Mixing
Solving equation with multi variable matrix input
Clash Royale CLAN TAG#URR8PPP
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1
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Background, here are the equations that I am trying to solve: 
Where R, E1, E2, V1, V2, P are all user inputs. X/A goes from -2 to 2 and Z/A goes from 0 to -2. Below is the code that I have so far. I created a list of inputs. Then created two arrays for the x and z inputs. The last is where I am having trouble. I'm trying to create a code such that it will hold a value for X constant in SX, SZ, and TXZ and plug in all the values for Z. Then move to the next value for X and plug all the values in for all the Z. The end goal is to create a density plot that for SX, SZ, and TXZ. Thank you!
R = .1;
E1 = 200*10^9;
E2 = 550*10^9;
P=1000;
V1 = 0.3;
V2 = 0.3;
E = 1/(((1-(V1^2))/E1)+((1-(V2^2))/E2));
A = ((.75*P*R)/(1.61172*10^11))^(1/3);
X = Range[-2 A, 2 A, 0.01*3*A];
Z = Range[0,-2 A, 0.005*3*A];
ZZ = ConstantArray[Z[[Range[Length[Z]]]], Length[X]];
XX = ConstantArray[X[[Range[Length[X]]]],Length[Z]];
For[i=1,i=Length[XX],
For[j=1,j = Length[ZZ],
M = Sqrt(.5*(((A^2-i^2+j^2)^2+4*i^2*j^2)^(.5)+(A^2-i^2+j^2)))
N = Sqrt(.5*(((A^2-i^2+j^2)^2+4*i^2*j^2)^(.5)-(A^2-i^2+j^2)))
SX = (-P/A)*M*((1-((j^2+N^2)/(M^2+N^2)))-2*N)
SZ = (-P/A)*M*((1-((j^2+N^2)/(M^2+N^2))))
SY = V1*(SX+SZ)
TXZ = (-P/A)*N*((M^2-j^2)/(M^2+N^2)),
DensityPlot[SX/P,XX/A,ZZ/A]
]
]
plotting system-variables
asked 2 hours ago
Kurt
62
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Kurt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
up vote
1
down vote
favorite
Background, here are the equations that I am trying to solve:
Where R, E1, E2, V1, V2, P are all user inputs. X/A goes from -2 to 2 and Z/A goes from 0 to -2. Below is the code that I have so far. I created a list of inputs. Then created two arrays for the x and z inputs. The last is where I am having trouble. I'm trying to create a code such that it will hold a value for X constant in SX, SZ, and TXZ and plug in all the values for Z. Then move to the next value for X and plug all the values in for all the Z. The end goal is to create a density plot that for SX, SZ, and TXZ. Thank you!
R = .1;
E1 = 200*10^9;
E2 = 550*10^9;
P=1000;
V1 = 0.3;
V2 = 0.3;
E = 1/(((1-(V1^2))/E1)+((1-(V2^2))/E2));
A = ((.75*P*R)/(1.61172*10^11))^(1/3);
X = Range[-2 A, 2 A, 0.01*3*A];
Z = Range[0,-2 A, 0.005*3*A];
ZZ = ConstantArray[Z[[Range[Length[Z]]]], Length[X]];
XX = ConstantArray[X[[Range[Length[X]]]],Length[Z]];
For[i=1,i=Length[XX],
For[j=1,j = Length[ZZ],
M = Sqrt(.5*(((A^2-i^2+j^2)^2+4*i^2*j^2)^(.5)+(A^2-i^2+j^2)))
N = Sqrt(.5*(((A^2-i^2+j^2)^2+4*i^2*j^2)^(.5)-(A^2-i^2+j^2)))
SX = (-P/A)*M*((1-((j^2+N^2)/(M^2+N^2)))-2*N)
SZ = (-P/A)*M*((1-((j^2+N^2)/(M^2+N^2))))
SY = V1*(SX+SZ)
TXZ = (-P/A)*N*((M^2-j^2)/(M^2+N^2)),
DensityPlot[SX/P,XX/A,ZZ/A]
]
]
plotting system-variables
asked 2 hours ago
Kurt
62
New contributor
Kurt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
You don't need to discretize the formula yourself, check the document ofDensityPlotcarefully. Also, notice e.g.EandNare built-in symbol in Mathematica (See their color? They're black, rather than blue ), you can't use them as variable names.
