@inproceedings{196bbf98ee6c48078fbd6652a472feb2,
title = "Topology optimization using wachspress-type interpolation with hexagonal elements",
abstract = "Traditionally, standard Lagrangian-type finite elements, such as quads and triangles, have been the elements of choice in the field of topology optimization. However, finite element meshes with these elements exhibit the well-known {"}checkerboard{"} pathology in the solution of topology optimization problems. A feasible alternative to eliminate this long-standing problem consists of using hexagonal elements with Wachspress-type shape functions. The features of the hexagonal mesh include 2-node connections (i.e. 2 elements are either not connected or connected by 2 nodes), and 3 edge-based symmetry lines per element. In contrast, quads can display 1-node connection, which can lead to checkerboard; and only have 2 edge-based symmetry lines. We explore the Wachspress-type hexagonal elements and show their advantages in solving topology optimization problems. We also discuss extensions of the work to account for material gradient effects.",
keywords = "Checkerboard, Topology optimization, Wachspress interpolation functions",
author = "Cameron Talischi and Paulino, {Glaucio H.} and Le, {Chau H.}",
year = "2008",
doi = "10.1063/1.2896796",
language = "English (US)",
isbn = "9780735404922",
series = "AIP Conference Proceedings",
pages = "309--314",
booktitle = "Multiscale and Functionally Graded Materials - Proceedings of the International Conference, FGM IX",
note = "9th International Conference on Multiscale and Functionally Graded Materials, FGM IX ; Conference date: 15-10-2006 Through 18-10-2006",
}