She wants her paintings -- in the gallery,but we don't think

1.“want + sth(her paintings) + done(displayed)”意思是“想要某事被做”,因为宾语her paintings和宾补动词display之间为被动关系,所以使用其过去分词displayed做宾语补足语.
2.want sth doing (sth)该结构不存在,更不会表示什么被动.
俺知道楼主想说的短语是sth want doing = sth want to be done,它才是用主动形式表示被动含义,此时want类似于need.
如：My hair wants cutting.= My hair wants/needs to be cut.
我的头发需要修剪.