Get "Matrix is is singular to working precision" when attempting a global stiffness matrix with four nodes

% initialise Globgal Stiffness Matrix Using Zeros In A 4X4 Grid
K = zeros(4);

% define Stiffness Constants [lbf/in]
k1 = 1000;
k2 = 2000;
k3 = 3000;

% define Applied Forces [lbf]
f2 = -500;
f4 = 1000;

% set-Up Structural Matrix In A 2X2 Grid
% between Nodes 1 & 2
ks = k1*[1 -1;-1 1];
K(1:2,1:2) = K(1:2,1:2) + ks;

% between Nodes 2 & 3
ks = k2*[1 -1;-1 1];
K(2:3,2:3) = K(2:3,2:3) + ks;

% between Nodes 3 & 4
ks = k3*[1 -1;-1 1];
K(3:4,3:4) = K(3:4,3:4) + ks;

% columnise Forces
  f = [0;f2;0

I understand I haven't initialised f3 yet but I am not too sure how. My main issue is regarding the error I get when I run it. That being: "Matrix is singular to working precision". This is a four node spring assembly and I am required to find the global stiffness matrix and subsequently the displacement of the springs from node 1.

;f4];

Unrecognized function or variable 'f3'.

% columnise Displacement
d = zeros(4,1)

% initialise Range Variable
range = (2:4)

% solve
d(range) = k(range,range)\f(range)

Answer 1

[David Goodmanson]

Hi Declan,

I am not sure how you are getting the error message. Running the code with k changed to K

d(range) = K(range,range)\f(range)

gives

d =
     0
0.5000
1.0000
1.3333

which is correct. You can keep f3 = 0 since f represents external forces and there is no external force on node 3.

[Declan Kelly]

Thank you very much! I must have missed that little typo. Cheers