A Stress-strain; strain-displacement in 2-D; uniqueness

Click For Summary
The discussion revolves around solving a 2-D planar problem involving stresses, strains, and displacements in a finite difference numerical solution for a square flat plate subjected to compressive loads. The stress matrix is symmetrical, leading to a situation where there are three knowns and four unknown displacement gradients, raising concerns about the uniqueness of the solution. The user seeks to impose an additional condition to resolve this issue, potentially using compatibility equations from literature. Boundary conditions are established, including fixed displacements on certain faces and stress conditions on others, to facilitate the simulation. The conversation highlights the importance of correctly defining boundary conditions to ensure a solvable and realistic model.
  • #61
Chestermiller said:
I have nothing to add, except to say simplify as much as possible. But please check that heat balance equation. It seems to be missing a derivative on the conduction term.
I took a hiatus from looking at the structural problem for awhile and recently picked up again the past couple of weeks. I just realized what I think is a huge issue when solving the transient equation. The issue is these structural constants are HUGE (when I was previously working on this, I had largely neglected the constants). For example, steel's elastic modulus is about O(10^11), and its lame's constants are around ~O(10^8). In solving the transient equation, I have to consider stability issues. The max dt that I can use is essentially INVERSELY proportional to lame's constants, thus severely limiting my timestep size to the point that the computational time is impractical for the purpose of my code.

I could potentially approach this problem as steady state. However, temperature and slight pressure (also low pressure) charges really would suggest that this problem is transient.
 

Similar threads

I Lagrangian for pendulum
  • · Replies 11 ·
Replies
11
Views
2K
I Some notes on stochastic physics
  • · Replies 1 ·
Replies
1
Views
2K
I Derivation of the Euler-Lagrangian
  • · Replies 12 ·
Replies
12
Views
5K
I Deriving Navier-Stokes Equation
  • · Replies 4 ·
Replies
4
Views
2K
I Maxwell stress tensor
  • · Replies 10 ·
Replies
10
Views
421
A Lame parameter mu = shear modulus derivation (rogue factor of 2)
  • · Replies 1 ·
Replies
1
Views
1K
A Inconsistency between definitions of power and work in continuum mechanics?
  • · Replies 9 ·
Replies
9
Views
1K
How should I use the Jacobi equation to determine the nature of this?
  • · Replies 5 ·
Replies
5
Views
1K
I Poincare lemma for one-form on ##\mathbb R^2 \backslash \{ 0 \}##
  • · Replies 15 ·
Replies
15
Views
2K
How should I use the Jacobi equation to show this?
  • · Replies 4 ·
Replies
4
Views
2K