عنوان

Introduction to Shape Optimization

شابک

9783642581069

شابک

9783642634710

شماره

b407330

عنوان اصلي

Introduction to Shape Optimization

نام عام مواد

[Book]

ساير اطلاعات عنواني

Shape Sensitivity Analysis /

نام نخستين پديدآور

by Jan Sokolowski, Jean-Paul Zolesio.

محل نشرو پخش و غیره

Berlin, Heidelberg :

نام ناشر، پخش کننده و غيره

Imprint: Springer,

تاریخ نشرو بخش و غیره

1992.

عنوان فروست

Springer Series in Computational Mathematics,

مشخصه جلد

16

شاپا ي ISSN فروست

0179-3632 ;

متن يادداشت

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 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 -- 3.5. 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. Elasto-Plastic torsion problems -- 4.9. Elasto-Visco-Plastic problems -- References.

بدون عنوان

0

متن يادداشت

This book is motivated largely by a desire to solve shape optimization prob lems that arise in applications, particularly in structural mechanics and in the optimal control of distributed parameter systems. Many such problems can be formulated as the minimization of functionals defined over a class of admissible domains. Shape optimization is quite indispensable in the design and construction of industrial structures. For example, aircraft and spacecraft have to satisfy, at the same time, very strict criteria on mechanical performance while weighing as little as possible. The shape optimization problem for such a structure consists in finding a geometry of the structure which minimizes a given functional (e. g. such as the weight of the structure) and yet simultaneously satisfies specific constraints (like thickness, strain energy, or displacement bounds). The geometry of the structure can be considered as a given domain in the three-dimensional Euclidean space. The domain is an open, bounded set whose topology is given, e. g. it may be simply or doubly connected. The boundary is smooth or piecewise smooth, so boundary value problems that are defined in the domain and associated with the classical partial differential equations of mathematical physics are well posed. In general the cost functional takes the form of an integral over the domain or its boundary where the integrand depends smoothly on the solution of a boundary value problem.

شماره استاندارد بين المللي کتاب و موسيقي

9783642634710

عنوان

Springer eBooks

موضوع مستند نشده

Engineering mathematics.

موضوع مستند نشده

Mathematical optimization.

موضوع مستند نشده

Mathematics.

موضوع مستند نشده

Numerical analysis.

موضوع مستند نشده

Systems theory.

مستند نام اشخاص تاييد نشده

Sokolowski, Jan.

مستند نام اشخاص تاييد نشده

Zolésio, J.-P.

مستند نام تنالگان تاييد نشده

SpringerLink (Online service)

تاريخ عمليات

20190307154600.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y