Computing Matrices with Multiple Variables that are Unknown

Please utilized following code to optimize solutions for unknown variables. Only need assistance with %Solve Section

%% PS3 - 1A
clear all

%% Givens

L = 10 %in

L = 10

E = 10 * 10^6 %PSI

E = 10000000

w = .5 %in

w = 0.5000

I = (w^4)/12

I = 0.0052

%% k1 = k2

j = E*I/(L^3)

j = 52.0833

k = j * [12 6*L -12 6*L
        6*L 4*L^2 -6*L 2*L^2
        -12 -6*L 12 -6*L
        6*L 2*L^2 -6*L 4*L^2]

k = 4x4

1.0e+04 * 0.0625 0.3125 -0.0625 0.3125 0.3125 2.0833 -0.3125 1.0417 -0.0625 -0.3125 0.0625 -0.3125 0.3125 1.0417 -0.3125 2.0833

%% K


K = [ k(1,1) k(1,2) k(1,3) k(1,4) 0 0
      k(2,1) k(2,2) k(2,3) k(2,4) 0 0
      k(3,1) k(3,2) (k(3,3) + k(1,1)) (k(3,4) + k(1,2)) k(1,3) k(1,4)
      k(4,1) k(4,2) (k(4,3) + k(1,2)) (k(4,4) + k(2,2)) k(2,3) k(2,4)
      0 0 k(1,3) k(2,3) k(3,3) k(4,3)
      0 0 k(1,4) k(2,4) k(3,4) k(4,4)]

K = 6x6

1.0e+04 * 0.0625 0.3125 -0.0625 0.3125 0 0 0.3125 2.0833 -0.3125 1.0417 0 0 -0.0625 -0.3125 0.1250 0 -0.0625 0.3125 0.3125 1.0417 0 4.1667 -0.3125 1.0417 0 0 -0.0625 -0.3125 0.0625 -0.3125 0 0 0.3125 1.0417 -0.3125 2.0833

%% U

v1 = 0

v1 = 0

%v2 = 
v3 = 0

v3 = 0

%t1 = 
%t2 = 
%t3 = 

syms v2 t1 t2 t3

U =  [v1 t1 v2 t2 v3 t3]'

U = 

%% F

q = 10 %lb/in

q = 10

F1R = 75 %lb RESULTANT FORCE

F1R = 75

F3R = 25 %lb RESULTANT FORCE

F3R = 25

F1 = F1R - (q*L)/4

F1 = 50

F2 = -(q*L)/4

F2 = -25

F3 = F3R

F3 = 25

M1 = -(q*L^2)/48

M1 = -20.8333

M2 = (q*L^2)/48

M2 = 20.8333

M3 = 0

M3 = 0

F = [F1 M1 F2 M2 F3 M3]'

F = 6x1

50.0000 -20.8333 -25.0000 20.8333 25.0000 0

%%Solve

Solved=solve(K.*U==F,[t1 v2 t2 t3])

Solved = struct with fields:
    t1: [0x1 sym]
    v2: [0x1 sym]
    t2: [0x1 sym]
    t3: [0x1 sym]

vpaSolved = vpa(struct2cell(Solved))

 
vpaSolved =
 
Empty sym: 0-by-1
 

[Walter Roberson]

There is no k2

[Romualdo Cipro]

@Walter Roberson code has been updated. That was for my reference.

[Torsten]

You must decide which of the variables you want to prescribe and which you want to solve for:

Solved=solve(K.*U==F,[f1 f3 F1 F3 v1 v2 v3 t1 t2 t3])

f1 and f3 are unknown variables in your code, F1 and F3 are set to numerical values - thus needn't be solved for, v1 and v3 are set to numerical values - thus needn't be solved for.

[Romualdo Cipro]

@Torsten I have updated code to try to solve for desired values. I now have empty matrices?

[Paul]

Hi Romualdo,

I modified the code a bit to use all symbolic constants, real variables, and used transpose, .' instead of ctranspose, ' as it seemed that is the intent. The final equation to be solved used element-wise multiplication times, .* with singleton expansion instead of matrix mutliplication mtimes, *; the former results in an obviously inconsistent set of equations. Still can't find a solution.

L = sym(10); %in
E = sym(10) * 10^6; %PSI

%w = .5 %in
w = sym(1)/2;
I = (w^4)/12;

%% k1 = k2
j = E*I/(L^3);

k = j * [12 6*L -12 6*L
        6*L 4*L^2 -6*L 2*L^2
        -12 -6*L 12 -6*L
        6*L 2*L^2 -6*L 4*L^2];
%% K
K = [ k(1,1) k(1,2) k(1,3) k(1,4) 0 0
      k(2,1) k(2,2) k(2,3) k(2,4) 0 0
      k(3,1) k(3,2) (k(3,3) + k(1,1)) (k(3,4) + k(1,2)) k(1,3) k(1,4)
      k(4,1) k(4,2) (k(4,3) + k(1,2)) (k(4,4) + k(2,2)) k(2,3) k(2,4)
      0 0 k(1,3) k(2,3) k(3,3) k(4,3)
      0 0 k(1,4) k(2,4) k(3,4) k(4,4)];
%% U
v1 = 0;
v3 = 0;

% assume real
syms v2 t1 t2 t3 real
% use transpose
U =  [v1 t1 v2 t2 v3 t3].' ;
 

%% F
q = sym(10); %lb/in

F1R = sym(75); %lb RESULTANT FORCE
F3R = sym(25); %lb RESULTANT FORCE
F1 = F1R - (q*L)/4;
F2 = -(q*L)/4;
F3 = F3R;
M1 = -(q*L^2)/48;
M2 = (q*L^2)/48;
M3 = 0;
% use transpose
F = [F1 M1 F2 M2 F3 M3].'  ;

Here's the equation to solve. It appears to not be correctly formulated, just by looking at the first row.

%%Solve
K.*U == F

ans = 

The preceding equation used element-wise multiplication. Maybe matrix multiplication was intended?

K*U == F

ans = 

Though these six equations in four unknowns also don't have a solution.

Solved=solve(K*U==F,[t1 v2 t2 t3])

Solved = struct with fields:
    t1: [0x1 sym]
    v2: [0x1 sym]
    t2: [0x1 sym]
    t3: [0x1 sym]