Which Solver can do eigenvalues with Lagrande multipliers
Which Solver can do eigenvalues with Lagrande multipliers
(OP)
I am trying to figure out which solver (in Fortran) will be able to calculate eigenvalues for a matrix that has been augmented with Lagrange multipliers.
Basically I have a FEM model with 20node solids and 4node plates that are coupled with Lagrange multies in a inhouse FE program. I have been using the Lapack DSPGVX subroutine in Fortran 90 with my other models but now with this coupling I am not able because of singular matrix.
Anyone with some words if advice would be of great help...
Basically I have a FEM model with 20node solids and 4node plates that are coupled with Lagrange multies in a inhouse FE program. I have been using the Lapack DSPGVX subroutine in Fortran 90 with my other models but now with this coupling I am not able because of singular matrix.
Anyone with some words if advice would be of great help...





RE: Which Solver can do eigenvalues with Lagrande multipliers
This means some zero value eignevalues
This means rigid body motion in structures or ill conditioning.
Am i right?
Dr. Costas J. Tsaprounis
RE: Which Solver can do eigenvalues with Lagrande multipliers
Your singualarity is caused by a degree of freedom without any structural stiffness (or very low), and as such cannot be inverted.
Typical usual examples of this are 1) forgetting to eliminate rigid body modes, 2) connecting dissimilar element types, 3) cross connecting wrong degrees of freedom.
RE: Which Solver can do eigenvalues with Lagrande multipliers
due to the mixed-elem type formulation, I'd guess that 40818's point 2) is the responsible. You wouldn't like to solve a singular system, I presume.
Regards
RE: Which Solver can do eigenvalues with Lagrande multipliers
Ansys, Hypermesh and other programs are able to come about eigen results even if the matrix is sigular or closed to it.
But my in house program with can not compute a structure that should have the first 6 eigenvalues =0 . I read about some solvers that can handle these situations but the Fortran Lapack DSPGVX subroutine can't.
So HOW do Ansys, Abaqus and ther FE programs deal with this sort of matrix?
Thank you for your time
J.Blair M.Sc.A,ing.
RE: Which Solver can do eigenvalues with Lagrande multipliers
I will have to delve back into some theory guides to tell you how the FE solves a singular matrix.
RE: Which Solver can do eigenvalues with Lagrande multipliers
This is done by applying an "eigen shift" , that is a factored amount of the mass matrix is added to the stiffness matrix to make the stiffness matrix non-singular, solution is then possible, the mode shapes are not affected by this procedure but all the eigen values are "shifted" to become greater than zero, the solver will then automatically remove this shift from the eigen values before presenting results to the user.
RE: Which Solver can do eigenvalues with Lagrande multipliers
RE: Which Solver can do eigenvalues with Lagrande multipliers
If you want to see how eigne shift is done see
the "Numerical Recipies".
Good luck
Dr. Costas J. Tsaprounis
RE: Which Solver can do eigenvalues with Lagrande multipliers
Kind regards
J Blair
RE: Which Solver can do eigenvalues with Lagrande multipliers
RE: Which Solver can do eigenvalues with Lagrande multipliers
The DGGEVX routine did the job quite well.
Thank you all for your input
Cheers