GATE 2020 AE – Question 19
Which condition makes $\phi=Ax^4+By^4+Cxy^3$ an Airy stress function?
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Correct answer: (B) A+B = 0
Explanation
For homogeneous isotropic plane elasticity without body-force complications, an Airy function must be biharmonic: $\nabla^4\phi=0$. The fourth x derivative is 24A, the fourth y derivative 24B, and the mixed fourth derivative vanishes for these terms. Thus $24(A+B)=0$, requiring A+B = 0, B.