Mechanical Engineering, Indian Institute of
Science, Bangalore 560 012, India
Optimization hinders evolution!
ME256
Variational methods and structural optimization
Jan.-May, 2007
Instructor: G. K.
Ananthasuresh, Room 106, ME Building, suresh at
mecheng.iisc.ernet.in
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Homework #5
Assigned: Feb. 1st, 2007
Due: Feb. 8th, 2007
Points: 30
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15 points
Consider a straight beam of length L in a 2-D plane. Let there be a
transverse force q(x) on it along the x-axis, which is its longitudinal
axis. Write down its potential energy considering only the beding strain
energy (and not axial strain energy). Minimize this functional and derive
the differential equation and boundary conditions for the following cases.
- Fixed
- Fuxed to a block that is guided vertically
- Free
- Pinned
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15 points
Now, consider also the axial load of p(x) and the axial deformation and
re-do the above problem.