Timeline for In FEM, why is the stiffness matrix positive definite?
Current License: CC BY-SA 3.0
11 events
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| Jul 21, 2020 at 16:10 | comment | added | Guido | This isn't always the case. For rigid body modal analysis with pre-stress negative eigenvalues occur (wrong ofc). | |
| Dec 10, 2015 at 14:30 | vote | accept | user123 | ||
| Nov 30, 2015 at 5:02 | history | tweeted | twitter.com/StackSciComp/status/671192568458141697 | ||
| Nov 28, 2015 at 12:30 | comment | added | ccorn | Caveat: Without boundary conditions, the complete system stiffness matrix, as assembled from element matrices, does not have full rank, as it has to map the equivalent of rigid body motions to zero forces. Thus the complete stiffness matrix can at best be positive semidefinite. With proper boundary conditions however, rigid body motions are disabled, and the constrained system is then nonsingular. (Otherwise one could not solve it). Therefore, to find actual positive definiteness, you have to look at the condensed matrix resulting from the application of boundary conditions. | |
| Nov 28, 2015 at 10:01 | history | edited | Kirill | CC BY-SA 3.0 |
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| Nov 28, 2015 at 9:59 | answer | added | Christian Clason | timeline score: 22 | |
| Nov 28, 2015 at 9:45 | answer | added | Nasser | timeline score: 3 | |
| Nov 28, 2015 at 9:33 | comment | added | user123 | Hi, @ChristianClason, thank you for your comment. I have added a concrete example of this problem. | |
| Nov 28, 2015 at 9:30 | history | edited | user123 | CC BY-SA 3.0 |
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| Nov 28, 2015 at 9:09 | comment | added | Christian Clason | This actually depends on the partial differential equation you are trying to solve. Can you add the one you are interested in? | |
| Nov 28, 2015 at 8:47 | history | asked | user123 | CC BY-SA 3.0 |