Spring semester, 1999 ( 3 hours)
Time and Place: JWB 208, T,Th, 12:25-1:45

1. A. Cherkaev. Variational Methods for Structural Optimization. Springer, 2000.
2. Notes

• 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. Springer, 1995

Quasiconvexity, Bounds Definitions of quasiconvexity, Null-Lagrangians. Minimizing sequences. Laminates Translation method Weierstrass test and Minimal extensions. Fields in optimal structures.
G-closures. The technique for bounds of G-closures Bounds on conducting constants. Polycrystals Bounds on complex properties Several materials Bounds on elastic moduli. Elastic polycrystals.
Variational problems for elastic structures. Optimization of stiffness Optimization of the mean stiffness Optimization of eigenvalues
	Various problems of structural optimization. Optimization of single-loaded system by arbitrary criteria Min-max problems of optimization: load versus structure Optimization and bio-materials. What does Nature want?

Course objectives

Examples of optimal design include:

• Elastic structures of maximal stiffness.
• Conducting structures, able to concentrate current.
• A game between the load and the structure.
• Composite with extremal properties.

First semester: M-7710 Homogenization (Fall Semester}

Announcement and the preliminary plan for the entire course

Optimization and Homogenization are placed on www.math.utah.edu/~cherk/teach/7710.htm

Fishes (by Esher)

=>

"Homogenized" Fishes

To Andrej Cherkaev homepage