Introduction to Elasticity/Compatibility example 1

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Example 1[edit | edit source]

Given:

The compatibility equations in terms of the strains are (in index notation)

The stress-strain relations for a linear elastic material are

Show:

Substituting the stress-strain relations into the compatibility equations, show that the compatibility equation of stress can be expressed as

Solution[edit | edit source]

Substituting the stress-strain relations into the left hand side of the compatibility equations and multiplying both sides by , we get,

Now, the rule states that

Therefore,

Recall that,

Therefore,

Hence,

Hence shown.