d
(d) Since the edges are clamped, displacement of the edges \(u(x,y) = 0\) for line -
\(OA\) i.e. \(y = 0\), \(0 \le x \le L\)
\(AB\) i.e.\(x = L\), \(0 \le y \le L\)
\(BC\) i.e.\(y = L\), \(0 \le x \le L\)
\(OC\) i.e.\(x = 0\), \(0 \le y \le L\)
The above conditions are satisfied only in alternatives \((b)\) and \((c).\)
Note that \(u(x,y) = 0\), for all four values e.g. in alternative \((d)\), \(u(x,y) = 0\) for \(y = 0,y = L\) but it is not zero for \(x = 0\) or \(x = L\). Similarly in option \((a).\) \(u(x,y) = 0\) at \(x = L,y = L\) but it is not zero for \(x = 0\) or \(y = 0\), 

while in options \((b)\) and \((c),\) \(u(x,y) = 0\) for \(x = 0,y = 0,x = L\) and \(y = L\)