For the plane stress problem, show that the neglected nonzero compatibility relations involving the out-of-plane component e

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For the plane stress problem, show that the neglected nonzero compatibility relations involving the out-of-plane component ez are:

Jez 2 = 0, a2ez 2 0, Fez  0

Next integrate these relations to show that the most general form for this component is given by:

e = ax +by+c

where a, b, and c are arbitrary constants. In light of relation (7.2.2)3, will this result for ez be satisfied in general? Explain your reasoning.

Data from equation 7.2 .2

ex ey ez exy (ox - voy) 1 - :(ay - vox) E V - 1/2 (ax + a) = -7 (ex + ey) 1- exz = Cyz = 0 1+v E -Txy,

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