How to superimpose certain indices of matrices.

In FEA, after we have the Global Stiffness Matrix of a Plane Frame Member, we construct and assemble the Plane Frame Structure Stiffness Matrix. To be able to so, one needs to determine a mapping between the rows and columns of the global stiffness matrix of a member and those of the structure stiffness matrix. Suppose I have 3 memeber Global Stiffness Matrices (shown below) and want to assemble the structural global matrix. How to I superimpose them such that the u2, v2, theta2 of the matrices are added when superimposed?

Answer 1

[Alan Stevens]

Here's one possible way (there are probably slicker ways!):

K111 = K1(1:3,1:3); K112 = K1(1:3,4:6); 
K121 = K1(4:6,1:3); K122 = K1(4:6,4:6);
K211 = K2(1:3,1:3); K212 = K2(1:3,4:6); 
K221 = K2(4:6,1:3); K222 = K2(4:6,4:6);
K311 = K3(1:3,1:3); K312 = K3(1:3,4:6); 
K321 = K3(4:6,1:3); K322 = K3(4:6,4:6);
Z3 = zeros(3);
KG = [K111  K112   Z3    Z3; 
      K121  K122   K212  Z3;
      Z3    K211   Z3    Z3;      
      Z3    K221   K222  Z3;
      Z3    K311   Z3    K312;
      Z3    K321   Z3    K322];

[Missael Hernandez]

So I tried these matrices

K1 = [1 1 1 1 1 1;
      1 1 1 1 1 1;
      1 1 1 1 1 1;
      1 1 1 1 1 1;
      1 1 1 1 1 1;
      1 1 1 1 1 1];
  
K2 = [1 1 1 1 1 1;
      1 1 1 1 1 1;
      1 1 1 1 1 1;
      1 1 1 1 1 1;
      1 1 1 1 1 1;
      1 1 1 1 1 1];
  
K3 = [1 1 1 1 1 1;
      1 1 1 1 1 1;
      1 1 1 1 1 1;
      1 1 1 1 1 1;
      1 1 1 1 1 1;
      1 1 1 1 1 1]; 
  
K111 = K1(1:3,1:3); K112 = K1(1:3,4:6); 
K121 = K1(4:6,1:3); K122 = K1(4:6,4:6);
K211 = K2(1:3,1:3); K212 = K2(1:3,4:6); 
K221 = K2(4:6,1:3); K222 = K2(4:6,4:6);
K311 = K3(1:3,1:3); K312 = K3(1:3,4:6); 
K321 = K3(4:6,1:3); K322 = K3(4:6,4:6);
Z3 = zeros(3);
KG = [K111  K112   Z3    Z3; 
      K121  K122   K212  Z3;
      Z3    K211   Z3    Z3;      
      Z3    K221   K222  Z3;
      Z3    K311   Z3    K312;
      Z3    K321   Z3    K322]

And the output was

KG =

     1     1     1     1     1     1     0     0     0     0     0     0
     1     1     1     1     1     1     0     0     0     0     0     0
     1     1     1     1     1     1     0     0     0     0     0     0
     1     1     1     1     1     1     1     1     1     0     0     0
     1     1     1     1     1     1     1     1     1     0     0     0
     1     1     1     1     1     1     1     1     1     0     0     0
     0     0     0     1     1     1     0     0     0     0     0     0
     0     0     0     1     1     1     0     0     0     0     0     0
     0     0     0     1     1     1     0     0     0     0     0     0
     0     0     0     1     1     1     1     1     1     0     0     0
     0     0     0     1     1     1     1     1     1     0     0     0
     0     0     0     1     1     1     1     1     1     0     0     0
     0     0     0     1     1     1     0     0     0     1     1     1
     0     0     0     1     1     1     0     0     0     1     1     1
     0     0     0     1     1     1     0     0     0     1     1     1
     0     0     0     1     1     1     0     0     0     1     1     1
     0     0     0     1     1     1     0     0     0     1     1     1
     0     0     0     1     1     1     0     0     0     1     1     1

But the matrix should be 12-by-12 and KG_44 KG_45 KG_46

KG_54 KG_55 KG_56

KG_64 KG_65 KG_66

should be 3.

[Alan Stevens]

Oops! You are right. I’ll try again!

KG = [K111  K112            Z3    Z3;      
      K121  K122+K211+K311  K212  Z3;      
      Z3    K221            K222  Z3;      
      Z3    K321            Z3    K322];    

[Missael Hernandez]

perfect! thanks!