Topology optimization for structure with multi-gradient materials
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RESEARCH PAPER
Topology optimization for structure with multi-gradient materials Yihao Dong1 · Xinfu Liu1 · Tao Song1
· Shaoming He1
Received: 25 April 2020 / Revised: 7 September 2020 / Accepted: 18 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Functionally gradient materials (FGM) widely exist in biological structures, which offer indispensable support and potential protection. In this paper, we expand topology optimization for coated-base materials to multi-gradient structure. In the process of modeling the biological bones, we define three levels of density gradients: a spongy bone as the base in between, wrapped by a layer of compact bone, and multi-layers of periosteum side by side. By defining the properties and thickness of each layer, the base domain is derived by the gradient norm while a modified non-monotone filter function is imposed to separate periosteum and compact bone. Meanwhile, periosteum is separated into multi-gradient layers by Heaviside projection function in order to further mimic the skeletal of bone structure. The method of robust control, using geometric constraints, is applied to the design domain in both solid and void phases to avoid local singularity during the optimal process. Finally, the validity of the algorithm is illustrated by two benchmark problems with a variety of layer combinations. Keywords Topology optimization · Coated-base structure · Multi-gradient · Robust control
1 Introduction Topology optimization methods are gradually accepted by structural designers (Zhu et al. 2015), since it maximizes the use of materials theoretically. This method also gives designers a reasonable distribution of materials under the given boundary conditions (BCs) in the design domain to improve the structural performance (Bendsøe and Sigmund 2003). Recently, by extending density-based topology optimization known as SIMP (Solid Isotropic Material with Penalization) (Bendsøe and Sigmund 2003), topology optimization with density gradient was presented by researchers. The optimal structure with coat and base (Clausen et al. 2015) was put forward to improve the structural stiffness by plating a layer of steel as the cover of acrylonitrile butadiene styrene (ABS). Based on the filter process, Luo et al. (2019) developed the coated-base structure with gradient surface by using the projection method, which is covered Responsible Editor: Ole Sigmund Tao Song
[email protected] 1
School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081, China
by FG material with prescribed variation rule in the outermost layer. Yoon and Yi (2019) proposed a new filter for coated structure. Conversely, to optimize microscopic arrangement of the infill, Wadbro and Niu (2019) presented a multi-scalar optimal process which combines the coatedbase structure with periodic infill pattern. Wu et al. (2017) developed the porous with bone-inspired micro-structures while Groen et al. (2019) with orthotropic infill. Wang et al. (2017) developed the spatial
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