- Title
- On topology optimization and canonical duality method
- Creator
- Gao, David
- Date
- 2018
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/165969
- Identifier
- vital:13371
- Identifier
-
https://doi.org/10.1016/j.cma.2018.06.027
- Identifier
- ISBN:0045-7825
- Abstract
- Topology optimization for general materials is correctly formulated as a bi-level knapsack problem, which is considered to be NP-hard in global optimization and computer science. By using canonical duality theory (CDT) developed by the author, the linear knapsack problem can be solved analytically to obtain global optimal solution at each design iteration. Both uniqueness, existence, and NP-hardness are discussed. The novel CDT method for general topology optimization is refined and tested by both 2-D and 3-D benchmark problems. Numerical results show that without using filter and any other artificial technique, the CDT method can produce exactly 0-1 optimal density distribution with almost no checkerboard pattern. Its performance and novelty are compared with the popular SIMP and BESO approaches. Additionally, some mathematical and conceptual mistakes in literature are explicitly addressed. A brief review on the canonical duality theory for modeling multi-scale complex systems and for solving general nonconvex/discrete problems are given in Appendix. This paper demonstrates a simple truth: elegant designs come from correct model and theory. © 2018
- Publisher
- Elsevier B.V.
- Relation
- Computer Methods in Applied Mechanics and Engineering Vol. 341, no. (2018), p. 249-277
- Rights
- Crown Copyright © Published by Elsevier B.V. All rights reserved.
- Rights
- Open Access
- Rights
- This is an Open Access article distributed under the terms of the Creative Commons Attribution License which permits restricted use, distribution, and reproduction in any medium, provided the original work is properly credited. Commercial use is not permitted and modified material cannot be distributed.
- Rights
- http://creativecommons.org/licenses/by-nc-nd/4.0/
- Rights
- This metadata is freely available under a CCO license
- Subject
- 01 Mathematical Sciences; 09 Engineering; Bi-level knapsack problem; Canonical duality theory; CDT algorithm; NP-hardness; Topology optimization
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