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    Wyświetlanie 1-13 z 13
    Tytuł:
    Second derivatives and sufficient optimality conditions for shape funetionals
    Autorzy:
    Eppler, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/206712.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optimal shape design
    second directional derivatives
    sufficient optimality conditions
    Opis:
    For sorne heuristic approaches to boundary variation in shape optimization the computation of second derivatives of domain and boundary integral functionals, their symmetry and a comparison to the velocity field or material derivative method are discussed. Moreover, for these approaches the functionals are Frechet-differentiable in some sense, because at least a local embedding into a Banach space problem is possible. This allows the discussion of sufficient condition in terms of a coercivity assumption on the second Frechet-derivative. The theory is illustrated by a discussion of the famous Dido problem.
    Źródło:
    Control and Cybernetics; 2000, 29, 2; 485-511
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An optimal shape design problem for a hyperbolic hemivariational inequality
    Autorzy:
    Gasiński, Leszek
    Powiązania:
    https://bibliotekanauki.pl/articles/729253.pdf
    Data publikacji:
    2000
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    optimal shape design
    mapping method
    hemivariational inequalities
    Clarke subdifferential
    Opis:
    In this paper we consider hemivariational inequalities of hyperbolic type. The existence result for hemivariational inequality is given and the existence theorem for the optimal shape design problem is shown.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2000, 20, 1; 41-50
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Shape optimization in problems governed by generalised Navier-Stokes equations: existence analysis
    Autorzy:
    Haslinger, J.
    Malek, J.
    Stebel, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/970130.pdf
    Data publikacji:
    2005
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optimal shape design
    paper machine headbox
    incompressible non-Newtonian fluid
    algebraic turbulence model
    Opis:
    We study a shape optimization problem for a paper machine headbox which distributes a mixture of water and wood fibers in the paper manufacturing process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to an optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by the generalised Navier-Stokes system with nontrivial boundary conditions. The objective of this paper is to prove the existence of an optimal shape.
    Źródło:
    Control and Cybernetics; 2005, 34, 1; 283-303
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Boundary integral representations of second derivatives in shape optimization
    Autorzy:
    Eppler, Karsten
    Powiązania:
    https://bibliotekanauki.pl/articles/729245.pdf
    Data publikacji:
    2000
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    optimal shape design
    fundamental solution
    boundary integral equation
    second-order derivatives
    optimality conditions
    Opis:
    For a shape optimization problem second derivatives are investigated, obtained by a special approach for the description of the boundary variation and the use of a potential ansatz for the state. The natural embedding of the problem in a Banach space allows the application of a standard differential calculus in order to get second derivatives by a straight forward "repetition of differentiation". Moreover, by using boundary value characerizations for more regular data, a complete boundary integral representation of the second derivative of the objective is possible. Basing on this, one easily obtains that the second derivative contains only normal components for stationary domains, i.e. for domains, satisfying the first order necessary condition for a free optimum. Moreover, the nature of the second derivative is discussed, which is helpful for the investigation of sufficient optimality conditions.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2000, 20, 1; 63-78
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal Shape Design for Elliptic Equations Via Bie-Methods
    Autorzy:
    Eppler, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/911209.pdf
    Data publikacji:
    2000
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    rozwiązanie podstawowe
    równanie całkowe
    optimal shape design
    fundamental solution
    boundary integral equation
    first-order necessary condition
    Opis:
    A special description of the boundary variation in a shape optimization problem is investigated. This, together with the use of a potential theory for the state, result in natural embedding of the problem in a Banach space. Therefore, standard differential calculus can be applied in order to prove the Frechet-differentiability of the cost function for appropriately chosen data (sufficiently smooth). Moreover, necessary optimality conditions are obtained in a similar way as in other approaches, and are expressed in terms of an adjoint state for more regular data.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2000, 10, 3; 487-516
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Dynamic programming approach to structural optimization problem - numerical algorithm
    Autorzy:
    Fulmański, P.
    Nowakowski, A.
    Pustelnik, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/255706.pdf
    Data publikacji:
    2014
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    elliptic equations
    optimal shape control
    structural optimization
    stationary Navier-Stokes equations
    dynamic programming
    sufficient optimality condition
    numerical approximation
    Opis:
    In this paper a new shape optimization algorithm is presented. As a model application we consider state problems related to fluid mechanics, namely the Navier-Stokes equations for viscous incompressible fluids. The general approach to the problem is described. Next, transformations to classical optimal control problems are presented. Then, the dynamic programming approach is used and sufficient conditions for the shape optimization problem are given. A new numerical method to find the approximate value function is developed.
    Źródło:
    Opuscula Mathematica; 2014, 34, 4; 699-724
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Application of finite variations to topology and shape optimization of 2D structures
    Zastosowanie modyfikacji skończonych w optymalizacji topologii i kształtu konstrukcji dwuwymiarowych
    Autorzy:
    Bojczuk, D.
