MATLAB FEM, Matlab and the modes of an element

Click For Summary
A Matlab code was developed to compute the stiffness matrix for a 4-noded plane strain element, yielding five non-zero and three zero eigenvalue modes. The three zero modes are expected to represent two translations and one rotation, but the output appears as combinations of these modes instead. The discussion involves the interpretation of eigenvectors derived solely from the stiffness matrix, raising questions about the physical meaning of these results without a mass matrix. Users seek methods to manipulate the eigenvectors in Matlab to achieve the desired pure translations and rotation forms. The conversation emphasizes the need for proper boundary conditions to address free body modes and highlights the challenge of obtaining distinct eigenvectors in the context of finite element analysis.
  • #31
Trying2Learn said:
Matlab reports these eigenvectors and I do not like the way they look. If I am a first time FE coder and I experiment to see the modes, and get those shapes, NOTHING in them informs me that three of the eigenvectors would have been MORE INFORMATIVE had I seen them as pure translations and one pure rotation. How would I have known this in advance.

Well, the zero-valued eigenvalues is a big give-away... They never occur for fully constraint problems.
 
Physics news on Phys.org
  • #32
Arjan82 said:
Well, the zero-valued eigenvalues is a big give-away... They never occur for fully constraint problems.
And, oddly, THAT was what I wanted to hear. Those last two sentences, were what I was looking for. And, now that you said them, it is obvious. I should have known that.

Thank you for patience (I know I can be stubborn -- sorry if it came across that way).
 
  • #33
Well, we took some detour, but we got there in the end :) All is ok!
 

Similar threads

Problem calculating eigenvalues and eigenvectors
  • · Replies 1 ·
Replies
1
Views
1K
The 8 Mode Shapes of a plane finite element
  • · Replies 2 ·
Replies
2
Views
1K
MATLAB Problem with Karhunen-Loève expansion in matlab
  • · Replies 2 ·
Replies
2
Views
2K
MATLAB Solving Linear System with Eigenvalues in Matlab
  • · Replies 6 ·
Replies
6
Views
2K
Thermoelasticity problem with FEM in MATLAB
  • · Replies 2 ·
Replies
2
Views
1K
MATLAB A Lorenz's system of ODEs doesn't get executed in Matlab
  • · Replies 5 ·
Replies
5
Views
2K
MATLAB Bilinear spline interpolation MATLAB using MESHGRID and SURF
  • · Replies 2 ·
Replies
2
Views
3K
Modal mass and kinetic energy in FEM modal analysis
  • · Replies 3 ·
Replies
3
Views
4K
Analysing the Normal Modes and Dynamics of a Cluster of Atoms
  • · Replies 1 ·
Replies
1
Views
1K
MATLAB MATLAB: anti-crossing eigenvalues
  • · Replies 1 ·
Replies
1
Views
3K