Consider the plane stress inhomogeneous case with only variation in elastic modulus given by E = E(y) = 1/ (Ay + B). Further assume that the Airy function depends only on y, ∅ = ∅(y). Show that governing relation (14.1.6) reduces to the ordinary differential equation:

Equation 14.1.6

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d b (Ay+B)- +2A- dy oldy = C/(y + B/A), thus giving the stress forms 0x d dy3 = Solve this relation to find that db C dy y+B/A where C and C are arbitrary constants of integration. 0 + C, ay = Txy = 0