To completely disable the possibility to search Projects/Documents for specific users in your WebCenter, you can customize their menu and remove the keyword search in the top right corner.
Procedure
WebCenter 10.1 up to WebCenter 12.1.2
Since WebCenter 10.1, you can hide the keyword search. This is practical when you want to limit the user access to documents and projects.
Follow these steps to remove the keyword search from the menu bar for non-Admin users:
Log in with an admin user to your WebCenter site.
Choose Preferences > Menus from the main admin menu.
Download the Default menu.
Using any text editor, add the following under the "NON_ADMIN" <menuitem>: