A thin rectangular plate laying on the x-y plane has edge sizes AB = 1 m AB = 2m and thickness t = 0.01 m. The plate is under a distributed transverse load, along the z axis. The plate Young modulus is: E = 200 GPa and the Poisson coefficient is v = 0.3. y D 2m A == q (x, y) Et 12(1-v) -Z C The mid-plane deflection function has been derived based on the governing differential equation and the boundary conditions of the plate, and is given as: w(x, y) = 1m 0.001 m B 0.005 + -y + m 0.01 m -X =yx 1. Calculate the deflection of the plate at the centre of the plate, ie x = 0.5m, y = 1m. 2. Calculate the bending moments on the centre of the plate. 3. Calculate the maximum normal stresses x, y on the centre of the plate x = 0.5m, y = 0.5m. The moment and the stresses on the plate are related to the curvature using the approximations: 1/Rx = Wxx and 1/Ry = Wyy: as: Mx (Wxx +VWyy),.My Et 12 (1-v) (Wyy+vwxx), and Ez Ez .Ox = _E22 (Wxx+vWyy), O =E22 (wyy+vwxx), respectively. 1-v2 Ty 1-12