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Title: Topology Optimization of Conformal Structures Using Extended Level Set Methods and Conformal Geometry Theory
In this paper, we propose a new method to approach the problem of structural shape and topology optimization on manifold (or free-form surfaces). A manifold is conformally mapped onto a 2D rectangle domain, where the level set functions are defined. With conformal mapping, the corresponding covariant derivatives on a manifold can be represented by the Euclidean differential operators multiplied by a scalar. Therefore, the topology optimization problem on a free-form surface can be formulated as a 2D problem in the Euclidean space. To evolve the boundaries on a free-form surface, we propose a modified Hamilton-Jacobi equation and solve it on a 2D plane following the conformal geometry theory. In this way, we can fully utilize the conventional level-set-based computational framework. Compared with other established approaches which need to project the Euclidean differential operators to the manifold, the computational difficulty of our method is highly reduced while all the advantages of conventional level set methods are well preserved. We hope the proposed computational framework can provide a timely solution to increasing applications involving innovative structural designs on free-form surfaces in different engineering fields.  more » « less
Award ID(s):
1762287
NSF-PAR ID:
10109644
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
Proceedings of Proceedings of the International Design Engineering Technical Conferences & Computers & Information in Engineering Conference
Volume:
2B: 44th Design Automation Conference
Page Range / eLocation ID:
V02BT03A038
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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