Mechanical Engineering, Indian Institute of
Science, Bangalore 560 012, India Optimization hinders evolution! ME256
Variational Methods and Structural Optimization
Jan.-May., 2016
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 Lecture Hall
Homework #7
Assigned: Mar. 15th, 2016
Due: Mar. 22nd, 2016
Points: 60 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".
20 points
Use bar optimization code to plot optimized strain energy vs. volume for the following data.
L = 10 m; E = 60 GPa; self-weight with g = 9.81 m/s2 and mass density = 7800 kg/m3, Amin = 4 m2, Amax = 100 m2. Plot SE* vs. V* for fixed-free and fixed-fixed bars.
20 points
Modify the bar problem for stiffest beam for given volume of material. Use files for beam finite element analysis . Use the following data:
L = 10 m; E = 210 GPa; q(x) = 100 kg/m, Amin = 0.02 m2, Amax = 0.64 m2, V* = 3 m3. Your programme should work for any boundary conditions of the beam that do not have rigid-body mode.
20 points
Propose a problem for your course project. The design problem you select should involve calculus of variations. That is, your design variable should be a function, and not a finite set of variables.
Please submit a one-page proposal comprising a clear mathematical statement of the problem with objective function, constraints, design variables, state variables, and data. If you do not have the mathematical expressions at this time, simply write it in words. Provide a one-paragraph of background to the problem. Write one line about the best result you would hope for.
See also the project web page.