Solving a strong form differential equation (FEM) using MATLAB
$begingroup$
I need some diagnosis on how I'm solving my differential equation. This was a template given to me by my professor and I manipulated it to the best of my ability.
The governing equations are here:
And here is my code:
clear;
clc;
close all;
% u,,xx=-(f/ea) on [0,L]
% u,x(L)= R
% u(0)=0
% Parameters
L= 1;
% Parameters in force function
A= .0001;
E= 70e9;
R= 1000;
a= 1000;
g= R/E*A;
f= @(x) ((((-1)*(a)*(x))/E*A));
% solve analytical solution
u1 = dsolve(['D2y = ' char(sym(f))], ['Dy(1) = ' num2str(g)], ['y(0) ='
num2str(0)] ,'x');
% change symbolic function to anonymous matlab function for easier
computing
u = matlabFunction(u1);
% plot the analytical solution
n= 20;
x = linspace(0, 1, n);
plot(x, u(x), '-ro', 'LineWidth', 4)
title('Analytical Solution u')
axis([0, 1, 0, 3])
xlabel('x')
ylabel('u')
I come across issues when I try to plot my values. The analytical solution should be around in the .21428 range or something. I figured that it has to be an issue with my differential solver or the way that I am plotting it but I definitely think its the ODE solving that's got me messed up.
I'm pretty much stuck at this point. I checked my equations to be sure they were right but alas no issues there so I could definitely use another brain.
If you need to see the question prompt let me know. I was wary of posting it because of my professor so I didn't think it'd be too necessary.
Note: u,xx is a second order and u,x is a first order.
matlab
asked 46 mins ago
Lil_TEELil_TEE
1
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add a comment |
$begingroup$
I need some diagnosis on how I'm solving my differential equation. This was a template given to me by my professor and I manipulated it to the best of my ability.
The governing equations are here:
And here is my code:
clear;
clc;
close all;
% u,,xx=-(f/ea) on [0,L]
% u,x(L)= R
% u(0)=0
% Parameters
L= 1;
% Parameters in force function
A= .0001;
E= 70e9;
R= 1000;
a= 1000;
g= R/E*A;
f= @(x) ((((-1)*(a)*(x))/E*A));
% solve analytical solution
u1 = dsolve(['D2y = ' char(sym(f))], ['Dy(1) = ' num2str(g)], ['y(0) ='
num2str(0)] ,'x');
% change symbolic function to anonymous matlab function for easier
computing
u = matlabFunction(u1);
% plot the analytical solution
n= 20;
x = linspace(0, 1, n);
plot(x, u(x), '-ro', 'LineWidth', 4)
title('Analytical Solution u')
axis([0, 1, 0, 3])
xlabel('x')
ylabel('u')
I come across issues when I try to plot my values. The analytical solution should be around in the .21428 range or something. I figured that it has to be an issue with my differential solver or the way that I am plotting it but I definitely think its the ODE solving that's got me messed up.
I'm pretty much stuck at this point. I checked my equations to be sure they were right but alas no issues there so I could definitely use another brain.
If you need to see the question prompt let me know. I was wary of posting it because of my professor so I didn't think it'd be too necessary.
Note: u,xx is a second order and u,x is a first order.
matlab
asked 46 mins ago
Lil_TEELil_TEE
1
New contributor
Lil_TEE is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I need some diagnosis on how I'm solving my differential equation. This was a template given to me by my professor and I manipulated it to the best of my ability.
The governing equations are here:
And here is my code:
clear;
clc;
close all;
% u,,xx=-(f/ea) on [0,L]
% u,x(L)= R
% u(0)=0
% Parameters
L= 1;
% Parameters in force function
A= .0001;
E= 70e9;
R= 1000;
a= 1000;
g= R/E*A;
f= @(x) ((((-1)*(a)*(x))/E*A));
% solve analytical solution
u1 = dsolve(['D2y = ' char(sym(f))], ['Dy(1) = ' num2str(g)], ['y(0) ='
num2str(0)] ,'x');
% change symbolic function to anonymous matlab function for easier
computing
u = matlabFunction(u1);
% plot the analytical solution
n= 20;
x = linspace(0, 1, n);
plot(x, u(x), '-ro', 'LineWidth', 4)
title('Analytical Solution u')
axis([0, 1, 0, 3])
xlabel('x')
ylabel('u')
I come across issues when I try to plot my values. The analytical solution should be around in the .21428 range or something. I figured that it has to be an issue with my differential solver or the way that I am plotting it but I definitely think its the ODE solving that's got me messed up.
I'm pretty much stuck at this point. I checked my equations to be sure they were right but alas no issues there so I could definitely use another brain.
If you need to see the question prompt let me know. I was wary of posting it because of my professor so I didn't think it'd be too necessary.
Note: u,xx is a second order and u,x is a first order.
matlab
asked 46 mins ago
Lil_TEELil_TEE
1
New contributor
Lil_TEE is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I need some diagnosis on how I'm solving my differential equation. This was a template given to me by my professor and I manipulated it to the best of my ability.
The governing equations are here:
And here is my code:
clear;
clc;
close all;
% u,,xx=-(f/ea) on [0,L]
% u,x(L)= R
% u(0)=0
% Parameters
L= 1;
% Parameters in force function
A= .0001;
E= 70e9;
R= 1000;
a= 1000;
g= R/E*A;
f= @(x) ((((-1)*(a)*(x))/E*A));
% solve analytical solution
u1 = dsolve(['D2y = ' char(sym(f))], ['Dy(1) = ' num2str(g)], ['y(0) ='
num2str(0)] ,'x');
% change symbolic function to anonymous matlab function for easier
computing
u = matlabFunction(u1);
% plot the analytical solution
n= 20;
x = linspace(0, 1, n);
plot(x, u(x), '-ro', 'LineWidth', 4)
title('Analytical Solution u')
axis([0, 1, 0, 3])
xlabel('x')
ylabel('u')
I come across issues when I try to plot my values. The analytical solution should be around in the .21428 range or something. I figured that it has to be an issue with my differential solver or the way that I am plotting it but I definitely think its the ODE solving that's got me messed up.
I'm pretty much stuck at this point. I checked my equations to be sure they were right but alas no issues there so I could definitely use another brain.
If you need to see the question prompt let me know. I was wary of posting it because of my professor so I didn't think it'd be too necessary.
Note: u,xx is a second order and u,x is a first order.
matlab
matlab
asked 46 mins ago
Lil_TEELil_TEE
1
New contributor
Lil_TEE is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 46 mins ago
Lil_TEELil_TEE
1
New contributor
Lil_TEE is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 46 mins ago
Lil_TEELil_TEE
1
New contributor
Lil_TEE is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 46 mins ago
Lil_TEELil_TEE
1
asked 46 mins ago
Lil_TEELil_TEE
1
1
New contributor
Lil_TEE is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Lil_TEE is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Lil_TEE is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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