Need to solve the differential equation for beam deflection and get the following plot
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Hi all
i am trying to solve the beam defelction equation and get the plot (as shown in image),
can someone guide me further how to code all this, i developed some of it but cant proceede further
thanks for your time
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/246532/image.jpeg)
clc
clear
for F=0:0.1:0.5 %force
%F=0;
d=0.6; %diameter mm
l=sqrt(72); %length mm
A=pi/4*d^2; %cross section dia
E=2460; %youngs modulus in MPa
mu=0.3;
G=E*2*(1+mu);
I=1/4*pi*(d/2)^4;
k=1/1.1; %shape factor
i=0;
w(1)=0;
th=35.264*pi/180;
a=F/(k^2*G*A);
b=F/(E*I);
th=32*pi/180;
for x=0:0.2:l
i=i+1;
%w(i)=-a*x+b*x^2/4*(2-l);
w(i)=-(a*x)+(b*x^3/6)-(b*x^2*l/4);
h(i)=w(i)*cos(th);
%w(1,43)=0;
end
x=0:0.2:l;
plot(x+h,w+h)
hold on
plot(-x+h,w+h)
end
3 件のコメント
David Wilson
2019 年 11 月 5 日
Are you sure you have the correct equations? Typically for beam problems you have a 4th order differential equation (not 1st as you have written), and therefore you need 4 boundary conditions, and to solve it you need bvp4c or equivalent.
採用された回答
Richard Brown
2019 年 11 月 5 日
I think the problem you're having is not fully figuring out your solution before diving in and coding it. You have a differential equation of the form
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/246537/image.png)
where
are constants. This equation is valid on the domain
. It's easy enough to solve by integrating directly
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/246538/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/246539/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/246540/image.png)
You can figure out what
is from the boundary condition (all the other terms go away when
). If you think of it this way and define the various constants
in terms of the physical parameters, it's a bit easier to see what's going on - all of the parameters "get in the way" and make the expressions look overcomplicated.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/246541/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/246542/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/246543/image.png)
So that's the mathematical part, which is pretty straightforward. The problem is relating it to your picture -- what are we looking at? What is the actual geometry of a problem? Where is the force being applied? The picture doesn't look like a cantilevered beam.
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