Topological Derivative for Nucleation of Non-Circular Voids

Tomasz Lewinski , Jan Sokolowski (1)

1 NUMATH - Mathematical Analysis and Numerical Simulation of Non-Linear Models

The hitherto existing literature concerning the topological derivative of shape functionals concerned perturbations of domains caused by introduction of circular or ball openings. In the present study the notion of the topologic- al derivative is generalized to the case of openings of arbitrary shape. The report is concerned with energy functionals related to the Neumann problem and the 2D elasticity system.

Mots clés: shape optimization; shape derivative; topological derivative; compound asymptotics; polya-szego mass matrix; Neumann problem

Domaines: Autre [cs.OH]

Tomasz Lewinski, Jan Sokolowski. Topological Derivative for Nucleation of Non-Circular Voids. [Research Report] RR-3798, INRIA. 1999, pp.37. ⟨inria-00072861⟩