Flexible Body Model Builder - Equations used inside the package

Hi,

I am experimenting with the Flexible body builder app and have some questions regarding the math behind it's implementation.

• StiffnessMatrix: I understand that the stiffness matrix in the output ROM data is calculated from the Young's modulus and the poison's ratio. But I want to change this young's modulus with every run of the simulation without building the flexible body ROM from scratch. For this, I first export the ROM data with E = 1MPa, define the flexible body using the exported ROM data in simscape, and multiply the stiffness matrix with E_flex which is the variable I want to change with every simulation run.

This is because K = EA/L and since E is a scalar, it can be scaled up or down with just a simple scalar multiplication.

I did some experimentation of this usage by exporting stiffness matrices for E = 1MPa, 2MPa,...etc and I can verify that

        det ([StiffnessMat.2MPa]-2*[StiffnessMat.1MPa]) = 0

It would be great if you could verify this usage.

• Number of Fixed-Interface Normal Modes: What is the optimal number of frequency modes to retain for a given geometry? It would depend on the geometry and the loading conditions themselves. Is there a way to assess what's a good estimate for this?
• Algorithm for model Generation: Is there a quantitative difference between the included integro-differential modeling framework and the PDE toolbox? What is the difference between the two methods. What is the recommended method?

It'd be great if you could provide some insights into these areas.

Answer 1

[Umang Pandey]

Hi,

1) Based on the provided information and your description, it seems you are correctly scaling the stiffness matrix with the Young's modulus. The relationship ( K = EA/L ) supports your approach, as the stiffness matrix ( K ) is linearly proportional to the Young's modulus ( E ). Your experimental verification using determinants also supports this. This indicates that the stiffness matrix scales linearly with ( E ), confirming that you can adjust the stiffness matrix by scaling it with E.

2) The optimal number of modes generally depends on the complexity of the geometry and the accuracy required for the simulation. A higher number of modes typically provides more accurate results but at the cost of increased computational effort. You can start with a moderate number and perform convergence studies by gradually increasing the number of modes until the results stabilize.

3) From what I understand, use the integro-differential framework for flexible body dynamics within multibody simulations, while the PDE toolbox is more general-purpose.

Hope this helps!

Best,

Umang