Suppose a 2D displacement field in a structure:
u = ax, v = by, where a and b are constants.
The question is, can this displacement field represent rigid body motion?
Answer 1: Yes, it can represent rigid body motion when a=b=0 because strains are all 0. When strains are all 0, there is rigid body motion. This is the special case for rigid body motion.
Answer 2: No, it cannot represent rigid body motion for any a and b, including the special case a=b=0, because when a=b=0, u=v=0, meaning there is no displacement everywhere in the structure, which means there is no rotation or translation (the definition of rigid body motion).
Which answer is correct? What do you think? @Yu_Group
I believe it is a 2D problem. It is a bit confusion. Strictly speaking, zero displacements can be interpreted as no motion (thus no rigid body motion). I will tend to choose answer 2.
@Wenbin yes it is a 2D problem. I agree that zero displacement means no motion, which is not really rigid body motion.
If this is a question on the exam, the focus of testing is shifted from the difference of elastic displacements and rigid body motion-induced displacements to what is considered as a rigid body motion 
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@Wenbin
So does that mean its a bad exam question? I also find out that students who took the test have different opinions on this. I am supposed to grade this question.
My answer is answer 2, the answer key provided by the instructor is answer 1, so I argued with the instructor for quite some time, because it affects grading, and I intend on giving both answers full credits. This is not really a good question in my opinion.
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