Homework #7
Assigned: Mar. 11th, 2008
Due: Mar. 25th, 2008
Points: 30

1. 30 points
   Consider a fixed-fixed bar of length 1 m. It is made of steel with an Young's modulus of 210 GPa. It has a strength of 100 MPa. The bar has three point loads. The first load is applied at x = 0.3 m towards right and its magnitude is 0.5 kN. The second load is applied at x = 0.5 m towards right and its magnitude is 0.5 kN. The third load is applied at x = 0.7 m towards left and its magnitude is 0.5 kN. Design the area of cross-section of this bar for maximizing the stiffness for given amount of material. The area of cross-section has to be between lower and upper limits: 3 mm diameter and 30 mm diamter assuming circular cross-section. The volume of material given is 15 mm diamter circular cross-section multiplied by 1 m length.
   Write the conditions analytically and then solve it numerically using fmincon in Matlab as well as the optimality criteria method.
2. 20 points
   Extra points for imposing the strength criterion. Here, you can solve it using only fmincon.