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1
Content available remote Shape sensitivity analysis of temperature distribution in heating tissue
Majchrzak E., Kałuża G.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2005
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Vol. 4, nr 1
157-164
EN
In the paper the numerical analysis of heat transfer process proceeding in domain of biological tissue is presented (2D problem). The temperature distribution results from the action of external heat source emanating the boundary heat flux. The sensitivity analysis of this process with respect to the geometrical parameters of biological tissue is considered. The explicit differentiation method basing on the material derivative approach is used. On the stage of numerical computations the boundary element method is applied. In the final part of the paper the results obtained are shown.
2
Content available remote Application of boundary element method to shape sensitivity analysis
Majchrzak E., Dziewoński M., Freus S.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2005
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Vol. 4, nr 1
137-146
EN
In the paper the boundary element method to shape sensitivity analysis is applied. The Laplace equation is analyzed and the aim of investigations is to estimate the changes of temperature in the 2D domain due to the change of local geometry of the boundary. Here the implicit differentiation method of shape sensitivity analysis is used. In the final part of the paper the example of numerical computations is shown.
3
Content available remote Topological derivative for linear elastic plate bending problems
Novotny A. A., Feijoo R. A., Padra C., Taroco E.
Control and Cybernetics
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2005
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Vol. 34, no 1
339-361
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 Analysis, leads to a constructive procedure to obtain the Topological Derivative. Utilising the well known terminology of structural optimization, we adopt, the total potential strain energy as the cost function and the equilibrium equation as the constraint. Variational formulation as well as the direct differentiation method are used to perform the shape derivative of the cost function. Finally, in order to obtain a uniform distribution of bending moments in several plate problems, the Topological Derivative was approximated, by the Finite Element Method, and used to find the best place to insert holes. A simple hard-kill like topology algorithm, which furnishes satisfactory qualitative results in agreement with those reported in the literature, is also shown.
4
Content available remote Application of shape sensitivity analysis in numerical modelling of solidification process
Majchrzak E., Jasiński M., Kałuża G.
Archiwum Odlewnictwa
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2005
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R. 5, nr 15
259--264
EN
In the paper the influence of the casting geometrical parameters on the course of solidification process is discussed. In order to solve the problem, the methods of sensitivity analysis are applied. Here the direct approach of shape sensitivity analysis is used and then the special methods of the governing equations and boundary initial conditions differentiation should be introduced. The basic problem and additional one connected with the shape sensitivity analysis are solved using the boundary element method. Th e BEM algorithm for parabolic equations is adapted to the solidification process modelling by the introduction of numerical procedure called the artificial heat source method. In the final part of the paper the results of computations are presented.
PL
W artykule analizowano wpływ parametrów geometrycznych odlewu na przebieg procesu krzepnięcia. W celu rozwiązania tak sformułowanego zadania zastosowano metodę analizy wrażliwości. Wykorzystano tzw. podejście bezpośrednie bazujące na definicji pochodnej materialnej, które polega na różniczkowaniu równań tworzących opis matematyczny procesu względem parametru kształtu. Zadanie podstawowe i dodatkowe związane z analizą wrażliwości rozwiązano stosując metodę elementów brzegowych uzupełnioną procedurą sztucznego źródła ciepła. W końcowej części artykułu przedstawiono wyniki obliczeń numerycznych.
5
Content available remote Modelling of temperature distribution in heating tissue with regard to the shape sensitivity analysis
Majchrzak E., Kałuża G.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2004
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Vol. 3, nr 1
121--126
EN
In the paper the numerical analysis of heat transfer process proceeding in domain of biological tissue is presented. In particular, the 1D problem is considered. The temperature distribution results from the action of the disk emanating the constant heat flux. The problem corresponds, among others, to chronic heating caused by implants being a heat source [1]. The sensitivity analysis of this process with respect to the thickness of biological tissue is presented. On the stage of numerical computations the boundary element method is used. In the final part of the paper the results obtained are shown.
6
Content available remote Shape sensitivity analysis in nonlinear transient heat transfer
Majchrzak E., Kałuża G.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2003
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Vol. 2, nr 1
87--92
EN
In the paper the 1D model of nonlinear transient heat transfer process is assumed. Thermophysical parameters of the material considered are strongly temperature dependent. The sensitivity analysis of this process with respect to the thickness of plate is presented. On the stage of numerical computations the finite difference method is used. In the final part of the paper the results obtained are shown.
7
Content available remote Sensitivity analysis of solidification with respect to the mould thickness
Majchrzak E., Jasiński M., Kałuża G.
Archiwum Odlewnictwa
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2003
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R. 3, nr 9
305--310
EN
In the paper the sensitivity analysis of solidification process with respect to the mould thickness is presented. On the stage of numerical computations the boundary element method is used. In the final part of the paper the results obtained are shown.
PL
W pracy przedstawiono analizę wrażliwości procesu krzepnięcia ze względu na grubość formy odlewniczej. Na etapie obliczeń wykorzystano metodę elementów brzegowych. W końcowej części artykułu pokazano wyniki obliczeń.
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