Sanity check of a stiffness matrix

[aeroaero]

Hi all,

I have a stiffness matrix sent to me and was asked to check the sanity of it and identify the physical process that it might have come from. I have gone through a number of FEM texts to get an idea about sanity, but was of no use. Can someone give me a clue atleast as to how I can do this ?

Thanks,
Chandra

 

[SWComposites]

Stiffness matrix of what?? material, structure, ? What is the purpose of this "sanity check"?

 

[aeroaero]

Hi, it is the stiffness matrix of a structure. The purpose is to see if matrices of this type could be assembled to form the global stiffness. Infact, the only thing that could prevent the latter is the rigid body motion which is clearly removed since this matrix is non-singular. The example of such a matrix is the following:

[K] = [1,2,0,0;2,5,1,0;0,1,6,2;0,0,2,8] N/mm

(Each row seperated by a semi-colon. There are 4 rows in total)

Other than the rigid body motion, I can't see why this can't be assembled. I need help in identifying what other kinds of sanity checks could be done to a stiffness matrix apart from the singularity check I described above.

Thanks in advance,
Chandra

 

[EricZhao]

The stiffness matrix at element level doesn't necessarily to be no singular. rigid body motion is removed after the assembly.

If my memory is right. Element stiffness matrix should be symmetric, non-negtive definite (no negtive eigenvalues). Other issue from assemly is DOFs matching. For example, If your global matrix doesn't have rotational DOFs, while your element matrix has. You will have some trouble.

 

[mastroit2002]

>The stiffness matrix at element level doesn't necessarily >to be no singular. Rigid body motion is removed after the >assembly.

This settence is true but not so common: if one is working with element stiff matrix normally forgets the dof not elastically connected (see CROD element for nodal rotation). So all the element matrices are nonsingular.

If you have to checkthe singularity of a big, sparse, matrix, I guess that the best way is to look for the smallest eigenvalue (note that if the ratio between biggest and smallest is greatest than give value [machine precision] the matrix is numerically singular).

.if zero. matrix is singular
.if near zero. matrix is numerically singular

At the end you can try the Singular Value Decomposition algorithm to find mechanism between DOF.

http://www.library.cornell.edu/nr/bookcpdf/c2-6.pdf

I hope this will be of help.