A connection between topological ligaments in shape optimization and thin tubular inhomogeneities
Optimization and Control
2019-12-30 v1 Numerical Analysis
Numerical Analysis
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.
Cite
@article{arxiv.1912.11810,
title = {A connection between topological ligaments in shape optimization and thin tubular inhomogeneities},
author = {Charles Dapogny},
journal= {arXiv preprint arXiv:1912.11810},
year = {2019}
}