Example #1
Cantilever beam under the concentrated moment
code
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debug
M=1
EJ=50
L=49.9
function dz=f(x,y)
dz=[y(2),(M/EJ)*(1+(y(2))^2)^1.5]
endfunction
z0=[0;0];x0=0;x=0:L/100:L;
y=ode(z0,x0,x,f)
plot(x,y)
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result is 1/4 of circle (curve of constant curvature - blue)
'y' is the vector in the code above, it is why we have 2 curves (solution and derivative)
![](data:image/png;base64,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)
Cantilever beam under the concentrated moment
code
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debug
M=1
EJ=50
L=49.9
function dz=f(x,y)
dz=[y(2),(M/EJ)*(1+(y(2))^2)^1.5]
endfunction
z0=[0;0];x0=0;x=0:L/100:L;
y=ode(z0,x0,x,f)
plot(x,y)
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result is 1/4 of circle (curve of constant curvature - blue)
'y' is the vector in the code above, it is why we have 2 curves (solution and derivative)
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