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

  4. Domains of extremal conductivity
  5. Optimization of an arbitrary goal functional

    6. Part III. Quasiconvexity and relaxations

  6. Quasiconvex envelope
  7. Minimizing sequences and Laminate composites
  8. Lower bound: Translation method
  9. Necesary conditions and minimal extensions

    10. Part IV. G-closures

  10. Getting G-closures
  11. Examples of G-closures
  12. Multicomponent mixtures
  13. Supplement: Variational principles for dissipative media

    14. Part V. Optimization of Elastic Structures

  14. Elasticity of inhomogeneous media
  15. Elastic composites of extremal energy
  16. Bounds on elastic properties
  17. Some problems of structural optimization