– xzczd
2 hours ago
What do you want to determine from these equations?
– Alex Trounev
2 hours ago
So I just want to graph the equations. Im not looking for any numerical results. The formulas will tell me the stress and shear below the surface of a material, and I'd like to see the counter plots.
– Kurt
2 hours ago
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Background, here are the equations that I am trying to solve:
Where R, E1, E2, V1, V2, P are all user inputs. X/A goes from -2 to 2 and Z/A goes from 0 to -2. Below is the code that I have so far. I created a list of inputs. Then created two arrays for the x and z inputs. The last is where I am having trouble. I'm trying to create a code such that it will hold a value for X constant in SX, SZ, and TXZ and plug in all the values for Z. Then move to the next value for X and plug all the values in for all the Z. The end goal is to create a density plot that for SX, SZ, and TXZ. Thank you!
R = .1;
E1 = 200*10^9;
E2 = 550*10^9;
P=1000;
V1 = 0.3;
V2 = 0.3;
E = 1/(((1-(V1^2))/E1)+((1-(V2^2))/E2));
A = ((.75*P*R)/(1.61172*10^11))^(1/3);
X = Range[-2 A, 2 A, 0.01*3*A];
Z = Range[0,-2 A, 0.005*3*A];
ZZ = ConstantArray[Z[[Range[Length[Z]]]], Length[X]];
XX = ConstantArray[X[[Range[Length[X]]]],Length[Z]];
For[i=1,i=Length[XX],
For[j=1,j = Length[ZZ],
M = Sqrt(.5*(((A^2-i^2+j^2)^2+4*i^2*j^2)^(.5)+(A^2-i^2+j^2)))
N = Sqrt(.5*(((A^2-i^2+j^2)^2+4*i^2*j^2)^(.5)-(A^2-i^2+j^2)))
SX = (-P/A)*M*((1-((j^2+N^2)/(M^2+N^2)))-2*N)
SZ = (-P/A)*M*((1-((j^2+N^2)/(M^2+N^2))))
SY = V1*(SX+SZ)
TXZ = (-P/A)*N*((M^2-j^2)/(M^2+N^2)),
DensityPlot[SX/P,XX/A,ZZ/A]
]
]
plotting system-variables
asked 2 hours ago
Kurt
62
New contributor
Kurt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Background, here are the equations that I am trying to solve:
Where R, E1, E2, V1, V2, P are all user inputs. X/A goes from -2 to 2 and Z/A goes from 0 to -2. Below is the code that I have so far. I created a list of inputs. Then created two arrays for the x and z inputs. The last is where I am having trouble. I'm trying to create a code such that it will hold a value for X constant in SX, SZ, and TXZ and plug in all the values for Z. Then move to the next value for X and plug all the values in for all the Z. The end goal is to create a density plot that for SX, SZ, and TXZ. Thank you!
