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

Step 1: Understanding the Concept:
Elasticity problems involve solving a set of differential equations (equilibrium and compatibility).
Step 2: Detailed Explanation:
The uniqueness theorem states that if a solution for stress and displacement satisfies:
1. The equations of equilibrium.
2. The compatibility equations.
3. The prescribed boundary conditions (loads and displacements).
Then that solution is the only possible (unique) solution for that problem. This provides a mathematical guarantee that the calculated stress state is the one that actually occurs in the material.
Step 3: Final Answer:
The theorem ensures there is only one unique solution for the specified boundary conditions.