Multiphase Shape Optimization Problems
نویسندگان
چکیده
This paper is devoted to the analysis of multiphase shape optimization problems, which can formally be written as min { g ( (F1(Ω1), . . . , Fh(Ωh) ) +m ∣∣ h ⋃ i=1 Ωi ∣∣ : Ωi ⊂ D, Ωi ∩ Ωj = ∅}, where D ⊆ R is a given bounded open set, |Ωi| is the Lebesgue measure of Ωi and m is a positive constant. For a large class of such functionals, we analyse qualitative properties of the cells and the interaction between them. Each cell is itself subsolution for a (single-phase) shape optimization problem, from which we deduce properties like finite perimeter, inner density, separation by open sets, absence of triple junction points, etc. As main examples we consider functionals involving the eigenvalues of the Dirichlet Laplacian of each cell, i.e. Fi = λki .
منابع مشابه
A Multiphase Shape Optimization Problem for Eigenvalues: Qualitative Study and Numerical Results
We consider the multiphase shape optimization problem
متن کاملSecond order sensitivity analysis for shape optimization of continuum structures
This study focuses on the optimization of the plane structure. Sequential quadratic programming (SQP) will be utilized, which is one of the most efficient methods for solving nonlinearly constrained optimization problems. A new formulation for the second order sensitivity analysis of the two-dimensional finite element will be developed. All the second order required derivatives will be calculat...
متن کاملMathematics in paper
*Correspondence: [email protected] Centre of Computational Engineering and Integrated Design (CEID) and Department of Mathematics and Physics, Lappeenranta University of Technology, P.O. Box 20, Lappeenranta, FI-53851, Finland Abstract This paper aims to give a general overview of industrial mathematics applied to papermaking. Modelling challenges vary from computational fluid dynamics (CF...
متن کاملTopological Shape Optimization of Multiphysics Actuators using Level Set Method
This paper proposes a topological shape optimization method for the design of multi-physics piezoelectric actuators using a level set method of piecewise constants. A level set function taking level sets of piecewise constants is applied to implicitly represent design boundaries in a multiphase design domain, in which each constant level set denotes one material phase. As a result, only one lev...
متن کاملOptimization of Emc-properties of a Symmetric Multithread 3-phase Cable
The optimization problems of properties of a symmetric multiconductor three-phase cable are examined from the viewpoint of electromagnetic compatibility (EMC). The goal functions are: the minimization of an external magnetic field created by the cable current; the minimization of losses in the cable. For the optimization the genetic algorithm is used. Results can be applied to the optimization ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Control and Optimization
دوره 52 شماره
صفحات -
تاریخ انتشار 2014