R = .1;
E1 = 200*10^9;
E2 = 550*10^9;
P=1000;
V1 = 0.3;
V2 = 0.3;
E = 1/(((1-(V1^2))/E1)+((1-(V2^2))/E2));
A = ((.75*P*R)/(1.61172*10^11))^(1/3);
X = Range[-2 A, 2 A, 0.01*3*A];
Z = Range[0,-2 A, 0.005*3*A];
ZZ = ConstantArray[Z[[Range[Length[Z]]]], Length[X]];
XX = ConstantArray[X[[Range[Length[X]]]],Length[Z]];
For[i=1,i=Length[XX],
For[j=1,j = Length[ZZ],
M = Sqrt(.5*(((A^2-i^2+j^2)^2+4*i^2*j^2)^(.5)+(A^2-i^2+j^2)))
N = Sqrt(.5*(((A^2-i^2+j^2)^2+4*i^2*j^2)^(.5)-(A^2-i^2+j^2)))
SX = (-P/A)*M*((1-((j^2+N^2)/(M^2+N^2)))-2*N)
SZ = (-P/A)*M*((1-((j^2+N^2)/(M^2+N^2))))
SY = V1*(SX+SZ)
TXZ = (-P/A)*N*((M^2-j^2)/(M^2+N^2)),
DensityPlot[SX/P,XX/A,ZZ/A]
]
]
plotting system-variables
plotting system-variables
asked 2 hours ago
Kurt
62
New contributor
Kurt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 hours ago
Kurt
62
New contributor
Kurt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 hours ago
Kurt
62
New contributor
Kurt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 hours ago
Kurt
62
asked 2 hours ago
Kurt
62
62
New contributor
Kurt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Kurt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Kurt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
You don't need to discretize the formula yourself, check the document ofDensityPlotcarefully. Also, notice e.g.EandNare built-in symbol in Mathematica (See their color? They're black, rather than blue ), you can't use them as variable names.
– xzczd
2 hours ago
What do you want to determine from these equations?
– Alex Trounev
2 hours ago
So I just want to graph the equations. Im not looking for any numerical results. The formulas will tell me the stress and shear below the surface of a material, and I'd like to see the counter plots.
– Kurt
2 hours ago
add a comment |Â
You don't need to discretize the formula yourself, check the document ofDensityPlotcarefully. Also, notice e.g.EandNare built-in symbol in Mathematica (See their color? They're black, rather than blue ), you can't use them as variable names.
– xzczd
2 hours ago
What do you want to determine from these equations?
– Alex Trounev
2 hours ago
So I just want to graph the equations. Im not looking for any numerical results. The formulas will tell me the stress and shear below the surface of a material, and I'd like to see the counter plots.
– Kurt
2 hours ago
You don't need to discretize the formula yourself, check the document of
DensityPlot carefully. Also, notice e.g. E and N are built-in symbol in Mathematica (See their color? They're black, rather than blue ), you can't use them as variable names.– xzczd
2 hours ago
You don't need to discretize the formula yourself, check the document of
DensityPlot carefully. Also, notice e.g. E and N are built-in symbol in Mathematica (See their color? They're black, rather than blue ), you can't use them as variable names.– xzczd
2 hours ago
What do you want to determine from these equations?
– Alex Trounev
2 hours ago
What do you want to determine from these equations?
– Alex Trounev
2 hours ago
So I just want to graph the equations. Im not looking for any numerical results. The formulas will tell me the stress and shear below the surface of a material, and I'd like to see the counter plots.
– Kurt
2 hours ago
So I just want to graph the equations. Im not looking for any numerical results. The formulas will tell me the stress and shear below the surface of a material, and I'd like to see the counter plots.
– Kurt
2 hours ago
add a comment |Â
1 Answer
1
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oldest
votes
up vote
4
down vote
After correcting all errors and normalization to A, we have
R = .1;
E1 = 200*10^9;
E2 = 550*10^9;
P = 1000;
V1 = 0.3;
V2 = 0.3;
E3 = 1/(((1 - (V1^2))/E1) + ((1 - (V2^2))/E2));
A = ((.75*P*R)/(1.61172*10^11))^(1/3);
X = Range[-2 A, 2 A, 0.01*3*A];
Z = Range[0, -2 A, 0.005*3*A];
m = Sqrt[.5*(((1 - i^2 + j^2)^2 + 4*i^2*j^2)^(.5) + (1 - i^2 + j^2))];
n = Sqrt[.5*(((1 - i^2 + j^2)^2 + 4*i^2*j^2)^(.5) - (1 - i^2 +
j^2))];
SX = (-P)*m*((1 - ((j^2 + n^2)/(m^2 + n^2))) - 2*j);
SZ = (-P)*m*((1 - ((j^2 + n^2)/(m^2 + n^2)))); SY = V1*(SX + SZ);
TXZ = (-P)*n*((m^2 - j^2)/(m^2 + n^2)); DensityPlot[
SX/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (x)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
DensityPlot[SY/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (y)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
