Global matrix assemblage

My question is really broken into two separate parts.

I have a system of linear bars which are subject to a moment force, each with one degree of freedom per end. I need to find out how much they rotate, this is a pretty simple "stiffness method" matrix problem, I know how to solve it by hand, I just have no idea where to begin in matlab.

We have created the following code to produce a 3 element matrix:

 nel= 3; %number of elements
 nnodes= 4; %number of nodes
 nDOF= 1; % number of degrees of freedom per node
 sDOF= nnodes*nDOF; % total number of degrees of freedom in our structure.

 G= [80*10^9;40*10^9;20*10^9]; %shear modulus
 L= [0.5;08;0.3]; %length of members 
 d= [0.08; 0.06; 0.04]; %diameters of members as defined in a vector.

 F= [3000; 2000; 800]; %force vector collectiong all of the applied moments 

 K= zeros(sDOF); %preallocation of the global stiffness matrix

 for iel= 1:nel

    elk= torsion1(G,L,d(iel));

    K(iel:iel+1, iel:iel+1)= elk + K(iel:iel+1, iel:iel+1);

 end %for

 K_ff= K(2:end, 2:end); %apply boundary condistions ( partition ) 

 U_f= K_ff\F;

 K_sf= K(1, 2:end);

 P_s= K_sf*U_f;

With function:

 function [elk]= torsion1(G,L,d) %G = shea modulus in pascals, L = length in meters and d = diameter in meters.

 Ip= pi*d^4/32; % polar intertia for shaft

 K_T= G*Ip/L; % stiffness 

 elk= K_T*[1 -1;-1 1]; % nodal stiffness matrix

We now have to modify the code to have nvalue of bars(I.e 1 to infinite), each with its own element stiffness matrix with unique values for the bars properties... I have basically labelled the following :

 function [U_f,T_s]= Shaft(N,G,L,d,T)

 % N = number of elements
 % G = vector for shear modulus of each element
 % L = vector for length of each element
 % d = vector for diameter of each element
 % T = vector for externally applied moments

I just dont know how to create the individual matricies and then assemble them into a global matrix, I need to some how create a different K_T based on the vector values for each bar, the number of K_T's and indeed the number of matricies required will obviously be set by N... am i right ? any help would be greatly appreciated.

P.s i have been using matlab for about 5 days so apologies if this is all really simple stuff to me it makes very little sense currently .. :(

Thanks for any help, kind regards.

Jake.

Answer 1

[ali badr]

I have the same problem Can anyone clarify the whole situation of assembling a global matrix from local matrices? Thanks

Answer 2

[Sean de Wolski]

Step back and write out how to assemble to element stiffness matrices (transformed if necessary) into a big stiffness matrix. The nodes that are shared are overlapped and summed when the big matrix is formed. It really is just a bunch of book keeping and organization in how you label your nodes/elements.