Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India
Optimization hinders evolution!
ME256 Variational Methods and Structural Optimization Jan.-May., 2018
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 MMCR

Homework #2
Assigned: Jan. 11th, 2018
Due: Jan. 18th, 2018
Points: 70
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. 54 points

    2. Shown in the figure are stress-free (dashed curve) arch-profile given by H(x) and stressed arch-profile (solid curve) given by W(x) for pinned-pinned condition. If the two profiles are stable, the following equations hold.

    Now, obtain Ai, i = 1, 2, ..., N for a value of your choice for N>1 such that {H(0.5)-W(0.5)}2 is maximized subject to the inequality constraint:
    .
  2. 16 points
    Consider f and h that are functions of x,y,z. If we minimize f subject to h = 0, prove that, at the optimum point, the ratio of the rate of change of f to the rate of change of h is the same with respect to x,y,z.