On topology optimization with elliptical masks and honeycomb tessellation with explicit length scale constraints
- PDF / 4,177,141 Bytes
- 25 Pages / 595.276 x 790.866 pts Page_size
- 28 Downloads / 166 Views
RESEARCH PAPER
On topology optimization with elliptical masks and honeycomb tessellation with explicit length scale constraints Nikhil Singh 1 & Prabhat Kumar 2 & Anupam Saxena 1 Received: 20 August 2019 / Revised: 3 February 2020 / Accepted: 13 February 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Topology optimization using gradient search with negative and positive elliptical masks and honeycomb tessellation is presented. Through a novel skeletonization algorithm for topologies defined using filled and void hexagonal cells/elements, explicit minimum and maximum length scales are imposed on solid states in the solutions. An analytical example is presented suggesting that for a skeletonized topology, optimal solutions may not always exist for any specified volume fraction, minimum and maximum length scales, and that there may exist implicit interdependence between them. A sequence for length scale (SLS) methodology is proposed wherein solutions are sought by specifying only the minimum and maximum length scales with volume fraction getting determined within a specified range systematically. Through four benchmark problems in small deformation topology optimization, it is demonstrated that solutions by-and-large satisfy the length scale constraints though the latter may get violated at certain local sites. The proposed approach seems promising, noting especially that solutions, if rendered perfectly black and white with minimum length scale explicitly imposed and boundaries smoothened, are quite close in performance compared with the parent topologies. Attaining volume-distributed topologies, wherein members are more or less of the same thickness, may also be possible with the proposed approach. Keywords Topology optimization . Honeycomb tessellation . Skeletonization . Explicit length scales . Elliptical positive and negative masks
1 Introduction and background Topology optimization formulations, which entail finding optimal continua for given sets of objectives and constraints, in 2D, are fairly well developed (Eschenauer and Olhoff 2003; Bendsoe et al. 2005; Guo and Cheng 2010; Sigmund and Maute 2013). These include density based (Bendsoe and Sigmund 2003), phase field (Wang and Zhou 2004a; Wang and Zhou 2004b), level set (Sethian and Wiegmann 2000; Wang et al. 2005; Luo et al. 2008), evolutionary (Yang et al. 1999; Huang and Xie 2010) and other approaches with rectangular, regular hexagonal (Saxena and Saxena 2003; Saxena and Saxena 2007; Langelaar 2007; Talischi et al. 2009; Responsible Editor: Hyunsun Alicia Kim * Anupam Saxena [email protected] 1
Indian Institute of Technology, Kanpur 208016, India
2
Technical University of Denmark, Lyngby, Denmark
Saxena 2008; Saxena 2011) and, in general, irregular hexagonal and polygonal (Talischi et al. 2012; Kumar and Saxena 2015) discretization of the design domain. Topology optimization methods are generalized to cater to a wide range of problems in mechanics, heat transfer, electrothermal, electrostatic and other fields (Bendsoe
Data Loading...
