Question

What is the primary purpose of the uniqueness theorem in elastic analysis?

• A. To determine material properties
• B. To ensure a unique solution for given boundary conditions
• C. To calculate stresses directly
• D. To simplify equations

Hint:

Remember: If solution satisfies all conditions → it is the only solution.

Answer 1

The Correct Option is B

Concept: The uniqueness theorem in elasticity ensures that the solution to a boundary value problem is one and only one if it satisfies equilibrium, compatibility, and boundary conditions.
Step 1: Understanding the theorem.
It states that if a solution satisfies all governing equations and boundary conditions, then no other solution exists.
Step 2: Importance.
This guarantees that the obtained stress and displacement fields are correct and reliable.
Step 3: Evaluating the options.

• To determine material properties $\rightarrow$ Incorrect
• To ensure a unique solution for given boundary conditions $\rightarrow$ Correct
• To calculate stresses directly $\rightarrow$ Incorrect
• To simplify equations $\rightarrow$ Incorrect

Step 4: Conclusion.
Thus, the uniqueness theorem ensures a unique solution for given boundary conditions.