Why Does MATLAB Show NaN for Truss Deflections?

[nate9519]

Homework Statement

I'm using MATLAB to design a truss and the output is suppose to be the deflections caused by the applied loads. But I keep getting "not a number" for my deflections . here is the warnings I get.

Warning: System may be partially constrained.
> In truss3 (line 222)
In truss3ex2 (line 26)
Warning: Matrix is singular to working precision.
> In truss3 (line 224)
In truss3ex2 (line 26)

Homework Equations

relevant lines from truss3 starting at line 219

% Solve the force-displacement equations.AA = [a,zero1;e,d]; BB = [b,zero2]'; detAA = det(AA);

if abs(detAA) < 1e-16

warning('System may be partially constrained.')

end

AAinv = inv(AA); sol = AAinv*BB;

% Prepare the output quantities.

pp = 0;

for i = 1:nJforce(i,1) = i; Jdispl(i,1) = i;

isol = 2*m+p+3*(i-1);

Jdispl(i,2) = sol(isol+1); Jdispl(i,3) = sol(isol+2);

Jdispl(i,4) = sol(isol+3);

[\code][h2]The Attempt at a Solution[/h2] 
[/B]
here is the code.

[code=matlab]
% class design project example%

% all of the members are quenched steel

% k = 2000 k-lb, Pmax = 1500 k-lb (A = 100 sq-inch)

%

clear

n = 24; m = 60; LOADZ = -20000; LOADY = 1000; A = 100;

joint = [0,0,0;0,0,-10;0,0,-20;12,0,0;12,0,-10;12,0,-20;...

0,10,0;0,10,-10;12,10,0;12,10,-10;0,20,0;0,20,-10;...

12,20,0;12,20,-10;0,30,0;0,30,-10;12,30,0;12,30,-10;...

0,40,0;0,40,-10;0,40,-20;12,40,0;12,40,-10;12,40,-20];

assembly = [1,2;1,4;1,7;2,3;2,4;2,5;2,6;2,7;2,8;3,6;3,8;...

4,5;4,9;5,6;5,9;5,10;6,10;7,8;7,9;7,11;8,9;8,10;8,11;...

8,12;9,10;9,13;10,13;10,14;11,12;11,13;11,14;11,15;11,16;...

12,14;12,16;13,14;13,17;13,18;14,18;15,16;15,17;15,19;15,20;...

16,17;16,18;16,20;16,21;17,18;17,22;17,23;18,23;18,24;19,20;...

19,22;20,22;20,23;20,24;21,24;22,23;23,24];

forceJ = [3,1,1,1;3,1,1,1;3,1,1,1;3,1,1,1;3,1,1,1;...

3,1,1,1;-1,0,0,0;-1,0,0,0;...

-1,0,0,0; -1,0,0,0;-1,0,LOADY,LOADZ;-1,0,0,0;...

-1,0,LOADY,LOADZ;-1,0,0,0;-1,0,0,0;-1,0,0,0;-1,0,0,0;-1,0,0,0;...

3,1,1,1;3,1,1,1;3,1,1,1;3,1,1,1;3,1,1,1;3,1,1,1];

for i = 1:m; stretch(i) = 2000*1000; end; stretch(1);

%

index = 1;

[Jforce,Mforce,Jdispl,Mdispl] = ...                                                ([B]LINE 26)[/B]

truss3(n,m,joint,assembly,forceJ,stretch,index);

%

peak_klb = 18*A

maxMforce_klb = max(abs(Mforce/1000))

maxJdispl = max(abs(Jdispl*12));

maxDX_in = maxJdispl(2),maxDY_in = maxJdispl(3),maxDZ_in = maxJdispl(4)

[\code]for forceJ, (3,1,1,1) indicates a external joint with 3 reaction forces. (-1,0,0,0) indicates an internal joint with no loads.
Can anyone help me figure out this problem with the matrices? I have no idea what to do

 

[BvU]

Hi, you want to use $[$code=matlab$]$
$[$code=matlab$]$

(code goes here)​

$[$\code$]$
to keep it legible:

% Solve the force-displacement equations.