DensityPlot[SZ/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (z)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
DensityPlot[TXZ/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Tau]), (xz)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"]
ContourPlot[SX/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (x)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
ContourPlot[SY/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (y)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
ContourPlot[SZ/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (z)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
ContourPlot[TXZ/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Tau]), (xz)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"]
answered 1 hour ago
Alex Trounev
3,4201313
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
4
down vote
After correcting all errors and normalization to A, we have
R = .1;
E1 = 200*10^9;
E2 = 550*10^9;
P = 1000;
V1 = 0.3;
V2 = 0.3;
E3 = 1/(((1 - (V1^2))/E1) + ((1 - (V2^2))/E2));
A = ((.75*P*R)/(1.61172*10^11))^(1/3);
X = Range[-2 A, 2 A, 0.01*3*A];
Z = Range[0, -2 A, 0.005*3*A];
m = Sqrt[.5*(((1 - i^2 + j^2)^2 + 4*i^2*j^2)^(.5) + (1 - i^2 + j^2))];
n = Sqrt[.5*(((1 - i^2 + j^2)^2 + 4*i^2*j^2)^(.5) - (1 - i^2 +
j^2))];
SX = (-P)*m*((1 - ((j^2 + n^2)/(m^2 + n^2))) - 2*j);
SZ = (-P)*m*((1 - ((j^2 + n^2)/(m^2 + n^2)))); SY = V1*(SX + SZ);
TXZ = (-P)*n*((m^2 - j^2)/(m^2 + n^2)); DensityPlot[
SX/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (x)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
DensityPlot[SY/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (y)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
DensityPlot[SZ/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (z)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
DensityPlot[TXZ/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Tau]), (xz)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"]
ContourPlot[SX/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (x)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
ContourPlot[SY/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (y)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
ContourPlot[SZ/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (z)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
ContourPlot[TXZ/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Tau]), (xz)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"]
answered 1 hour ago
Alex Trounev
3,4201313
add a comment |Â
up vote
4
down vote
After correcting all errors and normalization to A, we have
R = .1;
E1 = 200*10^9;
E2 = 550*10^9;
P = 1000;
V1 = 0.3;
V2 = 0.3;
E3 = 1/(((1 - (V1^2))/E1) + ((1 - (V2^2))/E2));
A = ((.75*P*R)/(1.61172*10^11))^(1/3);
X = Range[-2 A, 2 A, 0.01*3*A];
Z = Range[0, -2 A, 0.005*3*A];
m = Sqrt[.5*(((1 - i^2 + j^2)^2 + 4*i^2*j^2)^(.5) + (1 - i^2 + j^2))];
n = Sqrt[.5*(((1 - i^2 + j^2)^2 + 4*i^2*j^2)^(.5) - (1 - i^2 +
j^2))];
SX = (-P)*m*((1 - ((j^2 + n^2)/(m^2 + n^2))) - 2*j);
SZ = (-P)*m*((1 - ((j^2 + n^2)/(m^2 + n^2)))); SY = V1*(SX + SZ);
TXZ = (-P)*n*((m^2 - j^2)/(m^2 + n^2)); DensityPlot[
SX/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (x)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
DensityPlot[SY/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (y)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
DensityPlot[SZ/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (z)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
DensityPlot[TXZ/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Tau]), (xz)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"]
ContourPlot[SX/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (x)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
ContourPlot[SY/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (y)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
ContourPlot[SZ/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (z)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
ContourPlot[TXZ/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Tau]), (xz)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"]
answered 1 hour ago
Alex Trounev
3,4201313
add a comment |Â
up vote
4
down vote
up vote
4
down vote
After correcting all errors and normalization to A, we have
R = .1;
