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A Riemannian View on Shape Optimization [PDF]
Foundations of Computational Mathematics, 2014 Shape optimization based on the shape calculus is numerically mostly performed by means of steepest descent methods. This paper provides a novel framework to analyze shape-Newton optimization methods by exploiting a Riemannian perspective.
Schulz, Volker
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On the Topological Derivative in Shape Optimization [PDF]
SIAM Journal on Control and Optimization, 1999 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jan Sokołowski, Antoni Źochowski
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Aerodynamic Shape Optimization with Grassmannian Shape Parameterization Method
Energies, 2022 The conventional method of optimizing the aerodynamic performance of an airfoil heavily depends on the confines of the design space. The design variables create a non-normalized space that is fragmented into several different clusters of airfoils.
Yang Zhang +3 more
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Shape optimum design of porous structure for minimizing maximum thermal stress
Nihon Kikai Gakkai ronbunshu, 2023 In this study, we propose a solution to a shape optimization problem for the strength design of porous structures under thermal loading. The homogenization method is used to bridge the macrostructure and the porous microstructures, in which the elastic ...
Mihiro TORISAKI, Masatoshi SHIMODA
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Optimum space frames with rectangular plans
Magazine of Civil Engineering, 2023 In this article, the object of research is spatial framed systems, one of the most commonly used types of spatial structures. The main feature of the research is the expansion of proven design solutions to the area of large-span frames with rectangular ...
Mushchanov Vladimir +3 more
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Fluids, 2023 This paper investigates the adequacy of radial basis function (RBF)-based models as surrogates in uncertainty quantification (UQ) and CFD shape optimization; for the latter, problems with and without uncertainties are considered. In UQ, these are used to
Varvara Asouti +2 more
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Effect of Dynamic Loading Conditions on Maximizing Energy Dissipation of Metallic Dampers
Applied Sciences, 2022 Diversification of the optimum designs is practical for metallic dampers due to their advantages of low cost, stability, and ease of fabrication. Therefore, this paper presents a novel approach—dynamic optimization—to derive various optimum shapes of ...
Ji Woon Park +3 more
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Journal of Mathematical Physics, 2007 This paper presents the solution to the following optimization problem: What is the shape of the two-dimensional region that minimizes the average Lp distance between all pairs of points if the area of this region is held fixed? Variational techniques are used to show that the boundary curve of the optimal region satisfies a nonlinear integral equation.
Bender, Carl M., Bender, Michael A.
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Shape Optimum Design by Basis Vector Method Considering Partial Shape Dependence
Applied Sciences, 2020 Regarding the case of complicated structural shape optimization, there are cases where there are partial shapes such as holes and irregularities inside the structure.
Qiong Wu +3 more
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Multiphase Shape Optimization Problems [PDF]
SIAM Journal on Control and Optimization, 2014 This paper is devoted to the analysis of multiphase shape optimization problems, which can formally be written as $\min\Big\{{g}(F_1(Ω_1),\dots,F_h(Ω_h))+ m\vert\,\bigcup_{i=1}^hΩ_i\vert :\ Ω_i\subset D,\ Ω_i\cap Ω_j =\emptyset\Big\},$ where $D\subset\mathcal{R}^d$ is a given bounded open set, $\vertΩ_i\vert$ is the Lebesgue measure of $Ω_i$ and $m$ is
Bucur D., Velichkov B.
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