Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India
Optimization hinders evolution!
ME256 Variational Methods and Structural Optimization Jan.-May., 2016
Instructor: G. K. Ananthasuresh , Room 106, ME Building, suresh at mecheng.iisc.ernet.in
Lectures: Tu, Th: 08:30 AM - 10:00 AM; Venue: ME Lecture Hall

Homework #8
Assigned: Mar. 22nd, 2016
Due: Mar. 29th, 2016
Points: 50
Additional points for work that is beyond instructor's expectation!
Look up Homework #1 of 2010 offering of this course and the solution posted there to know what is meant by "beyond instructor's expectation".

1. 30 points
   In the figure show in below, P is the load applied and u is the displacement at that point. Let P = 2000 N. All truss members are made of aluminium with E = 70 GPa. The cross-section areas, Ais, are the optimization variables. Take V* as 0.2 m3. SE denotes twice the strain energy stored in the loaded truss. Use truss fem Matlab code and the optimality criteria method to solve the problem. You need matcut.m and veccut.m in the same folder to run femtruss.m.
   Use many more truss elements so that all pairs of grid points are taken as elements.
2. 20 points
   Pose the problem of minimizing the volume of a flat plate for given upper bound on the strain energy, as a calclulus of variations problem and show that uniform stress is the optimality condition. The thickness of the plate, t(x,y), is the design variable. Extra points of 20 for handling the boundary conditions too.