A design of an optimal shape of domain described by NURBS curves using the topological derivative and boundary element method

• Autorzy: Freus K. , Freus S.

Identyfikatory

DOI

10.17512/jamcm.2017.2.06

• Języki publikacji: EN

Abstrakty

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 of its topology. As a numerical approach, the boundary element method is considered. To check the effectiveness of the proposed approach, the example of computations was carried out.

Słowa kluczowe

EN

Laplace equation; boundary element method; topological derivative; NURBS curves

PL

równanie Laplace'a; metoda elementów brzegowych; pochodna topologiczna; krzywa NURBS

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2017
• Tom: Vol. 16, nr 2
• Strony: 67--76
• Opis fizyczny: Bibliogr. 7 poz., rys.

Twórcy

autor

Freus K.

• Institute of Mathematics, Czestochowa University of Technology, Poland

autor

Freus S.

• Institute of Computer and Information Science, Czestochowa University of Technology Czestochowa, 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] Anflor C., Marczak R.J., A boundary element approach for shape and topology design in orthotropic heat transfer problems, Mecanica Computacional vol. XXVII, 2473-2486, San Luis, Argentina, 10-13 Noviembre 2008.
• [5] Brebbia C.A., Dominguez J., Boundary Elements, An Introductory Course, CMP, McGraw-Hill Book Company, London 1992.
• [6] Majchrzak E., Boundary Element Method in Heat Transfer, Publ. of the Techn. Univ. of Czest., Czestochowa 2001 (in Polish).
• [7] Piegl L., Tiller W., The NURBS Book, Springer, 1995.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).