Homework #8
Assigned: Mar. 15th, 2007
Due: Mar. 22th, 2007
Points: 40

1. 20 points
   We have done bar optimization problems in the class. Now, do the same for beam optimization. For both the problems listes below, write the COMPLETE problem statement in mathematical form, the Lagrangian and its variations with respect to the design variables and state variables, show that you have enough equations to solve for all the unknowns including the Lagrange multipliers, and adequately simplify it to comment on the nature of the solution or solve the problem completely.
   • Maximize the stiffness of a fixed-fixed beam for a given volume under a half-sign wave load distributed along the length of the beam. Take the length of the beam as L, Young's modulus as E, maximum load as P and volume as V*.
   • Repeat the above problem to minimize the maximumm magnitude of the bending stress for given volume.
2. 20 points
   Download the truss finite element code in Matlab by clicking here . Use this to write a topology optimization program for optimal truss design for maximum stiffness for given volume of material under given load. Write a general program so that any boundary conditions with any discretization can be tried out. And then, try two benchmark problems that we discussed in the class and ensure that your program is working well.