Mechanical Engineering, Indian Institute of
Science, Bangalore 560 012, India
Optimization hinders evolution!
ME256
Variational methods and structural optimization
Jan.-May, 2008
Instructor: G. K.
Ananthasuresh, Room 106, ME Building, suresh at
mecheng.iisc.ernet.in
Back to homepage of the course
Homework #5
Assigned: Feb. 13th, 2009
Due: Feb. 19, 2009
Points: 20
-
10 points
- Derive the transversality conditions for a functional whose integrand is of the type F(x,y,y',y'') and
ends of y(x) lies on a given curve phi(x).
- Apply what you have derived to a beam whose ends are guided along two straight slots that are perpendicular
to each other. The beam is inclined to both the slots at an angle of 45 degrees. Consider a load of 100 N at
the mid-point of the beam oriented in a direction passing through the intersection of the two slots.
Let the beam have a length of 1 m and a square cross-section of 1 cm side. It is made of steel with
an Young's modulus of 210 GPa. Plot the deformed profile of the beam.
-
10 points
Find the functionals which, when minimized, give the following minimizing functions.
- y = x7/7! + C1 x5 + C2 x4 +
C3 x3 + C4 x2 + C5 x + C6.
-
a y'' + b y' + c y = 0