Core jQuery only has a slideDown and slideUp (one of jQuery's many unfortunate idiosyncrasies). But there's jQuery UI (User Interface), an extension to the jQuery framework, with which you can achieve this. It has a slide effect that accepts parameters for direction and speed (see documentation on http://docs.jquery.com/UI/Effects/Slide).
An example would be
$("leftshutter").hide("slide", { direction: "left" }, 1000);
$("rightshutter").hide("slide", { direction: "right" }, 1000);
although that might do the exact opposite.
I'm not sure what kind of motion openDoor would need. How would you project rotation around the Z axis to the two-dimensional plane? If you figure it out mathematically, there might be a way to do it using the core .animate() function, which animates a custom set of CSS attributes. That is, however, probably limited to manipulations that result in rectangles and not the rhombuses you might want.