Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India
Optimization hinders evolution!
ME256 Variational methods and structural optimization May-Jun., 2006
Instructor: G. K. Ananthasuresh, Room 106, ME Building, suresh at mecheng.iisc.ernet.in
Back to homepage of the course

Homework #5
Assigned: Jun. 9th, 2006
Due: Jun. 16th, 2006
Points: 30

  1. 10 points
    Minimize the volume of material of a beam which has a deflection d* at x = x1 under the given load q(x). The beam is fixed at both the ends. It has rectangular cross-section, width = w but with variable depth, t(x). Write down the complete problem statement using L (length of the beam), E (Young's modulus) and other quantities noted above and the additonal ones that are needed. Then, write the necessary conditions and set up the update formula for the depth of the beam using the optimality criteria method.
  2. 20 points
    Write a Matlab program for designing the stiffest truss for a given volume of material under a given static loading. Use Matlab's fmincon routine for optimization. Use analytical sensitivity analysis for computing the gradients. The areas of the cross-section of the truss members are the design variables.
    Download the trussFEM files here.
    Download the fmincondemo files here .