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 #5
Assigned: Feb. 16th, 2016
Due: Feb. 23rd, 2016
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".
20 points
Show in the figure below is a beam (length L, moment of area I, and Young's modulus E) with a transverse load at its midpoint. It is fixed at the
right end and is attached to a slider-crank rigid-body linkage at the left end. Notice that the beam is attached not to the slider but to the connecting rod.
Write the differential equation and boundary conditions and solve for the deflection and reactions of the beam.
20 points
Write the general boundary conditions for a plate for different physical situations. Use the potential energy expression and obtain the expressions
for the quantities missing in the boundary term.
20 points
Obtain the differential equation and boundary conditions for the linear elasticity problem by solving the following problem.
20 points
The figure below depicts an adventure sports person attached to a bungee cord of length l tied to a support. The bungee cord has stiffness k. When she lets go of her hands, her descent beings. Use Hamilton's principle to write the equation of motion assuming that she stays in the initial vertical plane. Assume also that particle mass of the person is m.
