Finding the absolute maximum of a 3 variable function
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How do I approach finding the maximum for an $f(x,y,z)$?
$f(x,y,z)$= $6.365+7335000y-24450xy-0.5* sqrt {10614564y^4+2391210000x^2y^2-1434726000000xy^2+31858027.2zy^2+215208923890984y^2+23904276.64z^2-1244994xy+373498200y-19947.936z+166.2145}$
I need to calculate the maximum value of the function for both of these seperately.
The locus is the cylinder $0<=x<=a$, $:y^2+z^2<= b$ where $a,b$ are parameters.
Context: This is an expression for the principal stresses in a cylindrical beam, in a project I was working. I wish to find the maximum value of stress, and the element in which it occurs. Also, I have Finite Element Analysis results to compare with. a=0.3 b=0.025.
Here is the relevant MATLAB code
clear all
syms x;
syms y;
syms z;
syms rho;
A=[(12.73+(1467-4.89*x)*y*10000)-rho 2444.6*z-1.02+1629*y^2 2444.6*y; 2444.6*z-1.02+1629*y^2 0-rho 0; 2444.6*y 0 0-rho ];
eqn = det(A)==0
roots = solve(eqn, rho)
r1=roots(1)
r2=roots(2)
r3=roots(3)
calculus 3d
asked Nov 17 at 3:57
Rohit
1589
|
show 3 more comments
up vote
0
down vote
favorite
How do I approach finding the maximum for an $f(x,y,z)$?
$f(x,y,z)$= $6.365+7335000y-24450xy-0.5* sqrt {10614564y^4+2391210000x^2y^2-1434726000000xy^2+31858027.2zy^2+215208923890984y^2+23904276.64z^2-1244994xy+373498200y-19947.936z+166.2145}$
I need to calculate the maximum value of the function for both of these seperately.
The locus is the cylinder $0<=x<=a$, $:y^2+z^2<= b$ where $a,b$ are parameters.
Context: This is an expression for the principal stresses in a cylindrical beam, in a project I was working. I wish to find the maximum value of stress, and the element in which it occurs. Also, I have Finite Element Analysis results to compare with. a=0.3 b=0.025.
Here is the relevant MATLAB code
clear all
syms x;
syms y;
syms z;
syms rho;
A=[(12.73+(1467-4.89*x)*y*10000)-rho 2444.6*z-1.02+1629*y^2 2444.6*y; 2444.6*z-1.02+1629*y^2 0-rho 0; 2444.6*y 0 0-rho ];
eqn = det(A)==0
roots = solve(eqn, rho)
r1=roots(1)
r2=roots(2)
r3=roots(3)
calculus 3d
asked Nov 17 at 3:57
Rohit
1589
Explicit function $f(x,y,z)$ is also needed.
– Rócherz
Nov 17 at 4:00
The question may need some update for better understanding but it really sounds to me like you didn't notice that you have a Lagrange's Multipliers problems in hand.
– Mefitico
Nov 17 at 4:30
@Mefitico yes, out of my depth here
– Rohit
Nov 17 at 4:53
Are you able to provide a factored version of the radical? Something like $sqrt{(ax^2+by^2)^2+(cz-dx)^2}$? Where does the expression for $f$ come from?
– Mefitico
Nov 17 at 19:55
@Mefitico from taking the determinant of the matrix in the code, equating it to zero, and solving for rho.
– Rohit
Nov 17 at 22:00
|
show 3 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
How do I approach finding the maximum for an $f(x,y,z)$?
$f(x,y,z)$= $6.365+7335000y-24450xy-0.5* sqrt {10614564y^4+2391210000x^2y^2-1434726000000xy^2+31858027.2zy^2+215208923890984y^2+23904276.64z^2-1244994xy+373498200y-19947.936z+166.2145}$
I need to calculate the maximum value of the function for both of these seperately.
The locus is the cylinder $0<=x<=a$, $:y^2+z^2<= b$ where $a,b$ are parameters.
Context: This is an expression for the principal stresses in a cylindrical beam, in a project I was working. I wish to find the maximum value of stress, and the element in which it occurs. Also, I have Finite Element Analysis results to compare with. a=0.3 b=0.025.
Here is the relevant MATLAB code
clear all
syms x;
syms y;
syms z;
syms rho;
A=[(12.73+(1467-4.89*x)*y*10000)-rho 2444.6*z-1.02+1629*y^2 2444.6*y; 2444.6*z-1.02+1629*y^2 0-rho 0; 2444.6*y 0 0-rho ];
eqn = det(A)==0
roots = solve(eqn, rho)
r1=roots(1)
r2=roots(2)
r3=roots(3)
calculus 3d
asked Nov 17 at 3:57
Rohit
1589
How do I approach finding the maximum for an $f(x,y,z)$?
