Mathematics 7710. II Semester. Optimization of Structures
Spring semester, 1999 ( 3 hours)
Time and Place: JWB 208, T,Th, 12:25-1:45
The reference books:
- A. Cherkaev. Variational Methods for Structural Optimization. Springer, 2000.
- V.V.Jikov, S.M.Kozlov, O.A.Olejnik. Homogenization of differential
operators and integral functionals Springer, 1991
- K. Lurie. Applied Optimal Control. Plenum 1993
- M.Bendsoe. Optimization of structural topology, shape, and materials.
Plan Spring semester
The course discusses structural optimization. The main problems are to find "the best" geometrical composition of the structure and to determine the distribution of the optimal structures in the design.
Examples of optimal design include:
Mathematically, we are dealing with variational problems with non-convex Lagrangians. We develop the technique that enables to correctly formulate and solve these variational problems with non-stable solutions. We discuss special methods based on the quasiconvex envelopes. Applying the technique to the mechanical and transport problems, we are able to find optimal structures for the above mentioned problems.
- Elastic structures of maximal stiffness.
- Conducting structures, able to concentrate current.
- A game between the load and the structure.
- Composite with extremal properties.
M-7710 Homogenization (Fall Semester}
Announcement and the preliminary plan for the entire course
Optimization and Homogenization are placed on
To Andrej Cherkaev homepage
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