Trying to solve for a number of variables in a matrix. Getting a structfun error.

Tyring to solve the below matrix for u variables. Getting a structfun error - unsure what is causing this. Error message below. Does anybody have an insight as to how to fix the structfun error? Setting uniform output to 'false' does not resolve the error.

E = 10;
v = 0.4;
rho = 950;
Lt = 2000;
Li = 250;
A = 7853.98;

u1=0;
S = (A*E/Li);
K = [1 -1 0 0 0 0 0 0 0; -1 2 -1 0 0 0 0 0 0; 0 -1 2 -1 0 0 0 0 0; 0 0 -1 2 -1 0 0 0 0; 0 0 0 -1 2 -1 0 0 0; 0 0 0 0 -1 2 -1 0 0; 0 0 0 0 0 -1 2 -1 0; 0 0 0 0 0 0 -1 2 -1; 0 0 0 0 0 0 0 -1 1]

F1=146.37;
F2=18.3;
F3=18.3;
F4=18.3;
F5=18.3;
F6=18.3;
F7=18.3;
F8=18.3;
F9=9.15;

syms u2 u3 u4 u5 u6 u7 u8 u9 real;


F = [F1; F2; F3; F4; F5; F6; F7; F8; F9];
d = [u1; u2; u3; u4; u5; u6; u7; u8; u9];



RHS = S*K*d
for i = 1:length(F)
    eqn(i,1) = F(i) == RHS(i);
end

unknowns = [u2, u3, u4, u5, u6, u7, u8, u9];

solution = solve(eqn, unknowns);
solution = vpa(structfun(@double,solution))

K =

1 -1 0 0 0 0 0 0 0

-1 2 -1 0 0 0 0 0 0

0 -1 2 -1 0 0 0 0 0

0 0 -1 2 -1 0 0 0 0

0 0 0 -1 2 -1 0 0 0

0 0 0 0 -1 2 -1 0 0

0 0 0 0 0 -1 2 -1 0

0 0 0 0 0 0 -1 2 -1

0 0 0 0 0 0 0 -1 1

RHS =

-(2763373546982447*u2)/8796093022208

(2763373546982447*u2)/4398046511104 - (2763373546982447*u3)/8796093022208

(2763373546982447*u3)/4398046511104 - (2763373546982447*u2)/8796093022208 - (2763373546982447*u4)/8796093022208

(2763373546982447*u4)/4398046511104 - (2763373546982447*u3)/8796093022208 - (2763373546982447*u5)/8796093022208

(2763373546982447*u5)/4398046511104 - (2763373546982447*u4)/8796093022208 - (2763373546982447*u6)/8796093022208

(2763373546982447*u6)/4398046511104 - (2763373546982447*u5)/8796093022208 - (2763373546982447*u7)/8796093022208

(2763373546982447*u7)/4398046511104 - (2763373546982447*u6)/8796093022208 - (2763373546982447*u8)/8796093022208

(2763373546982447*u8)/4398046511104 - (2763373546982447*u7)/8796093022208 - (2763373546982447*u9)/8796093022208

(2763373546982447*u9)/8796093022208 - (2763373546982447*u8)/8796093022208

Error using structfun

Non-scalar in Uniform output, at index 1, output 1.

Set 'UniformOutput' to false.

Answer 1

[Stephen23]

You have 9 equations but only 8 unknowns (u2–u9). Since u1=0 is already substituted in, MATLAB's solve sees an overconstrained system, finds no exact solution, and returns empty.

This is a classic FEM boundary condition issue. The correct approach is to partition the stiffness matrix : remove the row/column corresponding to the known DOF (u1=0) and solve the reduced 8×8 system:

E   = 10;
Li  = 250;
A   = 7853.98;
u1  = 0;
S   = (A*E/Li);

K = [1 -1 0 0 0 0 0 0 0; -1 2 -1 0 0 0 0 0 0; 0 -1 2 -1 0 0 0 0 0;
    0 0 -1 2 -1 0 0 0 0; 0 0 0 -1 2 -1 0 0 0; 0 0 0 0 -1 2 -1 0 0;
    0 0 0 0 0 -1 2 -1 0; 0 0 0 0 0 0 -1 2 -1; 0 0 0 0 0 0 0 -1 1];

F = [146.37; 18.3; 18.3; 18.3; 18.3; 18.3; 18.3; 18.3; 9.15];

% --- Partition: remove row 1 & col 1 (known DOF u1=0) ---
K_red = S * K(2:end, 2:end);          % 8x8 reduced stiffness matrix
F_red = F(2:end) - S*K(2:end,1)*u1;   % 8x1 reduced force vector (u1 term = 0 here)

% Solve the 8x8 system directly
u_free = K_red \ F_red;

% Assemble full displacement vector
u_all = [u1; u_free]

u_all = 9×1

0 0.4369 0.8155 1.1359 1.3980 1.6019 1.7475 1.8349 1.8640

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% Reaction force at node 1
R1 = S * K(1,:) * u_all

R1 = -137.2500

Answer 2

[Steven Lord]

Let's look at what solution is after the call to solve. I just added in a few semicolons to suppress some of the output.

E = 10;
v = 0.4;
rho = 950;
Lt = 2000;
Li = 250;
A = 7853.98;
u1=0;
S = (A*E/Li);
K = [1 -1 0 0 0 0 0 0 0; -1 2 -1 0 0 0 0 0 0; 0 -1 2 -1 0 0 0 0 0; 0 0 -1 2 -1 0 0 0 0; 0 0 0 -1 2 -1 0 0 0; 0 0 0 0 -1 2 -1 0 0; 0 0 0 0 0 -1 2 -1 0; 0 0 0 0 0 0 -1 2 -1; 0 0 0 0 0 0 0 -1 1];
F1=146.37;
F2=18.3;
F3=18.3;
F4=18.3;
F5=18.3;
F6=18.3;
F7=18.3;
F8=18.3;
F9=9.15;
syms u2 u3 u4 u5 u6 u7 u8 u9 real;
F = [F1; F2; F3; F4; F5; F6; F7; F8; F9];
d = [u1; u2; u3; u4; u5; u6; u7; u8; u9];
RHS = S*K*d;
for i = 1:length(F)
	eqn(i,1) = F(i) == RHS(i);
end
unknowns = [u2, u3, u4, u5, u6, u7, u8, u9];
solution = solve(eqn, unknowns)

solution = struct with fields:
    u2: [0×1 sym]
    u3: [0×1 sym]
    u4: [0×1 sym]
    u5: [0×1 sym]
    u6: [0×1 sym]
    u7: [0×1 sym]
    u8: [0×1 sym]
    u9: [0×1 sym]

% solution = vpa(structfun(@double,solution))

Your system doesn't appear to have any solutions. I would expect the structfun call to work if there was a unique solution, or in this case if you told MATLAB to return a non-uniform output.

structfun(@double, solution, UniformOutput = false)

ans = struct with fields:
    u2: [0×1 double]
    u3: [0×1 double]
    u4: [0×1 double]
    u5: [0×1 double]
    u6: [0×1 double]
    u7: [0×1 double]
    u8: [0×1 double]
    u9: [0×1 double]

If the solution is unique and convertible to double:

syms a b
sol = solve(a+b==6, a-b==0)

sol = struct with fields:
    a: 3
    b: 3

structfun(@double, sol)

ans = 2×1

3 3

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