Finding velocity to use in non-constant boundary conditions, PDE toolbox

I am trying to create a transient structural simulation using the PDE toolbox. As part of my simulation, I want to apply a frictional force to an object that is moving. Imagine that there is a surface of the object that is dragging on the ground. I would like the distributed traction force to be a fixed magnitude in a direction opposite the direction of motion.

To do this, I planned to use the location,state variables with a function handle to calculate the direction of motion, then multiply this unit vector by my friction magnitude and output that as a distributed traction. However, neither the location or state variable seem to include velocity.

My question is:

1) Is there an "easy" way to get the velocity using location,state?

2) If there isn't an easy way, would the next best thing be to:

- Create a persistent variable to store the last known displacement (from state.u) of a point at a given location (from location).

- At each iteration, use the location to look up the last known location, then use the last known time, the current time, the last known displacement, and the current displacement to calculate the velocity.

Seems kind of silly to have to calculate velocity when it is available in the results after solving, though I guess it must just calculate the velocity in post-processing.

Thanks for any help.

Answer 1

[Ayush]

Hey Malachi,

I understand that you want to apply a frictional force to an object in motion in a transient structural simulation using the PDE Toolbox. You planned to use the location and state variables to calculate the direction of motion, but you noticed that neither of these variables includes velocity information. You want to know that whether there is an easy way of finding velocity using location and states and if there isn’t, what is the next best approach.

In the PDE Toolbox, the location and state variables do not directly provide velocity information. They primarily represent the spatial coordinates and the solution values at those coordinates, respectively. Therefore, there is no built-in "easy" way to obtain velocity directly from these variables.

Regarding your observation about velocity being available in post-processing, you are correct. After solving the transient structural simulation, you can access the velocity information as part of the results. However, if you need velocity during the simulation itself, the workaround which you described above can be a viable option.

For more information regarding PDE toolbox , you can refer to its documentation here : Get Started with Partial Differential Equation Toolbox - MathWorks India

Hope this helps!

Regards,

Ayush Goyal