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 #5
Assigned: Feb. 17th, 2018
Due: Feb. 24th, 2018
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".
11 + 10 = 21 points
(a) The mass desnity of a chain of length 1.5 m varies as 4(x-x2) kg/m. If it is hung between two supports separated by 1 m at the same height, what shape will it take under gravity? Pose it as a calculus of variations and obtain the differential equation and boundary conditions.
(b) Solve this problem numerically using Matlab.
15 + 14 = 29 points
(a) Consider the problem:
Write the necessary conditions to solve this problem. What physical situation(s) does this problem represent? Comment on the nature of the solution to this problem. Is it well-posed?
(b) Try to solve this problem using Matlab. What difficulties do you face? How would you modify this problem to get an interesting solution? Pose it and solve it.
