Wikipedia and Wiktionary still don't know that "complex objects" exist. As far as I can tell from cursory googling, it's just a term some teachers use to describe any object with some modifiers attached. It's not a very useful concept, since there are several completely different constructions that make predicates more complicated. Using one term as a catch-all can create a false sense of understanding.

In any case, it looks like the term for this construction is secondary predicate. Wikipedia also seems to group several ideas under that heading, but they all have the structure of action verb + [object] + adjective:

• All men are created equal.
• His speech left me cold.
• She shot him dead.
• He ran himself ragged.

In this case, push is a bog standard verb for doors; click (=made ~ go 'click') is just a descriptive word for whatever action caused that noise to be made. In this case, there's probably a light latch.

In your examples, the extra adjective at the end is describing the result of the action: He ~ the door [so that it was] shut... He ~ the door [so that it was] open... You could also understand the second one by thinking of it as a limit: She ~ the door [until it was] open...

Wikipedia and Wiktionary still don't know that "complex objects" exist. As far as I can tell from cursory googling, it's just a term some teachers use to describe any object with some modifiers attached. It's not a very useful concept, since there are several completely different constructions that make predicates more complicated. Using one term as a catch-all can create a false sense of understanding.

In any case, it looks like the term for this construction is secondary predicate. Wikipedia also seems to group several ideas under that heading, but they all have the structure of action verb + [object] + adjective:

• All men are created equal.
• His speech left me cold.
• She shot him dead.
• He ran himself ragged.

In this case, push is a bog standard verb for doors; click (=made ~ go 'click') is just a descriptive word for whatever action caused that noise to be made. In this case, there's probably a light latch.

In your examples, the extra adjective at the end is describing the state resulting from the action: He ~ the door [and then it was] shut... He ~ the door [and then it was] open... You could also think about the structure in a few other ways: He ~ the door [so that it was] shut... She ~ the door [until it was] open...