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 #5
Assigned: Feb. 11th, 2014
Due: Feb. 18, 2014
Points: 40 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 the principle of minimum potential energy to derive the differential equation and boundary conditions for static equilibrium of of a 3D elastic solid.
Consider u(x,y,z), v(x,y,z), and w(x,y,z) as the three displacement functions. Use linear (small) strain and linear stress-strain relationship.
Interpret the boundary conditions.
20 points
Four boundary conditions are obtained when we minimize the potential energy of a beam under transverse load. Think of a physical arrangement of a beam where
two or more boundary conditions are coupled to one another so that the four boundary conditions are not all independently zero.Sketch your physical
arrangement clearly and mathematically interpret how the boundary conditions are coupled.
