Inverse shape optimization problems and application to airfoils

Szczegóły
Opis

Tytuł:: Inverse shape optimization problems and application to airfoils
Autorzy:: Desideri, J.-A.
Zolesio, J.-P.
Data publikacji:: 2005
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:: równanie różniczkowe cząstkowe
metody obliczeniowe
optymalizacja kształtu
rachunek wariacyjny
Partial-Differential Equations (PDEs)
computational methods
shape optimization
calculus of variations
Źródło:: Control and Cybernetics; 2005, 34, 1; 165-202
0324-8569
Język:: angielski
Prawa:: Wszystkie prawa zastrzeżone. Swoboda użytkownika ograniczona do ustawowego zakresu dozwolonego użytku
Dostawca treści:: Biblioteka Nauki
: Artykuł

Przejdź do źródła

We consider a set of parameterized planar arcs (x(t), y(t)) (0 1. We first prove the strict convexity of the functional for alpha > 2. Under the less stringent condition alpha > 1, we derive the stationarity condition and the formal expression for the Hessian, and prove that if a point exists at which the functional is stationary w.r.t. variations in y = y(t), for fixed x = x(t), then it is unique and realizes a global minimum; the functional is then unimodal. We also observe that the stationarity condition (Euler-Lagrange quation) is an integral-differential equation depending only on the arc shape and not on the parameterization per se, which gives the variational problem a certain intrinsic character. Then, we solve the inverse problem: given an admissible parameterized arc, we construct a smooth weighting function omega(t) for which the stationarity condition is satisfied, thus making the functional unimodal, and derive certain asymptotics. A numerical example pertaining to optimum-shape design in aerodynamics is computed for illustration.

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Inverse shape optimization problems and application to airfoils

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