Compute Craig Bampton model reduction using structural PDE toolbox of MATLAB (FEM SuperElements - Component Mode Synthesis)

Is it possible to extract a reduced model (also called Superelement) using Craig-Bampton technique (also called Component Mode Synthesis) from a structural model in PDE toolbox?

Regards

Alberto

Answer 1

[Alberto Mora]

It seems that with the 2020a release, Mathworks introduced the superelements!

You can find the documentation here.

If you have interesting suggestion, please, share here for other users. Thank you.

[Atif Laiche]

Dear Sir Alberto Mora,

I have a prb with craig-bamptom method in finite element analisys, my structure is a simple wing and i want to get the reduce roder model [M] and [K] by C-B method

1- Here is shown a simple analysis of a simple beam using

structuralmodel = createpde('structural','transient-solid');
gm = multicuboid(0.1,0.01,0.01);;.......

In my case i have a wing structure which is extruded by aifoil's coordinates.

--------Is there any commands like this one

model = createpde;
g = importGeometry(model,'CooledBlade2D.STL')

to do the same analisys like Structural Modal or Transient and get the matrices by C-B method? Thanks a lot

[Alberto Mora]

I think that you should import your geometry using standard format (like STL or STEP), then mesh it, and finally perform craig-bampton method as in the example. Or you can also import directly the mesh if you already created it in a third-part software. Have a look around MATLAB ANSWER and MATLAB documentation that is full of these info.

Regards, A

Answer 2

[Ravi Kumar]

Hi Alberto,

I see have asked this question a while ago, hope it is still relevant to you. Could you elaborate your use case a bit more?

How would you like to set up the mode? Do you want to set up the problem using StructuralModel approach for analysis and then instead of calling solve, do you want to call some other function that would reduce the model and return an output that is not the solution for a specific loading?

What all do you expect as a part of reduced model, like Component modes, Fixed-Interface modes, degree-of-freedom mapping to boundary etc.?

Regards,

Ravi

[Alberto Mora]

Hi Ravi,

first of all thank for your interest on the topic.

I usually export the SuperElement from a commercial FEM (NX Nastran) and I would like to do the same procedure (or similar) in MATLAB.

Hence, I would like to:

1. Create the FE model (mesh, material, boundary condition)
2. Select the Indipendent Boundary DOF
3. Compute craig bampton reduction: keep fixed Indipendent Boundary DOF for normal modes computing and with enforced static displacement for evaluate the static deformation shapes
4. Get a reduced model in [K], [M], [shapes], [ID nodes] matrices (or maybe in terms of ABCD model by specifying the input force DOF and output displacement, velocity, acceleration DOF in the state space notation).

If I remember well, between #3 and #4 NX Nastran compute a modal solution because the static mode shapes do not allows a diagonalization of the matrices.

Obviously this list is not mandatory and can be modifyied.

Since I think that is quite relevant on this topic, I also remark one my previous question about the computing of FRF using PDEToolbox.

[Ravi Kumar]

Hello Alberto,

Thanks for your inputs. This is helpful information. I think I understand your use case. One question though, do you want to construct super element for component of an assembly or just a single component?

Currently, you can get the system matrices using assebleFEMatrices once you setup the model using coefficients based interface. However, the reduction of the model is not yet available. I document this requirement for the development team. I or someone might reach out to you to gather additional inputs.

Regards,

Ravi

[Alberto Mora]

Dear Ravi,

I'm sorry but a am not sure that I understand your question, anyhow in my opinion the superlements would be able to create for both connection to other superelements (and/or un-reduced mesh) as well as to a connection to other external system.

For example, for the first case I would like to create a superelement of each rod and then connected them toghedar to get the assembly of a car suspension. Or in the second case I would like to create a superelement of a flexible structure (e.g. a screw connected to motor) and then load the superelement in Simulink to implement the PID control of the motor.

Please tell me if you have further questions. I will be happy to help development staff to improve MATLAB performances.