Assembly of Global Stiffness Matrix

Hey Guys,

I am developing the code for a special 1D FEM problem for beam elements where each element has 2 nodes but each node has 6 degree of freedom.

So I have per element stiffness matrix of 12x12.

If I want to assemble its global stiffness matrix, I am having trouble how to do it.

I have everything else ready, element connectivity matrix, nodal list and also indivual element stiffness matrix, but I dont know how to do it using 2 nodes.

I know it can be done if my element has 12 nodes each having 1 degree of freedom, but with 2 nodes and 12 degree of freedom. I dont know how to do it.

I am attaching my code, If it is possible, kindly tell me how to do it?

% number of elements in the beam

nE =2

% generate number of nodes

nN=nE+1;

% DOFs per node

dpn = 6;

% Nodes per element

npe = 2;

% step size

step=(xb-xa_1)/nE;

if nE<1

error('Number of elements <1');

end

%initiliasation ( speeds up calculations)

Nod= zeros(nN,1);

Elm = zeros(nE,2);

%generate list of nodes

for i=1:1:nN

Nod(i,1) = xa + (i-1)*(xb-xa)/nE;

end

%generate connectivity array for elelments:

for kk=1:1:nE

Elm(kk,1)=kk;

Elm(kk,2)=kk+1;

end

%nodelabel and mark if node is a degree of dfreedon ( nodeLabel=0)

%or a boubdary node ( nodeLabel>0) and assign index of boundaryValue

nodeLabel=zeros(size(Nod));

nodeLabel(1) = 1 ;

nodeLabel(nN)=2;

%initialisation of A matrix

A=sparse(nN,nN);

disp('matrix assemly')

tic % start stopwatch

for n=1:1:nE

Se=alpha*local_element_matrix_K % Element Stiffness Matrix

Te=beta*local_element_matrix_M % Element Mass Matrix

Ge= local_element_matrix_G % Element Gyroscopic Matrix

Ce= (Se + Te)+Ge; % Element Damping Matrix

% Total Element Stiffness Matrix for 1 element

Ke=Se+Te+Ce; % size(Ke) = 12x12(Linear interpolation in 1D, multiple DOF per node)

for i=1:1:size(Ke,1)

glo_i= Elm(n,i);

if(nodeLabel(glo_i)>0)%Dirichlet boundary?%

A(glo_i,glo_i)=1.0;

else

for j = 1:1:size(Ke,2)

glo_j=Elm(n,j);

A(glo_i,glo_j)= A(glo_i,glo_j)+ Ke(i,j);

end

end

end %i

end %k

disp('')

spy(A) %