    Sztebelak, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/280313.pdf
    Data publikacji:
    2006
    Wydawca:
    Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
    Tematy:
    2D structures
    optimal topology and shape
    topological derivative
    finite modification
    structure evolution
    Opis:
    The method of simultaneous topology and shape optimization of 2D structures by finite topology modification is presented in the paper. Both, structures in a plane state of stress and bending Kirchhoff's plates are analyzed here. Conditions for the introduction of finite topology modification based on the topological derivative are specified. When the respective condition is satisfied, finite holes and finite variations of existing boundaries are introduced into the structure. Next, standard shape optimization of new holes and variable boundaries is performed. Two basic types of modification are considered here, namely the introduction of holes of a prescribed size and shape and the introduction of holes of an unknown size and shape together with the introduction of finite changes of other boundaries. A heuristic algorithm for optimal design of topology and shape is proposed in the paper. Illustrative examples confirm applicability of the proposed approach.
    W pracy rozpatrywana jest metoda jednoczesnej optymalizacji topologii i kształtu konstrukcji dwuwymiarowych przy użyciu skończonych modyfikacji topologii. Rozważania dotyczą zarówno konstrukcji tarczowych pracujących w płaskim stanie naprężenia, jak i płyt Kirchhoffa pracujących w stanie zgięciowym. Przy wykorzystaniu pochodnej topologicznej wyprowadzono warunki wprowadzania skończonych modyfikacji topologii. Gdy spełniony jest odpowiedni warunek modyfikacji, do konstrukcji wprowadzane są otwory o skończonych wymiarach oraz ewentualnie skończone modyfikacje pozostałych brzegów. Następnie wykonywana jest standardowa optymalizacja kształtu otworów i brzegów zewnętrznych. Analizowane są dwa podstawowe typy modyfikacji, a mianowicie wprowadzanie otworów o zadanej wielkości i kształcie oraz wprowadzanie otworów o nieznanej wielkości i kształcie wraz z ewentualną skończoną zmianą pozostałych brzegów. W pracy sformułowano odpowiedni algorytm heurystyczny optymalizacji topologii i kształtu rozpatrywanych konstrukcji. Przedstawione przykłady ilustracyjne potwierdzają przydatność zaproponowanego podejścia.
    Źródło:
    Journal of Theoretical and Applied Mechanics; 2006, 44, 2; 323-349
    1429-2955
    Pojawia się w:
    Journal of Theoretical and Applied Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Experimental Modeling to Facilitate Removal of Inclusion Contaminants from the Contact Surface in Transversal Extrusion Processes
    Autorzy:
    Skorulski, G.
    Piwnik, J.
    Hościło, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/379917.pdf
    Data publikacji:
    2014
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    innovative foundry technologies
    innovative foundry materials
    extrusion
    aluminium alloys
    experimental modelling
    optimal shape
    inclusion
    contaminants
    innowacyjne technologie odlewnicze
    materiały innowacyjne
    stopy aluminium
    wyciskanie
    modelowanie eksperymentalne
    Opis:
    The paper presents experimental optimization of geometrical conditions regarding the shape of billet’s end pieces in the extrusion process of aluminum alloys. The experiments were performed using appropriately pre-treated plasticine as a substitute material. A special test stand was built using a Plexiglass die in order to make it possible to conduct observations and measurements of the modeled contamination surface. To find the best solution, a great number of shape variants of the billets and of their heating temperatures were experimentally analyzed. An attempt was made to find such a solution that could not only resolve the issue of the removal of contaminants from the contact surface of the pre- heated billets but also develop the least complicated technology of billet fabrication. The test results show how to develop the design process and production technology and also offer advice how to improve the quality of the produced profiles. Finally the authors recommend such a shape for the billets that will ensure effective removal of contaminants from the contact surfaces.
    Źródło:
    Archives of Foundry Engineering; 2014, 14, 1 spec.; 209-212
    1897-3310
    2299-2944
    Pojawia się w:
    Archives of Foundry Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal reliability for components under thermomechanical cyclic loading
    Autorzy:
    Bittner, L.
    Gottschalk, H.
    Powiązania:
    https://bibliotekanauki.pl/articles/205661.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    shape optimization
    probabilistic failure times
    optimal reliability
    Opis:
    We consider the existence of optimal shapes in a context of the thermo-mechanical system of partial differential equations (PDE) using the recent approach based on elliptic regularity theory (Gottschalk and Schmitz, 2015; Agmon, Douglis and Nirenberg, 1959,1964; Gilbarg and Trudinger, 1977). We give an extended and improved definition of the set of admissible shapes based on a class of sufficiently differentiable deformation maps applied to a baseline shape. The obtained set of admissible shapes again allows to prove a uniform Schauder estimate for the elasticity PDE. In order to deal with thermal stress, a related uniform Schauder estimate will be derived for the heat equation. Special emphasis is put on Robin boundary conditions, which are motivated by the convective heat transfer processes. It is shown that these thermal Schauder estimates can serve as an input to the Schauder estimates for the elasticity equation (Gottschalk and Schmitz, 2015). This is needed to prove the compactness of the (suitably extended) solutions of the entire PDE system in some state space that carries a C2-Hölder topology for the temperature field and a C3-Hölder topology for the displacement. From this, one obtains the property of graph compactness, which is the essential tool to prove the existence of optimal shapes. Due to the topologies employed, the method works for objective functionals that depend on the displacement and its derivatives up to third order, as well as on the temperature field and its derivatives up to second order. This general result in shape optimization is then applied to the problem of optimal reliability, i.e. the problem of finding shapes that have minimal failure probability under cyclic thermomechanical loading.
