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Foundations of Civil and Environmental Engineering
2006 No. 7 229-259
EN The concept of topologicai derivative is introduced and applied to optimal design of structural elements and to study the material microstructure evolution. For structural design the objective function and constraints provide the optimal design, for material microstructure the free energy and dissip[...]
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Control and Cybernetics
EN In the present paper, a new approach for structural topology optimization based on dynamic implicit surface function (DISF) is proposed. DISF is used to describe the shape/topology of a structure, which is approximated in terms of the nodal values. Then, a relationship is established between the ele[...]
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Control and Cybernetics
EN We consider some singular perturbations of the boundary of a smooth domain. Such domain variations are not differentiable within the classical theory of shape calculus. We mimic the topological asymptotic and we derive an asymptotic expansion of the shape function in terms of a size parameter. The t[...]
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Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska
2015 nr 1 7--13
PL W pracy przedstawiono matematyczne aspekty dotyczące pochodnej topologicznej oraz jej zastosowań w różnych dziedzinach nauki, takich jak optymalizacja kształtu czy problemy odwrotne. W pierwszej części podano nieformalna˛ definicje˛ pochodnej topologicznej oraz sformułowano problem optymalizacji ksz[...]
EN The paper is devoted to present some mathematical aspects of the topological derivative and its applications in different fields of sciences such as shape optimization and inverse problems. First the definition of the topological derivative is given and the shape optimization problem is formulated. [...]
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Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska
2016 nr 2 4--8
PL W dziedzinie optymalizacji kształtu i topologii zaproponowano nową koncepcję pochodnej topologicznej danego funkcjonału kształtu. Zastosowano asymptotyczną analizę w celu określenia pochodnej topologicznej funkcjonału kształtu dla zagadnień eliptycznych. Pochodna Topologiczna – PT (ang. the topologi[...]
EN In the field of shape and topology optimization the new concept is the topological derivative of a given shape functional. The asymptotic analysis is applied in order to determine the topological derivative of shape functionals for elliptic problems. The topological derivative (TD) is a tool to meas[...]
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Przegląd Elektrotechniczny
2019 R. 95, nr 6 137--140
PL W artykule przedstawiono rekonstrukcję badanych obiektów 2D z wykorzystaniem pochodnej topologicznej i funkcji zbiorów poziomicowych w elektrycznej tomografii impedancyjnej, która jest nieinwazyjną metodą obrazowania, w której nieznany obiekt fizyczny jest badany za pomocą pomiarów na jego krawędzi.[...]
EN The article presents the reconstruction of 2D objects studied using the topological derivative and level set function in electrical impedance tomography, which is a non-invasive imaging method in which an unknown physical object is examined using measurements on its edge. The internal distribution o[...]
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International Journal of Applied Mathematics and Computer Science
EN We consider a linear damped wave equation defined on a two-dimensional domain [...], with a dissipative term localized in a subset [...]. We address the shape design problem which consists in optimizing the shape of [...] in order to minimize the energy of the system at a given time T. By introducin[...]
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International Journal of Applied Mathematics and Computer Science
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 exp[...]
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International Journal of Applied Mathematics and Computer Science
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 ex[...]
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Control and Cybernetics
EN This study concerns the application of the Topological-Shape Sensitivity Method as a systematic procedure to determine the Topological Derivative for linear elastic plate bending problems within the framework of Kirchhoff's kinematic approach. This method, based on classical Shape Sensitivity Analys[...]
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Journal of Applied Mathematics and Computational Mechanics
EN The aim of this paper is to create an optimal shape of the 2D domain that is described by the Non-Uniform Rational B-Splines (NURBS) curves. This work presents a method based on the topological derivative for the Laplace equation that determines the sensitivity of a given cost function to the change[...]
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Journal of Applied Mathematics and Computational Mechanics
EN In the paper, the topological derivative for the Laplace equation is taken into account. The governing equation is solved by means of the Boundary Element Method. The topological-shape sensitivity method is used to determine the points showing the lowest sensitivities. On the selected points, materi[...]
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