Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India
Optimization hinders evolution!
ME256 Variational methods and structural optimization Jan.-May, 2013
Instructor: G. K. Ananthasuresh, Room 106, ME Building, suresh at mecheng.iisc.ernet.in
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Homework #6
Assigned: Mar. 19, 2013
Due: Mar. 26th, 2013
Points: 100
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
    Write down the derivation of necessary conditions for the beam problem for minimizing the mean compliance for given volume. Write down the design equation, adjoint equation, and comlementarity conditions, etc., including the boundary conditions.
  2. 80 points
    Write a general purpose "optimality criteria method" for optimizating the cross-section area of beams for different objective functions (mean compliamce, square of transverse displacement, etc.). Run it for mean compliance and verify with the analytical solution obtained in the problem 1 in this homework.

    The finite element beam analysis implemented in Matlab is available at here.