Timeline for Is reduced stiffness matrix positive definite too?
Current License: CC BY-SA 3.0
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| Jan 12, 2018 at 18:34 | comment | added | hpc | @P.Mir, here's a post that shows the positive definiteness of $\mathbf{K}$ for a [Poisson problem]( scicomp.stackexchange.com/questions/21423/…). For linear elastic (static) problems, a nice proof of the positive definiteness of $\mathbf{K}$ is given in the FEM book by TJR Hughes. | |
| Jan 12, 2018 at 11:23 | comment | added | P. G. | @P.Mir What kind of statment is that? I'm an engineer, I didn't study mathematics and I know that the stiffness matrix is not positive definite, hence the need for boundary conditions..... Don't rely on what was taught to you, look into it yourself. | |
| Jan 10, 2018 at 9:25 | comment | added | P. Mir | @knl Thank you very much! So, my question is basically wrong. Because I thought that the original stiffness matrix is positive definite, but you say it is not. Honestly, we (engineers) don not study mathematics in a suitable manner. For example, we are taught that the stiffness matrix is positive definite without proof and mathematical preliminaries and always we are said that "proofs are not needed". | |
| Jan 10, 2018 at 7:55 | comment | added | knl | First of all, consider the simple case of linear elasticity. The original stiffness matrix $K$ typically has zero eigenvalue and, hence, it is not positive definite. By removing the rows and columns corresponding to Dirichlet boundary conditions you obtain a matrix $\overline{K}$ that is invertible and positive definite. Second, in the more complex case of plasticity, especially if you use Lagrange multipliers, the tangent matrix is not necessary positive definite. Sometimes it is not even symmetric. You should provide more details of your model. | |
| Jan 10, 2018 at 5:12 | review | First posts | |||
| Jan 10, 2018 at 16:59 | |||||
| Jan 10, 2018 at 5:08 | history | asked | P. Mir | CC BY-SA 3.0 |