Modelling varying gravity/acceleration field

[StavrosP]

Hello,

To simulate numerically as accurately as possible SSI experiments conducted in a centrifuge one needs to vary the acceleration field along the model. In the centrifuge the angular velocity of spinning is constant but the centrifugal acceleration is changing with distance from the center of rotation (a=ω2r). This results in an acceleration/gravity vector with varying value.

I suppose the ugly/cumbersome way to model this in STKO/OS is to split the structure into small sections (say per m) and calculate, based on the acceleration at the middle of each section, its corresponding mass and dimensions.

A better way to do this would be to have a (linearly) varying mass and section properties (eg width/radius) per meter. Could you please give me an example of how this can be done by using STKO?

Thank you very much in advance!

Stavros

[STKO Team]

Probably it can be done directly in STKO using the "function" tool in the boundary conditions.
Could you please write everything you need to change?

Is it just the self-weight? Or something else?

[StavrosP]

I need to adjust the following (hollow cylindrical section):

• diameter
• thickness
• the above lead to a change in the second moment of area(I), and area (A)
• mass (I apply this as an element property)

[STKO Team]

This is not clear to me...
I can understand that you want to vary linearly in space a property of the soil (mass in this case).
But what about section properties?

Please, could you please draw a sketch to better understand the typical scenario?

[StavrosP]

Apologies, not the best description from my side.
There is a structure as well, so I am after soil-structure interaction modelling.
The structure is a pile half embedded in the soil and half extended above the ground level.
The attached sketch gives an impression of how the setup looks like. It's a horizontal section view of the centrifuge and the model in it while spinning. There is a pier instead of a pile that I described above - please consider my description above instead. The centre of rotation is where the vector "ω" is placed.

The properties mentioned in my previous message are for the structure only.
I had in mind that if you could provide an example/description of how to do this for the structure I would be able to follow the same logic for adopting the soil properties. For the soil medium, varying only density would suffice for now.

[STKO Team]

Ok so if I understood correctly, the centrifuge test applies an angular acceleration, but you are not modeling it so you would like to include this effect in an alternative way.

First question, why are you saying that the mass density should change with space? It is a material property. If the acceleration changes due to the distance from the center of rotation, then what changes is the self weight, not the mass density.

Anyway, let's start step by step.
This is how you can write a Condition (load or mass, even though I think you need only the load...), using a function of spatial coordinates:

varload.png (90.8 KiB) Viewed 2546 times

Let me know if it works for you.
Then, we will proceed with the piles. Here I need more information: how is their property changing in space?

[StavrosP]

I understand the confusion and perhaps it partially comes from a misuse of terminology on my side.

Correction of terminology which I inaccurately wrote above: density remains the same, mass changes.
This is due to the scaling laws that apply in the centrifuge. Certain properties are scaled in accordance with the applied acceleration field (N*g, where N is constant in this case, depending on the centrifuge, say e.g. N=50 or N=100). See the attached jpg with a summary of the basic centrifuge scaling laws.

centrifuge_scaling_laws.jpg (36.96 KiB) Viewed 2544 times

The change is in all directions as the acceleration field changes with distance "r" from the center of rotation. See for example the attached fig "centrifuge acceleration variation".

centrifuge_model_sketch.jpg (53.86 KiB) Viewed 2544 times

centrifge acceleration variation.jpg (5.26 KiB) Viewed 2544 times

The structure is a pile as described previously. Its properties could vary in the z-direction only (good first approximation). It's a hollow cylindrical section. See attachment "pile properties". Until now I have been modeling the mass of the pile via the "massDens" property. See attached "element properties".

pile properties.jpg (133.35 KiB) Viewed 2544 times

element properties.jpg (30.37 KiB) Viewed 2544 times

[STKO Team]

Ok, so look at the previous post.
Instead of assigning mass in the element property (in this way it can only be constant), use VolumeMass (or VolumeForce for load) and EdgeMass (or EdgeForce for load) in Conditions. There you can use an equation.

Let me know if it works for you

[StavrosP]

Hello,

I am coming back to this post for clarification of the EdgeForce (and the rest) definition. Should the prescribed value be per meter of edge length, or the total/resultant for that edge?

Thanks,
Stavros

[StavrosP]

For others' future reference: the answer is already provided here:

Yes some elements have the body force as input.
But not all of them, that's why in STKO we developed utilities such as VoulumeForce, FaceForce, EdgeForce... to provide for distributed forces where not available in OpenSees