A level set method in shape and topology optimization for variational inequalities

• Autorzy: Piotr Fulmański , Antoine Laurain , Jean-Francois Scheid , Jan Sokołowski
• Języki publikacji: EN

Abstrakty

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 exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology variations in the form of small holes. The derivation of topological derivatives is performed within the framework proposed in (Sokołowski and Żochowski, 2003). Numerical results confirm that the method is efficient and gives better results compared with the classical shape optimization techniques.

Słowa kluczowe

EN

shape optimization; level set method; asymptotic analysis; variational inequality; topological derivative

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2007
• Tom: 17
• Numer: 3
• Strony: 413-430

Daty

wydano

2007

poprawiono

2006-05-10

(nieznana)

2006-12-15

Twórcy

autor

Piotr Fulmański

• Faculty of Mathematics, University of Łódź, ul. Banacha 22, 90-232 Łódź, Poland

autor

Antoine Laurain

• Institut Elie Cartan, Laboratoire de Mathématiques, Université Henri Poincaré Nancy I, B.P. 239, 54506 Vandoeuvre-les-Nancy Cedex, France

autor

Jean-Francois Scheid

• Institut Elie Cartan, Laboratoire de Mathématiques, Université Henri Poincaré Nancy I, B.P. 239, 54506 Vandoeuvre-les-Nancy Cedex, France

autor

Jan Sokołowski

• Institut Elie Cartan, Laboratoire de Mathématiques, Université Henri Poincaré Nancy I, B.P. 239, 54506 Vandoeuvre-les-Nancy Cedex, France

Bibliografia

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