Setting your question about the article aside, it takes a special context to justify
The steel of the bike is stainless.
which is grammatical but not idiomatic under most circumstances. Normally a native speaker would say
The {thing} is stainless steel.
The {thing} is made of stainless steel.
This is a stainless steel {thing}.
If the thing is made of several different metals, you might say something like
The roof of this building is made of aluminum, and the steel of the doors is stainless.
There, you are comparing or enumerating the different metals of the different pieces, which would justify the pattern you are asking about.
Let's say you were developing a specification for a building of some kind:
Roofing materials must be non-flammable.
In exterior application, steel should be stainless.
There, you could forego the article since you're referring to the generic material.
P.S. In a comment OP goes on to clarify:
I did not make myself clear. Some expressions of the structure
NP+of+NP (with the denotations of the two NPs in the part-whole
relation) are allowed to have a definite reading without using “the”,
e.g. Students of Southern Polytechnic were likewise concerned their
school's identity would be lost(from COCA). i want to find out if
“steel of the bike”, “punch lines of the jokes” and “oases of the
desert” can have a definite reading without using “the".
The word definite is rather indefinite, but let's look at a few sentences.
Without the definite article, NP1 (inNP1 of NP2constructions) will refer to the noun as generic or unspecified, defined only in terms of its association with, or its being a part of, or its being the essential fabric of NP2.
In front of the library, students of the university were protesting the firing of the Dean.
Some unidentified, unspecified students who attend the university.
I won't buy it. Handle of the teacup is broken off.
No. Ungrammatical. When referring to a specific component of an assembly, we use "the":
The handle of the teacup is broken off.
Restoring it would be quite a project. Steel of the bike's frame is rusting.
That is marginal. Unlike the handle of the teacup, steel is not a part of the frame; rather the frame is made from the material. The sentence could be made less marginal if we add a phrase:
Steel of the bike's frame is rusting in places.
or refer to the steel everywhere on the frame:
The steel of the bike's frame is rusting.
The comic was banned from daytime TV. Punchlines of the jokes were deemed inappropriate for daytime audiences.
This sentence has two problems. "the jokes" is ungrammatical without either some prior reference to those jokes
... banned from daytime TV for telling off-color jokes.
or some further restriction upon the NP: "the jokes he told".
The comic was banned from daytime TV. Punchlines of the jokes he told were deemed inappropriate for daytime audiences.
That is OK. A determiner is unnecessary but possible there:
[The] punchlines of the jokes he told were deemed inappropriate...
Notice the plural there with punchlines...jokes. The plural is what makes that example different from handle of the teacup. Some or many of his punchlines were inappropriate, a sufficient number, or more than a sufficient number, to get him banned from daytime TV.
In places where there is water underground oases of the desert flourish.
oases of the desert is a generic reference to a phenomenon, not to specific oases, except insofar as of the desert differentiates desert oases from other kinds of oases. But is there really any other kind, barring figurative ones?
Her class on Giotto was an oasis in a wasteland of art-theory.
P.P.S.
Whether Students of Southern Polytechnic means all or some can only be determined by context:
Students of Southern Polytechnic were involved in the car-jacking.
Students of Southern Polytechnic must take Electrical Engineering 101.
These sentences have equivalent meaning:
Steel of the bike's frame is rusting in places.
The steel of the bike's frame is rusting in places.
With respect to your final example, you have introduced the word that.
Oases of that desert.
Which can be quite different from
Oases of the desert.
In the latter, the desert can refer to all deserts (in which case oases of the desert can be paraphrased as desert oases) or it can refer to a specific aforementioned desert, the desert we have been speaking of. With the latter, that desert, we are referring only to a particular desert.
"oases of the desert" oases found in deserts the world over [unless the is anaphor or cataphor]
"oases of that desert" refers to oases found in a particular desert only.
