This article is cited in 33 papers

The topological derivative of the Dirichlet integral under formation of a thin ligament

S. A. Nazarov^a, J. Sokolowski<sup>b

a</sup> Institute of Problems of Mechanical Engineering, Russian Academy of Sciences
^b Université Henri Poincaré — Nancy I

Abstract: We construct and justify the asymptotic expansion of a solution and the corresponding energy functional of the mixed boundary-value problem for the Poisson equation in a domain with a ligament, i.e., thin curvilinear strip connecting two small parts of the boundary outside the domain. Asymptotic analysis is required in the theory of shape optimization; therefore, in contrast to other publications, we use no simplifying assumptions of the flattening of the boundary near the junction zones.

Keywords: asymptotic expansion, thin ligament, energy functional, shape optimization.

UDC: 517.946

Received: 21.01.2003

 English version: Siberian Mathematical Journal, 2004, 45:2, 341–355

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