Need to solve the differential equation for beam deflection and get the following plot

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

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

[Richard Brown]

What are you stuck with?

[Haris Hameed]

boundary conditions in it and plotting

[David Wilson]

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.

Answer 1

[Richard Brown]

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

where are constants. This equation is valid on the domain . It's easy enough to solve by integrating directly

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.

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.

[Haris Hameed]

its like four beams joined together, force is applied at top, the deformed and undeformed shapes are shown, (dotted as undeformed). i thought to model one beam and then mirror it to get this shape. the beam deflects in y direction but how to apply (move) it in x direction.