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This paper is devoted to the minimization of the thickness of an elastic structure under competitive loadings. We propose to determine an equilibrium thickness using game theory. We consider two loads exercised separately on two parts of the plate and we aim to optimize both compliances so we deal with a multiloading optimization problem. Firstly,...
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Context 1
... boundary of Ω is made of three disjoint parts ∂Ω = Γ D ∪ Γ N ∪ Γ, with Dirichlet boundary conditions on Γ D , and Neumann boundary conditions on Γ N ∪Γ. The boundary part Γ D is supposed to be fixed , while Γ N is submitted to a g surface load and Γ is free of any load(see figure 2). Boundary conditions for an elastic plate: single load ...
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The aim of this study is to compare two available numerical tools for solving of partial differential equations for the optimal design of structures. In the past years numerous methods were developed for topology optimization, from these we have adopted the optimality criteria (OC) approach. The main idea is that we state the optimal conditions, th...
Citations
... We propose here to solve the problem (PI) by using an original method based on a Nash game theory approach which has been frequently used in shape optimization. For instance, in [3], the authors have determined an equilibrium thickness of an elastic structure under competitive loadings. In [17], J. A. Désidéri applied Nash game method to aero-structural aircraft wing shape optimization, while in [24] a multidisciplinary optimization problem has been formulated by the Nash game framework where the players are the heat equation and the thermoelasticity system. ...
... In addition, we have reconstructed the missing component of the normal stress on c , that is, [σ (u)n] n for problem (3) and [σ (u)n] τ for problem (4) using both strategies. We obtain a very good results when comparing with the exact solution (see Fig. 3). ...
We consider the Cauchy-Stokes problem. We use a new method based on Nash game theory to recover the missing velocity and normal stress on some inaccessible part of the boundary. This method is used with two different approaches. The first one is compared to a control type one. The numerical study attests that both approaches give accurate results. We compare these results with those of the energy-like minimization method.
