Answer Happy

V= = Problem 1 (20pts) An open-ended thick-walled aluminium (E = 70GPa and v=0.25) cylinder has an inner radius of 120mm and outer radius of 150mm. The inner surface is traction-free while the outer surface is displaced S= 0.2mm in the outward radial direction (u(b) = 0). Assume and (i.e., plane stress with oz(r) = 0). You may use the equations for plane stress given in the thick-walled cylinder handout. (a) Determine the radial and hoop stresses, 0,(r) and odr), respectively. Show the equations, explicitly (must find A and B). Choose the unit as MPa. (b)Determine the von Mises/effective stress from oe(r) = V0,2 -0,0,+0. Simplify the expression to show it as a function of “r”. (c) Plot 0,(r), odr) and oe(r) for r = 120 to 150mm (computer generated, no hand- drawn sketch). Find the maximum von Mises stress and its location. (d) Suppose the aluminium has the yield stress of 0. 300MP and the outer displacement Sis gradually increased, at what value of d, the maximum von Mises stress reaches this yield stress? = = =