Finite Elements Method creating global stiffness matrix

Hi everyone, I am really stuck in creating a code that creates global stiffness matrix that changing local stiffness matrixes value in every cycle.

For example it has to be

k1 -k1 0 0

-k1 k1+k2 - k2 0

0 - k2 k2+k3 -k3

0 0 -k3 k3

but my code doesn't change k1 to k2 for next step ... it only calculates for k1.

k1 -k1 0 0

-k1 k1+k1 - k1 0

0 - k1 k1+k1 -k1

0 0 -k1 k1

Please help me to solve this problem. Thanks.

clear
tp=[1 2]
for i=2:4
    tp(i,:)=tp(i-1,:)+1
end
tpmax=max(max(tp));
KG=zeros(tpmax,tpmax); 
for i=1:4 
d(i)=32+(28/1200)*(2*i-1)*50
G(i)=(77000*pi*d(i).^4)/3200
k=[G(i) -G(i);-G(i) G(i)]  
end
for n=1:4
    i=n+[0 1]
    j=i
    KG(i,j)=KG(i,j)+k    
end

[Mehmet Ali kurt]

Hi Omer ; If you have solition of 'Derived stiffness matrix for 1D 3-Nodes elements' can you send me please ?

[Ghazi Fanar]

Answer

Answer 1

[Stephan]

Hi,

you overwrite k every time. Im sure it could be done much easier - but here s a quick solution without any code optimization (Matlab users usually try to avoid for loops...):

clear
tp=[1 2];
for i=2:4
    tp(i,:)=tp(i-1,:)+1;
end
tpmax=max(max(tp));
KG=zeros(tpmax,tpmax); 
for i=1:4 
d(i)=32+(28/1200)*(2*i-1)*50;
G(i)=(77000*pi*d(i).^4)/3200;
k(:,:,i)=[G(i) -G(i);-G(i) G(i)];  
end
for n=1:4
    i=n+[0 1];
    j=i;
    KG(i,j)=KG(i,j)+k(:,:,n);    
end

Result is:

KG =

   1.0e+08 *

    0.9147   -0.9147         0         0         0
   -0.9147    2.1154   -1.2006         0         0
         0   -1.2006    2.7494   -1.5488         0
         0         0   -1.5488    3.5165   -1.9677
         0         0         0   -1.9677    1.9677

I think this is what you expected.

Best regards

Stephan

[ömer altay]

Very educational. Thanks.

[Stephan]

If my answer was useful, please accept it.

[Yago Trias Vila]

Exactly what I needed, Thanks!