The Airy stress function, $\phi=\alpha x^{2}+\beta x y+\gamma y^{2}$ for a thin square panel of size $l \times l$ automatically satisfies compatibility. If the panel is subjected to uniform tensile stress, $\sigma_{o}$ on all four edges, the traction boundary conditions are satisfied by
(A) $\alpha=\sigma_{o} / 2 ; \beta=0 ; \gamma=\sigma_{o} / 2$.
(B) $\alpha=\sigma_{o} ; \beta=0 ; \gamma=\sigma_{o}$
(C) $\alpha=0 ; \beta=\sigma_{o} / 4 ; \gamma=0$.
(D) $\alpha=0 ; \beta=\sigma_{o} / 2 ; \gamma=0$.

Question ID - 156249 | SaraNextGen Top Answer

The Airy stress function, $\phi=\alpha x^{2}+\beta x y+\gamma y^{2}$ for a thin square panel of size $l \times l$ automatically satisfies compatibility. If the panel is subjected to uniform tensile stress, $\sigma_{o}$ on all four edges, the traction boundary conditions are satisfied by
(A) $\alpha=\sigma_{o} / 2 ; \beta=0 ; \gamma=\sigma_{o} / 2$.
(B) $\alpha=\sigma_{o} ; \beta=0 ; \gamma=\sigma_{o}$
(C) $\alpha=0 ; \beta=\sigma_{o} / 4 ; \gamma=0$.
(D) $\alpha=0 ; \beta=\sigma_{o} / 2 ; \gamma=0$.