A solid bar having a rectangular cross-section half inch wide and one inch high is subjected to a constant rate of twist along its axis. The stresses established in the bar can be related to the nondimensionalized Prandtl stress function, & (X, Y), which, for the geometry of this problem, satisfies the Poisson problem + = -1 on R = {(x,y) | 0 < x < 1/2,0 < y < 1} (x, 1) = (1/2, y) = 0, | ax (0,y) 4| == = 0 (x,0) Apply the finite difference method with spacing Ax = Ay = 0.05 to calculate an approximation to the solution (x, y). (a) Plot the approximated solution (b) Plot the approximated solution (x = 0, y) along the y axis. (x, y = 0.5) along the y axis. (c) Graph a contour-plot of the approximated solution (x, y). y 10 0.8 0.6 0.4 0.2 Stress in Bar W(0, y) 0.0 0.00 0.02 0.04 0.06 Wat x=0 0.08 0.10 x=0 y - inches 10 0.8- Stresses in bar - w(x,y) 0.120 0.105 0.090 0.075 0.6 0.060 0.4 0.045 0.2 0.030 0.015 0.0 0.000 0.0 0.1 0.2 0.3 0.4 0.5 X - inches 0.10 Stress in Bar (x, 0.5) 0.08 in 0.06 Wat y=0.5 0.04 0.02 0.00 y=0.5 0.0 0.1 0.2 0.3 0.4 0.5 x