Question

The compatibility conditions in theory of elasticity ensures

• A. the compatibility between stress components
• B. the relationships between stress and strain are consistent with the constitutive relations
• C. displacements are single valued and continuous
• D. stresses satisfy the bi-harmonic equation

Hint:

Compatibility is a geometric condition for deformation continuity.

Answer 1

The Correct Option is C

The question asks about compatibility conditions in the theory of elasticity.

Compatibility conditions in elasticity theory ensure the geometrical and physical consistency of the deformation process. Essentially, these conditions are needed because:

• Compatibility is about ensuring that the displacement fields are such that they do not lead to any physical inconsistency like material overlap or gaps.
• Mathematically, this means that the resulting strains (originating from displacement derivatives) must be continuous and single-valued.

Thus, the correct interpretation of the question is that the compatibility conditions ensure that displacements are single valued and continuous. This is crucial to have a physically realistic and geometrically possible deformation pattern.

In summary, the correct answer is: displacements are single valued and continuous.