Finite periodic topology optimization with oriented unit-cells

doi:10.1007/s00158-021-03045-4

2021-08-19

PRE

Simon Thomas *

李晴 (Qing Li)

Grant P. Steven

DOI：10.1007/s00158-021-03045-4

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摘要

En 中文

Periodic topology optimization has been suggested as an effective means to design efficient structures which address a range of practical constraints, such as manufacturability, transportability, replaceability and ease of assembly. This study proposes a new approach for design of finite periodic structures by allowing variable orientation states of individual unit-cells. In some design instances of periodic structures, the unit-cell may exhibit certain geometric features allowing multiple possible assembly orientations (e.g. facing up or down). For the first time, this work incorporates such assembly flexibility within the periodic topology optimization, which enables to greatly expand the conventional periodic design space and take more advantage of structural periodicity. Given its broad applications, a methodology for the design of more efficient periodic structures while maintaining the same degree of periodic constraint may be of significant benefit to engineering practice. In this study, several numerical examples are presented to demonstrate the effectiveness of this new approach for both static and vibratory criteria. Brute force analysis is also utilized to compare all possible assembly configurations for several periodic structures with a small number of unit-cells. A heuristic approach is suggested for selecting more beneficially oriented configurations in periodic structures with a large number of unit-cells for which an exhaustive search may be computationally infeasible. It is found that in all the presented cases, the oriented periodic structures outperform the conventional non-oriented (or namely translational) periodic counterparts. Finally, an educational MATLAB code is provided for replication of the design results in this paper.

Keyword:

Oriented periodicity

Periodic optimization

Topology optimization

Bi-directional evolutionary structural optimization (BESO)

Solid isotropic material with penalization (SIMP)

Level set method