Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India
Optimization hinders evolution!
ME256 Variational Methods and Structural Optimization Jan.-May., 2014
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 (Multimedia Classroom)

Homework #6
Assigned: Feb. 18th, 2014
Due: Feb. 25, 2014
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. 20 points
   Derive the variational derivative using Euler's discretization method for an integral functional whose integrand depends on the function and its first two derivatives. Extra credit of 20 points if you also derive the boundary conditions using the same or similar method.
2. 30 points
   Solve the problem of hanging-chain problem using constrained calculus of variations problem. The length of the chain is 1 m and the horizontal span between the points from which it hangs is 0.5 m. The two points are at the same height. The mass per unit length of the chain is 1 kg/m. Acceleration dues to gravity is 9.81 m/s². Compute the Lagrange multiplier and interpet it physically in the context of this problem.