The square plate is loaded so that the plate is in a state of plane strain (in other words, gamma_zx = gamma_zy = epsilon_zz = 0). The deformed shape is given by the dashed lines (all lines are...

The square plate is loaded so that the plate is in a state of plane strain (in other words, gamma_zx = gamma_zy = epsilon_zz = 0). The deformed shape is given by the dashed lines (all lines are straight). The displaced points A* and B* have the same y-displacement. The displaced points B* and C* have the same x-displacement. Assume that u = a_1 + a_2x + a_3y + a_4xy and v = b_1 + b_2x + b_3y + b_4xy with a's and b's that are constants to be determined. Determine the displacement functions u and v for the plate using the deformations shown and the strain components for the (x, y) coordinate axes. Determine the strain components for an X - Y coordinate system given by theta = 45 Degree. Determine the strains in the center of the plate (x = 0.5 m and y = 0.5 m) and the stresses in the center of the plate if v = 0.3 and E = 71 GPa. Determine the principal strains at the center of the plate.