6
votes
Accepted
Traction -> stress; stress->displacement gradient
In short, no. Neumann boundary conditions should be specified in terms of traction. This is clear when you move from a strong-form statement of the boundary value problem to a weak-form.
Strong form:
...
- 1,512
3
votes
Accepted
Well-posedness of Elasticity Boundary Conditions
For this problem you have mixed boundary conditions. Then, you really have 8 boundary conditions for the problem that you present in your sketch. Although, 4 of them are not explicitly written.
These ...
- 8,622
3
votes
Correctly setting boundary condition for periodic linear elasticity problem
Here is a description of a small FE model that might approximate the
case of an infinite number of holes in an infinite plate.
Create a model of a single repeating element with $1/4$ of a
hole ...
- 6,339
2
votes
Accepted
Analysis of nonlinear finite element methods
When one learn about functional analysis methods for PDEs, usually starts from common theorems like the Riesz representation and the Lax-Milgram lemmas, which work quite good with linear PDEs.
When ...
- 96
2
votes
Accepted
How to show that a problem is ill-posed
Your calculation is fine. You have discovered data $u(x,0)=\cos(kt)$ whose solution becomes unbounded. Now consider initial $v(x)$ having unit initial norm and combine them into initial data
$$U(x,0)=...
- 1,204
1
vote
Correctly setting boundary condition for periodic linear elasticity problem
As a first approach, you could do as @BillGreene suggests, that is increase the size of your model, increasing the number of cells each time. I guess that around 10 cells in each direction you should ...
- 8,622
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