Author | Sokolowski, Jan. author |
---|---|
Title | Introduction to Shape Optimization [electronic resource] : Shape Sensitivity Analysis / by Jan Sokolowski, Jean-Paul Zolesio |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1992 |
Connect to | http://dx.doi.org/10.1007/978-3-642-58106-9 |
Descript | IV, 250 p. online resource |
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 -- 2.7. 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 LaplaceโBeltrami 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 LaplaceโBeltrami 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 -- 3.5. 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 (?) -- 4.4. The Signorini problem -- 4.5. Variational inequalities of the second kind -- 4.6. Sensitivity analysis of the Signorini problem in elasticity -- 4.7. The Signorini problem with given friction -- 4.8. ElastoโPlastic torsion problems -- 4.9. ElastoโViscoโPlastic problems -- References