I use Kerkythea, which happens to have a nice exporter (SU2KT). You can install the exporter (without needing Kerkythea) and then look at the code. Basically, it looks at all entities in your Sketchup model and exports them as an XML file.
One challenge I see is that Sketchup entities are edges and faces. I would assume that you need volumes to perform the FE analysis.
Once you are done with your analysis, to put elements back into SU, you might be able to use something like the Cloud V6 plugin, which represents data as x,y,z points.
There is also an STL format but I am less familiar with it.
Juan