請問各位大大根據受詞的定義及物動詞後面通常會有一個受詞而且這個受詞通常是直接受詞那根據受與動詞裡的直接接受詞常指事物但是這個例句卻是指人為什麼? 例句:They elected Mr. Chen chairman.?

這類受詞稱為同位語，，Mr.Chen與chairman同為受詞且互為補充說明,另外一種是複合名詞（compound noun)例如：football 由二個名詞foot+ball組合,
同位語是同位階,而複合名詞則前一個名詞foot已蜕變成形容詞，知道其差異了吧

例句:They elected Mr. Chen chairman. (但,你所指出的動詞"elect"不屬於授與動詞)

The verb "elect", as well as some other verbs such as "make", "call", "name", "appoint" and etc., is a kind of special ditransitive verbs (雙及物動詞) called attributive ditransitive verb, which takes a direct object and an object complement (noun).

Sentence pattern: subject + verb + direct object + object complement (noun complement)
以上例句 Mr. Chen (direct object) = chairman (object complement)

More examples: (from Oxford dictionary)
1. make (指人): She made him her assistant. (him = her assistant)
2. call (指人或物): Are you calling me a liar? (me = a liar ?)
(指人或物): They decided to call the baby Mark. (the baby = Mark)
3. name (指人): I had no hesitation in naming him (as) captain. (him = captain)
(指人或物): They named their son John. (their son = John)
4. appoint (指人): They appointed him (as) captain of the English team. (him = captain of the English team)
5. elect (指人): He was elected (as) MP for Oxford East. (He = MP for Oxford East) often in passive voice for this use

** object complement (受詞補語) normally an adjective or a noun, renames or add information to the direct object to complete the meaning.

根據受與動詞 裡的直接受詞 常指事物, 但是這個例句卻是指人, 為什麼?

「授與動詞」Dative Verb 又稱｢雙賓動詞/雙及物動詞｣，基本上就是為｢某人｣做｢某樣東西｣，也就是指這類動詞後面會有兩個受詞，物品通常為直接受詞，人通常為間接受詞。
句型： 主詞 + 及物動詞 + 間接受詞（人）+ 直接受詞（物）
例句： I gave him a book.（我給他一本書。）

Apparently, the verb "elect" as appeared in your example does not belong to this group (but other group called factitive verb), so your question is irrelevant.
「作為動詞」Factitive Verb 或可稱｢不完全及物動詞 incomplete transitive verb｣ 直接受詞后須加補充說明 (補語)，意思才完整。
句型： 主詞 + 及物動詞 + 直接受詞（人或物）+ 受詞補語
https://www.thefreedictionary.com/Factitive-Verbs.htm

*** Within Factitive Verb group, there is a small subgroup of verbs which take only noun complement. They are called attributive ditransitive verbs because they look like ditransitive verbs taking two objects.

They elected Mr. Chen chairman.
主詞＋不完全及物動詞＋受詞＋受詞補語
不完全及物動詞：Incomplete transitive verb
除受詞外，不完全及物動詞還需要受詞補語以「補足」其意義。
受詞補語與受詞之的關係是to be的關係，所以受詞補語通常為「名詞」或「形容詞」或其相等語。
We called him Jack.（名詞）
Keep your teeth clean.（形容詞）

完全及物動詞(complete transitive verb)有兩種：
1. 主詞＋完全及物動詞＋受詞：I have a bicycle.
2.a.主詞＋完全及物動詞＋間接受詞＋直接受詞：He gave John a book.（此種動詞又稱為「授與動詞」dative verb）
2.b.主詞＋完全及笏動詞＋直接受詞＋to/for＋間接受詞：I wrote a letter to my friends in Taipei.

我想你問的意思是這兩個受詞"Mr. Chen"和"chairman"那個是直接...

雖然你引用"文法規則"理論發問，唯有按你的意向和理解說一下，

重點或理解應放在句子的文意，主詞是"THEY"(某一群人)+動詞"elected"(過去)選出了"，句意便是要表達他們選出了一個人，Mr. Chen便是那個人。但句意還要交代選出他當甚麼職位，結合為同一句其實可以寫成They elected Mr. Chen as the Chairman (of the company/organization/committee).或They elected Mr. Chen to be the Chairman.
由於句意一般人都會"明白"是表達這選出來的人的職位，所以不要中間的附加字組亦可明白，所以便把兩個名詞一齊寫下便可以了。