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A Density Result in Two-Dimensional Linearized Elasticity, and Applications

Chambolle, Antonin (2003), A Density Result in Two-Dimensional Linearized Elasticity, and Applications, Archive for Rational Mechanics and Analysis, 167, 3, p. 211-233. http://dx.doi.org/10.1007/s00205-002-0240-7

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Type
Article accepté pour publication ou publié
Date
2003
Journal name
Archive for Rational Mechanics and Analysis
Volume
167
Number
3
Publisher
Springer
Pages
211-233
Publication identifier
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Author(s)
Chambolle, Antonin cc
Abstract (EN)
We show that in a two-dimensional bounded open set whose complement has a finite number of connected components, the vector fields uH 1 (Ωℝ2) are dense in the space of fields whose symmetrized gradient e(u) is in L 2 (Ωℝ4). This allows us to show the continuity of some linearized elasticity problems with respect to variations of the set, with applications to shape optimization or the study of crack evolution.
Subjects / Keywords
Optimization; Geometrical shape; Modeling; Two dimensional model