How can I add a subdivision surface modifier to smooth the rounding of an object? I have a simple object with two rounded corners. The following screenshot shows the magnification of one of these corners. The corners were created with the bevel function.



Adding a subdivision surface modifier destroys the whole object.

Should I use more bevel segments from the beginning?

The object can be downloaded here: https://www.dropbox.com/t/JjbxccUV4YgI6zrG
You can solve this by using supporting geometry. In the case of your object, adding edge loops at the places I've highlighted will give a clean look with a subdivision surface. Be careful positioning the large rectangle loop, because It seemed to cause artifacts in the bottom left area if not placed just right.



Hope this helps.