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 #4
Assigned: Feb. 5th, 2019
Due: Feb. 12th, 2019
Points: 80
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
    Write Gauteuax variation and then Euler-Lagrange equations with boundary conditions for the following problems.
  2. 25 points
    Find f(x) such that the integral with integrand F = f2 - f"2, limits of x from 0 to pi/2, is minimized with boundary conditions f(0)= f'(0) = f(pi/2) = 0, and f'(pi/2) = 1. It is not enough to write the differential equation; you also need to solve it here. Show the solution graphically.
  3. 25 points
    Given two points (0,0) and (10,5), find a curve y(x) that passes through these two points to satisfy the following requirement. Under the influence of gravity in the y-direction, if two beads, one at each of the two points, are released from rest at the same time and follow the curve should meet each other in minimum time. Assume that there is no friction as the beads slide on f(x).