A connection between topological ligaments in shape optimization and thin tubular inhomogeneities

Charles Dapogny

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arXiv · 1912.11810

A connection between topological ligaments in shape optimization and thin tubular inhomogeneities

Charles Dapogny

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Abstract

In this note, we propose a formal framework accounting for the sensitivity of a function of the domain with respect to the addition of a thin ligament. To set ideas, we consider the model setting of elastic structures, and we approximate this question by a thin tubular inhomogeneity problem: we look for the sensitivity of the solution to a partial differential equation posed inside a background medium, and that of a related quantity of interest, with respect to the inclusion of a thin tube filled with a different material. A practical formula for this sensitivity is derived, which lends itself to numerical implementation. Two applications of this idea in structural optimization are presented.

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Charles Dapogny. 2019-12-26. A connection between topological ligaments in shape optimization and thin tubular inhomogeneities. https://arxiv.org/abs/1912.11810

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