With Joomla core you need to setup a menu structure that will correspond to what you want to achieve with your URLs. Menus are important in Joomla.
From the example of the URLs in your question - it seems like you have created a menu item for the article1.
If you want all articles of that category (cat1) to be reachable under the cat1/article1,art2,art3 pattern, then create a category type menu item for the cat1 category. You can create that menu item in a hidden menu (a menu with no menu module) - or set the menu item itself as hidden (Menu Item -> Link Type tab -> Display in Menu).
If you want to have a menu item in your menu that will link directly to the cat1/article1, then make the menu item of the article a child of your cat1 menu item.
Alternatively, there are 3rd party SEF extensions that offer various different capabilities. Check in JED for SEF extensions.