Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India
Optimization hinders evolution!
ME256 Variational Methods and Structural Optimization Jan.-May., 2019
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 #6
Assigned: Mar. 7th, 2019
Due: Mar. 19th, 2019
Points: 120
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. 50 points
    Use bar optimization code , and modify it as necessary, to minimize strain energy by finding the area profile of a fixed-fixed bar. The bar is 1 m long. The volume of material given is 0.005 m3. The area of c/s cannot be smaller than 0.001 m2 and cannot be larger than 0.006 m2. The axial loading is parabolic with zero load at bothe ends and maximum of 200 N/m at the midpoint. Compute the strain energy of the uniform c/s bar and that of the optimized bar. Obtain all Lagrange multipliers including those corresponding to the size constraints. Calculate the maximum stress in the bar. Submit a figure of the optimized c/s profile.
  2. 50 points
    Pose the problem of the stiffest beam optimization for a given volume where the depth of the beam is the design variable. Obtain the optimality conditions for the cantilver boundary condititon for uniform loading of q0.
  3. 20 points
    Submit a one-page project proposal as described in the project page .