    Źródło:
    Control and Cybernetics; 2016, 45, 4; 421-455
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Control problems for systems described by hemivariational inequalities
    Autorzy:
    Denkowski, Z.
    Powiązania:
    https://bibliotekanauki.pl/articles/206594.pdf
    Data publikacji:
    2002
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    konwergencja G i Gamma
    nierówność hemiwariacyjna
    operator pseudo-monotoniczny
    problem Boltza
    wielofunkcja
    wrażliwość
    zagadnienie poprawnie postawione
    zagadnienie sterowania
    Clarke subdifferential
    control problems (Bolza problem, identification of parameters, optimal shape design)
    G and Gamma convergence
    hemivariational inequalities
    multifunctions
    pseudo-monotone operators
    sensitivity
    well-posedness
    Opis:
    The paper considers some control problems for the systems described by the evolution, as well as the stationary hemivariational inequalities (HVIs for short). First, basing on surjectivity theorems for pseudo-monotone operators we formulate some existence results for the solutions of the HVIs and investigate some properties of the solution set (like sensitivity; i.e. its dependence on data and operators). Next we quote some existence theorems for optimal solutions for various classes of optimal control like distributed control (e.g. Bolza problem), identification of parameters, or optimal shape design for systems described by HVIs. Finally, we discuss some common features in getting the existence of optimal solutions as well as some "well-posedness" problems.
    Źródło:
    Control and Cybernetics; 2002, 31, 3; 713-738
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Shape sensitivity of optimal control for the Stokes problem
    Autorzy:
    Abdelbari, Merwan
    Nachi, Khadra
    Sokolowski, Jan
    Szulc, Katarzyna
    Powiązania:
    https://bibliotekanauki.pl/articles/2049935.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    Stokes equations
    optimal control problem
    coupled partial differential equations
    shape optimization
    shape gradient
    Opis:
    In this article, we study the shape sensitivity of optimal control for the steady Stokes problem. The main goal is to obtain a robust representation for the derivatives of optimal solution with respect to smooth deformation of the flow domain. We introduce in this paper a rigorous proof of existence of the material derivative in the sense of Piola, as well as the shape derivative for the solution of the optimality system. We apply these results to derive the formulae for the shape gradient of the cost functional; under some regularity conditions the shape gradient is given according to the structure theorem by a function supported on the moving boundary, then the numerical methods for shape optimization can be applied in order to solve the associated optimization problems.
    Źródło:
    Control and Cybernetics; 2020, 49, 1; 11-40
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal design of cylindrical shells
    Autorzy:
    Nestler, Peter
    Schmidt, Werner
    Powiązania:
    https://bibliotekanauki.pl/articles/729263.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    linear elasticity
    shell theory
    cylindrical tube
    optimal control
    shape optimization
    Opis:
    The present paper studies an optimization problem of dynamically loaded cylindrical tubes. This is a problem of linear elasticity theory. As we search for the optimal thickness of the tube which minimizes the displacement under forces, this is a problem of shape optimization. The mathematical model is given by a differential equation (ODE and PDE, respectively); the mechanical problem is described as an optimal control problem. We consider both the stationary (time independent) and the transient (time dependent) case. P. Nestler derives the model-equations from the Mindlin and Reissner hypotheses. Then, necessary optimality conditions for the optimal control problem are given. Numerical solutions are obtained by FEM, numerical examples are presented.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2010, 30, 2; 253-267
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Structure of Optimal Control in Optimal Shaping of the Steel Arch
    Autorzy:
    Mikulski, Leszek
    Jasińska, Dorota
    Dąbrowska, Olga
    Powiązania:
    https://bibliotekanauki.pl/articles/27314818.pdf
    Data publikacji:
    2022
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    shape optimization
    optimal control
    steel arch
    shaping the cross-section
    optymalizacja kształtu
    optymalna kontrola
    łuk stalowy
    kształtowanie przekroju
    Opis:
    The paper presents the problem of optimal shaping of the H-bar cross-section of a steel arch that ensures minimal mass. Nineteen combinations of nine basic load states are considered simultaneously in the problem formulation. The optimal shaping task is formulated as a control theory problem within the formal structure of the maximum Pontriagin’s principle. Since the ranges of constraint activity defining the control structure are a priori unknown and must be determined numerically, assuming the proper control structure plays a key role in the task solution. The main achievement of the present work is the determination of a solution of the multi-decision and multi-constraint optimization problem of the arch constituting a primary structural system of the existing building assuring the reduction of the structure mass up to 42%. In addition, the impact of the assumed state constraint value on the solution structure is examined.
    Źródło:
    Civil and Environmental Engineering Reports; 2022, 32, 3; 143--165
    2080-5187
    2450-8594
    Pojawia się w:
    Civil and Environmental Engineering Reports
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-13 z 13

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