Consider the plane strain field given by $\varepsilon_{x x}=A y^{2}+x, \quad \varepsilon_{y y}=A x^{2}+y$, $\gamma_{x y}=B x y+y .$ The relation between $A$ and $B$ needed for this strain field to satisfy the compatibility condition is

(A) $B=A$

(B) $B=2 A$

(C) $B=3 A$

(D) $B=4 A$

Consider the plane strain field given by $\varepsilon_{x x}=A y^{2}+x, \quad \varepsilon_{y y}=A x^{2}+y$, $\gamma_{x y}=B x y+y .$ The relation between $A$ and $B$ needed for this strain field to satisfy the compatibility condition is

(A) $B=A$

(B) $B=2 A$

(C) $B=3 A$

(D) $B=4 A$

127