Recent content by pyroknife

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...

Thank you for all the help. And oops, it should be ##\frac{\partial}{\partial x_i}(\kappa _{i,j} \frac{\partial T}{\partial x_j})##

The code I'm currently working with doesn't solve for the external flow field, although that may be something for the future. This code only models the material itself. The full blown Navier Stokes equations are not solved for. The momentum equation is reduced to Darcy's law for the internal...

Thanks a lot for the examples. Very helpful. The stuff I do is all computational, and so I lean more towards numerically solving the theoretical equations rather than making sense of it from a more practical aspect. This is just the base and to build on that would be to include/modify certain...

Also, I was thinking, the equation of motion is a hyperbolic PDE. When you compress a rod, you sent some finite traveling in the direction of compression, which takes time to reach the other end of the rod, leading to changes/oscillations over time. So I don't understand how the response is...

Hmm maybe that's where I'm confused. In thermophysics, if I apply a constant heat flux, that heat flux would continue to cause changes for the duration it is applied. I don't see why a constant compression load would not continue to cause displacement changes as long as it is being applied? I'm...

I'm still confused about the tensile loading. You mentioned that the solid would respond virtually instantaneously; are you implying that after this instantaneous response, the displacement would no longer be changing even though the constant load is still being applied? The pore pressures are...

Yes I know what static equilibrium means. Essentially some body at rest in which net forces sum to 0. I took a statics and dynamics class long ago. I'm still kind of confused on applied loading. With your tensile force applied to a rod example, if you apply this constant tensile force for...

No. Hmmm. So if the boundary conditions are not a function of time, does that essentially mean the displacement field will not change? Also, technically the density of the material I am modeling would change with time because as I mentioned the thermophysics part of the code models solid...

Aren't the displacement fields always changing with time?

I am working on a research project for modeling thermal protection systems that involves 2 major components: (1) Thermochemical physics modeling and to a lesser extent (2) Structural mechanics modeling (linear elastic should be sufficient). The thermochemical modeling involves solving transient...

I should have mentioned this early, but I am solving the transient equations, which includes the time derivative term. So instead of the 2 PDEs in post #22 being set equal to 0 on the RHS, they are instead set equal to ##\rho \frac{\partial^2 u}{\partial t^2}##. In this case, I think I would...

I agree! However, n this scenario, aren't the the stress BCs being applied at x,y=N? If so, then in Eqns (9) and (10), aren't the u&v values unknown at N?

The central difference formulas are: \begin{equation} \frac{\partial ^2 u}{\partial x^2} \approx \frac{u_{i+1,j}-2u_{i,j} + u_{i-1,j}}{\Delta x^2} \end{equation} \begin{equation} \frac{\partial ^2 u}{\partial x \partial y} \approx \frac{u_{i+1,j+1}-u_{i+1,j-1} - u_{i-1,j+1} +...

Thanks for all the help. I will type it out in the next post here in a little bit.