On second-order tensor representation of derivatives in shape optimization.
Philos Trans A Math Phys Eng Sci
; 382(2277): 20230300, 2024 Aug 23.
Article
en En
| MEDLINE
| ID: mdl-39005018
ABSTRACT
In this article, we study general properties of distributed shape derivatives admitting a volumetric tensor representation of order two. We obtain a general result providing a range of expressions for the shape derivative, with the distributed shape derivative at one end of the range and the standard Hadamard formula at the other end. We further apply this result to a cost functional depending on the solution of a fourth-order elliptic equation, and obtain the distributed shape derivative in the case of open sets, and the Hadamard formula for sets of class [Formula see text]. We also consider the case of polygons, for which a description of the weak singularities of the solution appearing in the neighbourhood of the vertices is required to obtain the Hadamard formula. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'.
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1
Colección:
01-internacional
Base de datos:
MEDLINE
Idioma:
En
Revista:
Philos Trans A Math Phys Eng Sci
Asunto de la revista:
BIOFISICA
/
ENGENHARIA BIOMEDICA
Año:
2024
Tipo del documento:
Article
País de afiliación:
Alemania