Just change your pattern from YYYY to yyyy (lower case) and it will work, check this:
function myFunction() {
var date = new Date("Tue Dec 31 2013 18:43:12 GMT+0530 (IST)");
//after formatting it in YYYYMMdd format
var format = Utilities.formatDate(date,"IST", "yyyyMMdd");
Logger.log(format);
}