Elastic constants of carbon nanotubes

Hi all,
 
I have some questions regarding the calculation of elastic constants of carbon nanotubes, and would be grateful if someone can help me:
1- How can I calculate elastic constants of a standalone carbon nanotube with certain diameter and length, without putting it in a periodic cell?

2- I've done the job for different armchair nanotubes and the young modulus decreased with increasing the CNT diameter, while in some published works the trend is inverse. Which one is correct?

2- Is it OK to calculate the elastic properties using GULP module? What is the appropriate force-field?

3- When generating a periodic nanotube, is it necessary to perform geometry optimization? If so, the transverse cell dimensions seem to be small compared to the cut-off distances, and need to be enlarged. Am I right?

Regards,
Farzin