The compatibility conditions in theory of elasticity ensures
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- the compatibility between stress components
- the relationships between stress and strain are consistent with the constitutive relations
- displacements are single valued and continuous
- stresses satisfy the bi-harmonic equation
The Correct Option is C
Solution and Explanation
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.
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