The way I see it, a static member function is the same as a standalone function, except it is in the namespace of the class and it has access to private and protected parts of the class.
I don't use them much, probably because I grew up with standalone functions and find them more natural.
Just to make your response a bit more clear to the OP.
From a static method you can only access static variables from your class. This make sense since the method is in the scope of class and so are the static variables. All the other variables are in the scope of object and therefore cannot be accessed, initialized, etc.