E1 = 200*10^9;
E2 = 550*10^9;
P = 1000;
V1 = 0.3;
V2 = 0.3;
E3 = 1/(((1 - (V1^2))/E1) + ((1 - (V2^2))/E2));
A = ((.75*P*R)/(1.61172*10^11))^(1/3);
X = Range[-2 A, 2 A, 0.01*3*A];
Z = Range[0, -2 A, 0.005*3*A];
m = Sqrt[.5*(((1 - i^2 + j^2)^2 + 4*i^2*j^2)^(.5) + (1 - i^2 + j^2))];
n = Sqrt[.5*(((1 - i^2 + j^2)^2 + 4*i^2*j^2)^(.5) - (1 - i^2 +
j^2))];
SX = (-P)*m*((1 - ((j^2 + n^2)/(m^2 + n^2))) - 2*j);
SZ = (-P)*m*((1 - ((j^2 + n^2)/(m^2 + n^2)))); SY = V1*(SX + SZ);
TXZ = (-P)*n*((m^2 - j^2)/(m^2 + n^2)); DensityPlot[
SX/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (x)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
DensityPlot[SY/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (y)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
DensityPlot[SZ/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (z)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
DensityPlot[TXZ/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Tau]), (xz)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"]
ContourPlot[SX/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (x)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
ContourPlot[SY/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (y)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
ContourPlot[SZ/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (z)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
ContourPlot[TXZ/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Tau]), (xz)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"]
answered 1 hour ago
Alex Trounev
3,4201313
After correcting all errors and normalization to A, we have
R = .1;
E1 = 200*10^9;
E2 = 550*10^9;
P = 1000;
V1 = 0.3;
V2 = 0.3;
E3 = 1/(((1 - (V1^2))/E1) + ((1 - (V2^2))/E2));
A = ((.75*P*R)/(1.61172*10^11))^(1/3);
X = Range[-2 A, 2 A, 0.01*3*A];
Z = Range[0, -2 A, 0.005*3*A];
m = Sqrt[.5*(((1 - i^2 + j^2)^2 + 4*i^2*j^2)^(.5) + (1 - i^2 + j^2))];
n = Sqrt[.5*(((1 - i^2 + j^2)^2 + 4*i^2*j^2)^(.5) - (1 - i^2 +
j^2))];
SX = (-P)*m*((1 - ((j^2 + n^2)/(m^2 + n^2))) - 2*j);
SZ = (-P)*m*((1 - ((j^2 + n^2)/(m^2 + n^2)))); SY = V1*(SX + SZ);
TXZ = (-P)*n*((m^2 - j^2)/(m^2 + n^2)); DensityPlot[
SX/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (x)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
DensityPlot[SY/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (y)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
DensityPlot[SZ/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (z)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
DensityPlot[TXZ/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Tau]), (xz)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"]
ContourPlot[SX/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (x)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
ContourPlot[SY/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (y)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
ContourPlot[SZ/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Sigma]), (z)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"],
ContourPlot[TXZ/P, i, -2, 2, j, -2, 0,
PlotLabel -> "!(*SubscriptBox[([Tau]), (xz)])/P",
PlotLegends -> Automatic, FrameLabel -> "x/a", "z/a"]
answered 1 hour ago
Alex Trounev
3,4201313
answered 1 hour ago
Alex Trounev
3,4201313
answered 1 hour ago
Alex Trounev
3,4201313
answered 1 hour ago
Alex Trounev
3,4201313
3,4201313
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Kurt is a new contributor. Be nice, and check out our Code of Conduct.
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Kurt is a new contributor. Be nice, and check out our Code of Conduct.
Kurt is a new contributor. Be nice, and check out our Code of Conduct.
Kurt is a new contributor. Be nice, and check out our Code of Conduct.
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You don't need to discretize the formula yourself, check the document of
DensityPlotcarefully. Also, notice e.g.EandNare built-in symbol in Mathematica (See their color? They're black, rather than blue ), you can't use them as variable names.– xzczd
2 hours ago
What do you want to determine from these equations?
– Alex Trounev
2 hours ago
So I just want to graph the equations. Im not looking for any numerical results. The formulas will tell me the stress and shear below the surface of a material, and I'd like to see the counter plots.
– Kurt
2 hours ago