Introduction to Shape Optimization: Shape Sensitivity Analysis: v. 16 (Springer Series in Computational Mathematics) - Hardcover

Sokolowski, Jan; Zolesio, Jean-Paul

Hardcover

ISBN 10: 3540541772 ISBN 13: 9783540541776

Verlag: Springer, 1992

Inhaltsangabe

1 Introduction to shape optimization.- 1.1. Preface.- 2 Preliminaries and the material derivative method.- 2.1. Domains in ?N of class Ck.- Surface measures on ?.- 2.3. Functional spaces.- 2.4. Linear elliptic boundary value problems.- 2.5. Shape functionals.- 2.6. Shape functionals for problems governed by linear elliptic boundary value problems.- 2.6.1. Shape functionals for transmission problems.- 2.6.2. Approximation of homogenuous Dirichlet problems.- 2.7. Convergence of domains.- 2.8. Transformations Tt of domains.- 2.9. The speed method.- 2.10. Admissible speed vector fields Vk(D).- 2.11. Eulerian derivatives of shape functionals.- 2.12. Non-differentiable shape functionals.- 2.13. Properties of Tt transformations.- 2.14. Differentiability of transported functions.- 2.15. Derivatives for t > 0.- 2.16. Derivatives of domain integrals.- 2.17. Change of variables in boundary integrals.- 2.18. Derivatives of boundary integrals.- 2.19. The tangential divergence of the field V on ?.- 2.20. Tangential gradients and Laplace-Beltrami operators on ?.- 2.21. Variational problems on ?.- 2.22. The transport of differential operators.- 2.23. Integration by parts on ?.- 2.24. The transport of Laplace-Beltrami operators.- 2.25. Material derivatives.- 2.26. Material derivatives on ?.- 2.27. The material derivative of a solution to the Laplace equation with Dirichlet boundary conditions.- 2.28. Strong material derivatives for Dirichlet problems.- 2.29. The material derivative of a solution to the Laplace equation with Neumann boundary conditions.- 2.30. Shape derivatives.- 2.31. Derivatives of domain integrals (II).- 2.32. Shape derivatives on ?.- 2.33. Derivatives of boundary integrals.- 3 Shape derivatives for linear problems.- 3.1. The shape derivative for the Dirichlet boundary value problem.- 3.2. The shape derivative for the Neumann boundary value problem.- 3.3. Necessary optimality conditions.- 3.4. Parabolic equations.- 3.4.1 Neumann boundary conditions.- 3.4.2 Dirichlet boundary conditions.- 3.5. Shape sensitivity in elasticity.- 3.6. Shape sensitivity analysis of the smallest eigenvalue.- 3.7. Shape sensitivity analysis of the Kirchhoff plate.- 3.8. Shape derivatives of boundary integrals: the non-smooth case in ?2.- 3.9. Shape sensitivity analysis of boundary value problems with singularities.- 3.10. Hyperbolic initial boundary value problems.- 4 Shape sensitivity analysis of variational inequalities.- 4.1. Differential stability of the metric projection in Hilbert spaces.- 4.2. Sensitivity analysis of variational inequalities in Hilbert spaces.- 4.3. The obstacle problem in H1 (?).- 4.3.1. Differentiability of the Newtonian capacity.- 4.3.2. The shape controlability of the free boundary.- 4.4. The Signorini problem.- 4.5. Variational inequalities of the second kind.- 4.6. Sensitivity analysis of the Signorini problem in elasticity.- 4.6.1. Differential stability of solutions to variational inequalities in Hilbert spaces.- 4.6.2. Shape sensitivity analysis.- 4.7. The Signorini problem with given friction.- 4.7.1. Shape sensitivity analysis.- 4.8. Elasto-Plastic torsion problems.- 4.9. Elasto-Visco-Plastic problems.- References.

Über diesen Titel

Reseña del editor

This book presents modern functional analysis methods for the sensitivity analysis of some infinite-dimensional systems governed by partial differential equations. The main topics are treated in a general and systematic way. They include many classical applications such as the Signorini problem, the elastic-plastic torsion problem and the visco-elastic-plastic problem. The "material derivative" from which any kind of shape derivative of a cost functional can be derived is defined. New results about the wave equation and the unilateral problem are also included in this book, which is intended to serve as a basic reference work for the algorithmic approach to shape optimization problems.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 1992
• Sprache: Englisch
• ISBN 10: 3540541772
• ISBN 13: 9783540541776
• Einband: Tapa dura
• Anzahl der Seiten: 262
• Kontakt zum Hersteller: ROXIO; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; 22391; Deutschland