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

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Haris Hameed
on 5 Nov 2019

Commented: Haris Hameed
on 5 Nov 2019

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

##### 3 Comments

David Wilson
on 5 Nov 2019

### Accepted Answer

Richard Brown
on 5 Nov 2019

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.

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