Layout optimization of continuum structures embedded with movable components and holes simultaneously
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RESEARCH PAPER
Layout optimization of continuum structures embedded with movable components and holes simultaneously Xuan Wang1,2
· Ping Hu3 · Zhan Kang3
Received: 24 March 2019 / Revised: 29 July 2019 / Accepted: 30 July 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract In this paper, the layout optimization problem of continuum structures embedded with movable components and holes simultaneously is solved for the first time. We propose a new methodology for the embedding problem under SIMP-based computational framework, where the positions and orientations of embedded components and holes and the topology of connecting structure are optimized concurrently to maximize the overall stiffness. To this end, the parameterized topology description function, combining the Kreisselmeier-Steinhauser (KS) function, is used to construct the geometric shapes of embedded components and holes. The material density defining the topology of connecting structure and the geometric parameters used to describe the location and orientation of embedded components and holes are considered as design variables of the optimization problem. To unite these two seemingly different representations into a single computational framework, we first project the embedded components and holes into two density fields on a fixed grid using a smoothed Heaviside function, then introduce a new SIMP-motivated material interpolation scheme invoked at the finite element level for material parameterization. The material parameterization scheme supports full analytical sensitivities, which can greatly improve the accuracy and efficiency of sensitivity analysis, and make it suitable for use with efficient gradient-based algorithms. Finally, the effectiveness of the proposed method is illustrated by several numerical examples. Keywords Layout optimization · Embedded components · Embedded holes · SIMP
1 Introduction Structural engineering design problems typically require the prior embedding of one or more fixed-shaped objects Responsible Editor: Juli´an Andr´es Norato Ping Hu
[email protected] Xuan Wang [email protected] Zhan Kang [email protected] 1
School of Civil Engineering, Hefei University of Technology, Hefei 230009, China
2
Anhui Key Laboratory of Civil Engineering Structures and Materials, Hefei University of Technology, Hefei 230009, China
3
State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, China
(components or holes) to meet certain functional or manufacturing design requirements (Zhang et al. 2011; Zhu et al. 2016). For example, in aerospace engineering, some functional equipments, which often also serves as a load-bearing structure, need to be embedded into the main structure to make full use of the available space. Other typical examples include the design problem of compliant smart structures with embedded movable PZT (lead zirconate titanate) actuators (Wang et al. 2014), and layout optimization of heat-transfer systems consistin
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