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

Question

Declan Kelly 2023-2-22

0
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https://ww2.mathworks.cn/matlabcentral/answers/1916785-get-matrix-is-is-singular-to-working-precision-when-attempting-a-global-stiffness-matrix-with-four

评论： Declan Kelly 2023-2-22

% 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)