AA = [a,zero1;e,d]; BB = [b,zero2]'; detAA = det(AA);

if abs(detAA) < 1e-16
    warning('System may be partially constrained.')
end

AAinv = inv(AA); sol = AAinv*BB;

% Prepare the output quantities.

pp = 0;

for i = 1:n

   Jforce(i,1) = i; Jdispl(i,1) = i;

   isol = 2*m+p+3*(i-1);

   Jdispl(i,2) = sol(isol+1); Jdispl(i,3) = sol(isol+2);

   Jdispl(i,4) = sol(isol+3);

end

% 3. The Attempt at a Solution 
% here is the code.

% class design project example
%
% all of the members are quenched steel
% k = 2000 k-lb, Pmax = 1500 k-lb (A = 100 sq-inch)
%

clear

n = 24; m = 60; LOADZ = -20000; LOADY = 1000; A = 100;

joint = [0,0,0;0,0,-10;0,0,-20;12,0,0;12,0,-10;12,0,-20;...

0,10,0;0,10,-10;12,10,0;12,10,-10;0,20,0;0,20,-10;...

12,20,0;12,20,-10;0,30,0;0,30,-10;12,30,0;12,30,-10;...

0,40,0;0,40,-10;0,40,-20;12,40,0;12,40,-10;12,40,-20];

assembly = [1,2;1,4;1,7;2,3;2,4;2,5;2,6;2,7;2,8;3,6;3,8;...

4,5;4,9;5,6;5,9;5,10;6,10;7,8;7,9;7,11;8,9;8,10;8,11;...

8,12;9,10;9,13;10,13;10,14;11,12;11,13;11,14;11,15;11,16;...

12,14;12,16;13,14;13,17;13,18;14,18;15,16;15,17;15,19;15,20;...

16,17;16,18;16,20;16,21;17,18;17,22;17,23;18,23;18,24;19,20;...

19,22;20,22;20,23;20,24;21,24;22,23;23,24];

forceJ = [3,1,1,1;3,1,1,1;3,1,1,1;3,1,1,1;3,1,1,1;...

3,1,1,1;-1,0,0,0;-1,0,0,0;...

-1,0,0,0; -1,0,0,0;-1,0,LOADY,LOADZ;-1,0,0,0;...

-1,0,LOADY,LOADZ;-1,0,0,0;-1,0,0,0;-1,0,0,0;-1,0,0,0;-1,0,0,0;...

3,1,1,1;3,1,1,1;3,1,1,1;3,1,1,1;3,1,1,1;3,1,1,1];

for i = 1:m; stretch(i) = 2000*1000; end; stretch(1);

%

index = 1;

[Jforce,Mforce,Jdispl,Mdispl] = ...                                     %           ([B]LINE 26)[/B]

truss3(n,m,joint,assembly,forceJ,stretch,index);

%

peak_klb = 18*A

maxMforce_klb = max(abs(Mforce/1000))

maxJdispl = max(abs(Jdispl*12));

maxDX_in = maxJdispl(2),maxDY_in = maxJdispl(3),maxDZ_in = maxJdispl(4)

 

[SteamKing]

Seems like this is old news.

In order for the stiffness matrix equations to have a solution, at least one or more nodes need to have an initial displacement specified. Thus usually is accomplished by specifying a zero displacement at the support points of the structure.

It's not clear from your code where such initial conditions are specified by the user. Without being able to specify an initial displacement for at least one node, the stiffness matrix equations are probably giving a singular result when the deflections are being solved for.

See p. 11 of the following article:

http://www.engr.sjsu.edu/ragarwal/ME273/pdf/Chapter 4 - Beam Element.pdf

More details can be found in the attached file below.