Variational methods for Structural Optimization

by Andrej Cherkaev

Springer Verlag, NY 2000. 



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Chapters

    Part I. Preliminaries

  1. Unstable one-dimensional variational problems
  2. Conducting composites
  3. Bounds and G-closures
  4. Part II. Optimization of conducting composites

  5. Domains of extremal conductivity
  6. Optimization of an arbitrary goal functional
  7. Part III. Quasiconvexity and relaxations

  8. Quasiconvex envelope
  9. Minimizing sequences and Laminate composites
  10. Lower bound: Translation method
  11. Necesary conditions and minimal extensions
  12. Part IV. G-closures

  13. Getting G-closures
  14. Examples of G-closures
  15. Multicomponent mixtures
  16. Supplement: Variational principles for dissipative media
  17. Part V. Optimization of Elastic Structures

  18. Elasticity of inhomogeneous media
  19. Elastic composites of extremal energy
  20. Bounds on elastic properties
  21. Some problems of structural optimization