Thoudsands of foreigners were attracted to the Shanghai Worl

Thoudsands of foreigners were attracted to the Shanghai World Expo （the day it opened.）括号里的句子是啥结构,看不懂啊,请英语高手分析下句子成分!
我想问下the day既然是时间状语,为什么前面不加介词on呢,

介词是一种用来表示词与词、词与句之间关系的虚词,英语中时间状语通常由in, on, at, for等介词引起,但有些情况下时间状语前不用介词.现就这几种情况加以归纳.

一、 当时间状语是today, yesterday, tomorrow, tonight, yesterday/tomorrow morning(afternoon, evening)等时,其前不用介词.例如：
There was a football match yesterday evening.昨天晚上有一场足球赛.
They will go to the zoo tomorrow.明天他们将要去动物园.

二、由this, that, these, those等构成的短语前不用介词.例如：
I'll visit my grandparents this week.这一周我要去看望我的祖父母.
They are picking apples on the farm these days.这些天他们在农场摘苹果.

三、由形容词last,next等指示代词修饰的名词词组用作时间状语时,前面的介词at, on, in一般省略.例如：
I saw him in the street sometime last week.上周我在街上见过他.
Please come to school earlier next time.下次请早点来学校.
但是,如果不是介词at, on, in,而是其他类型的介词,一般不能省略.如：I haven't been to my hometown since last year.从去年以来我就没回过家乡.

四、在以“the day (week, month, year)+before/after…”构成的时间状语前不用介词.例如：
Where did you go the day before yesterday? 前天你去哪里了?
They'll have a party the day after tomorrow.他们后天将举行一个聚会.

五、由every, each等表示频率的副词构成的短语用做时间状语时,其前不用介词.例如：
Do you watch TV every day? 你们每天看电视吗?
They go to school by bike each day.他们每天骑自行车去上学.

六、由on引出的特定日子,可以省略介词on.例如：
I can see him (on) New Year’s Day.在元旦我可以看见他.

七、for通常引出一段时间,当与表示静态的动词连用时可以省略.例如：I have stayed there (for) three hours.我在那里已经呆了三个小时.
注意：1.当与动态动词连用,或在句首及否定句中,介词for不能省略.如：I haven't heard from him for three years.我三年没有收到他的信了.
2.当walk, run, drive, travel等动词连用表示距离时,for可以省略.如：
He ran (for) a mile in four minutes.他四分钟跑了一英里

八、以all构成的短语做时间状语,如all day, all the week, all the year等前面通常不用介词.例如：
My mother was busy all day yesterday.昨天妈妈忙了一整天.
The girl was ill in bed all the week.这个女孩生病了,卧床整整一周.
注意：以all开头的短语前,介词通常省略.如：
I haven't seen her all day.我整整一天没有看见他了.

九、当at about…表示时间时,介词at可以省略.例如：
The sun rose (at) about six o'clock today.今天太阳大约在六点升起.