Determination of an optimal shape of domain using the topological derivative and the Boundary Element Method

• Autorzy: Freus K. , Freus S.
• Języki publikacji: EN

Abstrakty

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, material is eliminated by opening a hole, using the appropriate iterative process. This one is halted when a given amount of material is removed. The objective of this work is to obtain an optimal topology of the domain considered. In the final part of the paper, the example of computations is shown.

Słowa kluczowe

EN

topological derivative; topological sensitivity; topology optimization; heat transfer; Laplace equation; boundary element method

PL

pochodna topologiczna; wrażliwość topologiczna; optymalizacja topologiczna; wymiana ciepła; równanie Laplace'a; metoda elementów brzegowych

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2014
• Tom: Vol. 13, nr 4
• Strony: 41--48
• Opis fizyczny: Bibliogr. 5 poz., rys., tab.

Twórcy

autor

Freus K.

• Institute of Mathematics, Czestochowa University of Technology

autor

Freus S.

• Institute of Computer and Information Science, Czestochowa University of Technology Częstochowa, Poland

Bibliografia

• [1] Navotny A.A., Feijoo R.A., Taroco E., Padra C., Topological-shape sensitivity analysis, Comput. Methods Appl. Mech. Eng. 2003, 192, 803-829.
• [2] Marczak R.J., Topology optimization and boundary elements - a preliminary implementation for linear heat transfer, Engineering Analysis with Boundary Elements 2007, 31, 793-802.
• [3] Anflor C.T.M., Marczak R.J., Topological sensitivity analysis for two-dimensional heat transfer problems using the boundary element method, Optimization of Structures and Components Advanced Structured Materials 2013, 43, 11-33.
• [4] Brebbia C.A., Dominguez J., Boundary Elements - an Introductory Course, CMP, McGraw-Hill Book Company, London 1992.
• [5] Majchrzak E., Boundary Element Method in Heat Transfer, Publ. of the Techn. Univ. of Czest., Czestochowa 2001 (in Polish).