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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Shape optimization for dynamic contact problems

100%
Myśliński A.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2000
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tom 20
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nr 1
79-91
EN
The paper deals with shape optimization of dynamic contact problem with Coulomb friction for viscoelastic bodies. The mass nonpenetrability condition is formulated in velocities. The friction coefficient is assumed to be bounded. Using material derivative method as well as the results concerning the regularity of solution to dynamic variational inequality the directional derivative of the cost functional is calculated and the necessary optimality condition is formulated.
2
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Topological derivatives for semilinear elliptic equations

88%
Iguernane M., Nazarov S., Roche J.-R., Sokolowski J., Szulc K.
International Journal of Applied Mathematics and Computer Science
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2009
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tom 19
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nr 2
191-205
EN
The form of topological derivatives for an integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological derivatives is shown and the error estimates in the L∞ norm are obtained. The results of numerical experiments which confirm the theoretical convergence rate are presented.
3
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Optimal design of cylindrical shells

88%
Nestler P., Schmidt W.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2010
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tom 30
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nr 2
253-267
EN
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.
4
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A level set method in shape and topology optimization for variational inequalities

88%
Fulmański P., Laurain A., Scheid J.-F., Sokołowski J.
International Journal of Applied Mathematics and Computer Science
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2007
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tom 17
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nr 3
413-430
EN
The level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology variations in the form of small holes. The derivation of topological derivatives is performed within the framework proposed in (Sokołowski and Żochowski, 2003). Numerical results confirm that the method is efficient and gives better results compared with the classical shape optimization techniques.
5
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Approximation of a solidification problem

88%
Aboulaïch R., Haggouch I., Souissi A.
International Journal of Applied Mathematics and Computer Science
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2001
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tom 11
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nr 4
921-955
EN
A two-dimensional Stefan problem is usually introduced as a model of solidification, melting or sublimation phenomena. The two-phase Stefan problem has been studied as a direct problem, where the free boundary separating the two regions is eliminated using a variational inequality (Baiocchi, 1977; Baiocchi et al., 1973; Rodrigues, 1980; Saguez, 1980; Srunk and Friedman, 1994), the enthalpy function (Ciavaldini, 1972; Lions, 1969; Nochetto et al., 1991; Saguez, 1980), or a control problem (El Bagdouri, 1987; Peneau, 1995; Saguez, 1980). In the present work, we provide a new formulation leading to a shape optimization problem. For a semidiscretization in time, we consider an Euler scheme. Under some restrictions related to stability conditions, we prove an L^2 -rate of convergence of order 1 for the temperature. In the last part, we study the existence of an optimal shape, compute the shape gradient, and suggest a numerical algorithm to approximate the free boundary. The numerical results obtained show that this method is more efficient compared with the others.
6
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An existence result for an interior electromagnetic casting problem

75%
Barkatou M., Seck D., Ly I.
Open Mathematics
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2006
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tom 4
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nr 4
573-584
EN
This paper deals with an interior electromagnetic casting (free boundary) problem. We begin by showing that the associated shape optimization problem has a solution which is of class C 2. Then, using the shape derivative and the maximum principle, we give a sufficient condition that the minimum obtained solves our problem.
7
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An existence result for a quadrature surface free boundary problem

63%
Barkatou M., Seck D., Ly I.
Open Mathematics
|
2005
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tom 3
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nr 1
39-57
EN
The aim of this paper is to present two different approachs in order to obtain an existence result to the so-called quadrature surface free boundary problem. The first one requires the shape derivative calculus while the second one depends strongly on the compatibility condition of the Neumann problem. A necessary and sufficient condition of existences is given in the radial case.
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