2[x], y3[x]}, {x, 0, Pi / 2}], ListPlot[data]]
Out[192]=
0.0 0.5 1.0 1.5
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450
4 Hill za novi materijal.nb
In[149]:=
fun = LAMDA1 * (sigXX)^2 + LAMDA2 * (sigYY)^2 -
2 * NI * (sigYY * sigXX) + 2 * RO * (sigXY)^2 - sig0^2;
(*PODACI ZA sigma0 te parametre LAMDA1, LAMDA2,NI te RO preuzeti iz Excell-a za Hill funkciju *)
sig0 = 118.406428655297;LAMDA1 = 1;LAMDA2 = 0.784976941;NI = 0.451112717168747;RO = 1.20891408727571;sigXY = 0; sigYX = 0;g0 = ContourPlot[Evaluate@fun ,
{sigXX, -200, 200}, {sigYY, -200, 200}, Contours → {0.0},ContourShading → False, PlotPoints → 50, FrameLabel -> {"σ\!\(\*
StyleBox[\"xx\",\nFontSize->10]\)", "σ\!\(\*StyleBox[\"yy\",\nFontSize->10]\)"}, RotateLabel → False,
GridLines -> Automatic, LabelStyle → Directive[Black, 15]];c0 = Show[g0, Graphics[{PointSize[0.01],
Point[{{118.4, 0.0}, {0.0, 133.643}, {126.0248092, 126.0248092}}]}]]
-200 -100 0 100 200-200
-100
0
100
200
σxx
σyy
Hill za novi materijal.nb 5