$f(x,y,z)$= $6.365+7335000y-24450xy-0.5* sqrt {10614564y^4+2391210000x^2y^2-1434726000000xy^2+31858027.2zy^2+215208923890984y^2+23904276.64z^2-1244994xy+373498200y-19947.936z+166.2145}$
I need to calculate the maximum value of the function for both of these seperately.
The locus is the cylinder $0<=x<=a$, $:y^2+z^2<= b$ where $a,b$ are parameters.
Context: This is an expression for the principal stresses in a cylindrical beam, in a project I was working. I wish to find the maximum value of stress, and the element in which it occurs. Also, I have Finite Element Analysis results to compare with. a=0.3 b=0.025.
Here is the relevant MATLAB code
clear all
syms x;
syms y;
syms z;
syms rho;
A=[(12.73+(1467-4.89*x)*y*10000)-rho 2444.6*z-1.02+1629*y^2 2444.6*y; 2444.6*z-1.02+1629*y^2 0-rho 0; 2444.6*y 0 0-rho ];
eqn = det(A)==0
roots = solve(eqn, rho)
r1=roots(1)
r2=roots(2)
r3=roots(3)
calculus 3d
calculus 3d
asked Nov 17 at 3:57
Rohit
1589
asked Nov 17 at 3:57
Rohit
1589
edited Nov 17 at 13:14
asked Nov 17 at 3:57
Rohit
1589
asked Nov 17 at 3:57
Rohit
1589
asked Nov 17 at 3:57
Rohit
1589
1589
Explicit function $f(x,y,z)$ is also needed.
– Rócherz
Nov 17 at 4:00
The question may need some update for better understanding but it really sounds to me like you didn't notice that you have a Lagrange's Multipliers problems in hand.
– Mefitico
Nov 17 at 4:30
@Mefitico yes, out of my depth here
– Rohit
Nov 17 at 4:53
Are you able to provide a factored version of the radical? Something like $sqrt{(ax^2+by^2)^2+(cz-dx)^2}$? Where does the expression for $f$ come from?
– Mefitico
Nov 17 at 19:55
@Mefitico from taking the determinant of the matrix in the code, equating it to zero, and solving for rho.
– Rohit
Nov 17 at 22:00
|
show 3 more comments
Explicit function $f(x,y,z)$ is also needed.
– Rócherz
Nov 17 at 4:00
The question may need some update for better understanding but it really sounds to me like you didn't notice that you have a Lagrange's Multipliers problems in hand.
– Mefitico
Nov 17 at 4:30
@Mefitico yes, out of my depth here
– Rohit
Nov 17 at 4:53
Are you able to provide a factored version of the radical? Something like $sqrt{(ax^2+by^2)^2+(cz-dx)^2}$? Where does the expression for $f$ come from?
– Mefitico
Nov 17 at 19:55
@Mefitico from taking the determinant of the matrix in the code, equating it to zero, and solving for rho.
– Rohit
Nov 17 at 22:00
Explicit function $f(x,y,z)$ is also needed.
– Rócherz
Nov 17 at 4:00
Explicit function $f(x,y,z)$ is also needed.
– Rócherz
Nov 17 at 4:00
The question may need some update for better understanding but it really sounds to me like you didn't notice that you have a Lagrange's Multipliers problems in hand.
– Mefitico
Nov 17 at 4:30
The question may need some update for better understanding but it really sounds to me like you didn't notice that you have a Lagrange's Multipliers problems in hand.
– Mefitico
Nov 17 at 4:30
@Mefitico yes, out of my depth here
– Rohit
Nov 17 at 4:53
@Mefitico yes, out of my depth here
– Rohit
Nov 17 at 4:53
Are you able to provide a factored version of the radical? Something like $sqrt{(ax^2+by^2)^2+(cz-dx)^2}$? Where does the expression for $f$ come from?
– Mefitico
Nov 17 at 19:55
Are you able to provide a factored version of the radical? Something like $sqrt{(ax^2+by^2)^2+(cz-dx)^2}$? Where does the expression for $f$ come from?
– Mefitico
Nov 17 at 19:55
@Mefitico from taking the determinant of the matrix in the code, equating it to zero, and solving for rho.
– Rohit
Nov 17 at 22:00
@Mefitico from taking the determinant of the matrix in the code, equating it to zero, and solving for rho.
– Rohit
Nov 17 at 22:00
|
show 3 more comments
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Explicit function $f(x,y,z)$ is also needed.
– Rócherz
Nov 17 at 4:00
The question may need some update for better understanding but it really sounds to me like you didn't notice that you have a Lagrange's Multipliers problems in hand.
– Mefitico
Nov 17 at 4:30
@Mefitico yes, out of my depth here
– Rohit
Nov 17 at 4:53
Are you able to provide a factored version of the radical? Something like $sqrt{(ax^2+by^2)^2+(cz-dx)^2}$? Where does the expression for $f$ come from?
– Mefitico
Nov 17 at 19:55
@Mefitico from taking the determinant of the matrix in the code, equating it to zero, and solving for rho.
– Rohit
Nov 17 at 22:00