# Craig Bampton method

1. Sep 10, 2012

### millachin

Can anyone suggest a good reference book for learning Craig Bampton method? Also it will be of great help if you could give links on the internet which explain the CB method in a detailed manner and websites/webpages that have a good set of numericals based on the CB method.

2. Sep 17, 2012

### AlephZero

The motivation for CB is that most "big" stuctures are physically bult from subcomponents with which can be modeled separately. To make a reduced dynamics model of each subcomponent, you need to retain all the degrees of freedom at the boundaries which wll join to the other subcomponents. But if you eliminate everything else from the model, you lose the dynamic behaviour happening "inside" each subcomponent.

The basic idea of CB is to represent the internal dynamics of each subcomponent by its vibration modes with its boundaries fixed. This works well when the physical connections between the subcomponents are simple compared with the dynamics of each subcomponent, for example a satellite attached to its launch rocket at a small number of mounting points.

Another benefit is that each subcomponent model can often be checked against test vibration measurements indepedendently, which makes it easier to find and fix problems than working with just one large model. In fact the component models can be constructed directly from measured data, instead of making a conventional FE model.

There are variations on the basic idea - for example it is possible to the vibration modes of subcoomponents with the boundaries free to move instead of fixed (or with some parts of the boindary fixed and the rest free), which may improve the accuracy for a given size of model. Devising the "best" way (and even defining what "best" means) is an ongoing research topic.

This looks a pretty good summary of the math (it's slightly NASTRAN-flavored, but most of it should make sense if you don't know NASTRAN): http://femci.gsfc.nasa.gov/craig_bampton/index.html

THe guutar analysis example here is fairly typical of the practical issues with this type of dynamics modelling: http://www.sem.org/pdf/substructuring_tutorial_imac2010.pdf [Broken]

Last edited by a moderator: May 6, 2017
3. Sep 24, 2012

### millachin

Thanks AlephZero. Sorry for the late response. I was on a vacation, so, couldn't access the net.

What procedure is applied to study the DOFs? We have the analysis set which is split into boundary DOFs and interior DOFs. The boundary DOFs are reduced by Static condensation and we use the eigenvalue analysis in solving the interior DOFs (if I am not wrong). We generate two sub-matrices B = [I ϕR] and ϕ = [0 ϕL] (where R represents the boundary DOF and L represents interior DOF). The two sub-matrices are combined to generate a global transformation matrix.
B is called boundary node functions and ϕ is called fixed base shape nodes. The essence of CB method is to understand these two. Could you please elaborately explain them?

4. Nov 5, 2012

### millachin

@AlephZero
CB method can be divided into two parts - Static and Dynamic.
In static part, we essentially solve for the boundary DOF and express the elastic DOF in terms of boundary DOF. My question is - why do we give unit displacement to the interface DOF while solving for the displacements and keep the other contraint/interface DOF zero?