Greetings Maya enthusiasts!

I am new to Maya, and was hoping someone here can help me out with the following problem:

In Maya 2008, I am referring to the Smooth Mesh Preview feature (keyboard 1,2,3). When I imported a file (a DirectX Meta .X file converted to .OBJ), and tried to smooth the mesh (from 1 to 3), the polygons and edges detached and distorted into something I cannot really explain in words. Please examine the pictures I uploaded.

Before:


After:


If the pics don't show up, here are the direct links:
Keyboard 1, Original: https://i44.tinypic.com/34t64hy.jpg
Keyboard 3, Smooth: https://i40.tinypic.com/ne95yq.jpg

I just want to be able to smooth out the mesh the way every normal polygon surface/object is supposed to be smoothed. Not that mess you see in the picture above. Thanks!:p