MASS/Stiffness Matrix Interpretation

[Gholamreza]

Hello engineers,

I use Print A command to get Mass or Stiffness matrix for a system (let say SDOF) but I don't know how to interpret that. here is the example:
I got this 6x6 stiffness matrix for SDOF:

2.06761e+06 0 17848 -2.05571e+06 0 0
0 1.56867e+14 -3.13734e+14 0 -1.56867e+14 -3.13734e+14
17848 -3.13734e+14 8.36625e+14 0 3.13734e+14 4.18313e+14
-2.05571e+06 0 0 2.06761e+06 0 17848
0 -1.56867e+14 3.13734e+14 0 1.56867e+14 3.13734e+14
0 -3.13734e+14 4.18313e+14 17848 3.13734e+14 8.36625e+14

Why I opensees gives this 6x6 stiffness matrix while I just expect to get one stiffness value (k) for SDOF ? is it related to different nodes and different degrees of freedom ?
Thanks

[emjac]

Take a look at your model builder command:
http://opensees.berkeley.edu/OpenSees/m ... al/403.htm

Say you have the SDOF below:

x---------------o --->F

A fixed end support at "x" and element between "x" and "o" with no support at "o" and a force F applied at "o".
If you model the it with -ndm 3 -ndf 6 you will have a 6x6 matrix. You may only really be using (applying force to) 1 DOF which is why people call it an SDOF. But all the other DOFs are there ready to use them.

Take a look at Model 1 and Model 2 below. They are equivalent models in that the displacements at node 2 are the same. But the stiffness matrix in 1 is 1x1 and in 2 is 6x6.

##MODEL 1

model basic -ndm 1 -ndf 1

node 1 0.0
node 2 0.0

fix 1 1

set k 200000

uniaxialMaterial Elastic 1 $k

element zeroLength 1 1 2 -mat 1 -dir 1

set P 100

pattern Plain 1 "Linear" {

load 2 $P

}

system FullGeneral
constraints Plain
numberer RCM
test NormDispIncr 0.01 10 0
algorithm Newton
integrator LoadControl 0.1
analysis Static

recorder Node -file nodes.out -time -node 2 -dof 1 disp

analyze 10

remove recorders

printA -file matrix.txt

##MODEL 2

model basic -ndm 3 -ndf 6

node 1 0.0 0.0 0.0
node 2 10 0.0 0.0

fix 1 1 1 1 1 1 1

set k 200000
set A 10
set Iz 1
set G 1
set J 1
set Iy 1

geomTransf Linear 1 1 1 0

uniaxialMaterial Elastic 1 $k

element elasticBeamColumn 1 1 2 $A $k $G $J $Iy $Iz 1

set P 100

pattern Plain 1 "Linear" {

load 2 $P 0 0 0 0 0

}

system FullGeneral
constraints Plain
numberer RCM
test NormDispIncr 0.01 10 0
algorithm Newton
integrator LoadControl 0.1
analysis Static

recorder Node -file nodes_equiv.out -time -node 2 -dof 1 disp

analyze 10

remove recorders

printA -file matrix_equiv.txt

[selimgunay]

Are you using a 3D, 6DOF model, i.e ndm=3, ndf=6?