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Achieving minimum length scale in topology optimization using nodal design variables and projection functions
Abstract
A methodology for imposing a minimum length scale on structural members in discretized topology optimization problems is described. Nodal variables are implemented as the design variables and are projected onto element space to determine the element volume fractions that traditionally define topology. The projection is made via mesh independent functions that are based upon the minimum length scale. A simple linear projection scheme and a non‐linear scheme using a regularized Heaviside step function to achieve nearly 0–1 solutions are examined. The new approach is demonstrated on the minimum compliance problem and the popular SIMP method is used to penalize the stiffness of intermediate volume fraction elements. Solutions are shown to meet user‐defined length scale criterion without additional constraints, penalty functions or sensitivity filters. No instances of mesh dependence or checkerboard patterns have been observed. Copyright © 2004 John Wiley & Sons, Ltd.
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Cited by
Topology optimization approaches: A comparative review
Sigmund, O., & Maute, K. (2013) · Structural and Multidisciplinary Optimization · doi:10.1007/s00158-013-0978-6 · Cited by 2,890
Topology Optimization in Aircraft and Aerospace Structures Design
Zhu, J.-H., Zhang, W.-H., & Xia, L. (2016) · Archives of Computational Methods in Engineering · doi:10.1007/s11831-015-9151-2 · Cited by 980
A review of topology optimization for additive manufacturing: Status and challenges
ZHU, J., ZHOU, H., WANG, C., ZHOU, L., YUAN, S., & ZHANG, W. (2021) · Chinese Journal of Aeronautics · doi:10.1016/j.cja.2020.09.020 · Cited by 874
Current and future trends in topology optimization for additive manufacturing
Liu, J., Gaynor, A. T., Chen, S., Kang, Z., Suresh, K., Takezawa, A., Li, L., Kato, J., Tang, J., Wang, C. C. L., et al. (2018) · Structural and Multidisciplinary Optimization · doi:10.1007/s00158-018-1994-3 · Cited by 870
Topology optimization for nano‐photonics
Jensen, J. S., & Sigmund, O. (2011) · Laser & Photonics Reviews · doi:10.1002/lpor.201000014 · Cited by 767
Metadata
- Authors
- Guest, J. K., Prévost, J. H., & Belytschko, T.
- Venue
- International Journal for Numerical Methods in Engineering
- Publisher
- Wiley
- Published
- 2004-07-15
- Volume
- 61
- Issue
- 2
- Pages
- 238-254
- ISSN
- 0029-5981 (ISSN-L)
- 1097-0207
- OpenAlex
- W2120191698
- Cited by
- 1,300
- References
- 0
- FWCI
- 22.54
- Type
- journal article
- Language
- en
- Open access
- closed
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- Guest, J. K., Prévost, J. H., & Belytschko, T. (2004). Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International Journal for Numerical Methods in Engineering. https://doi.org/10.1002/nme.1064
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