An efficient multiscale optimization method for conformal lattice materials
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RESEARCH PAPER
An efficient multiscale optimization method for conformal lattice materials Tongyu Wu1 · Shu Li1 Received: 27 May 2020 / Revised: 3 September 2020 / Accepted: 8 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This article presents a multiscale optimization method to solve size distribution problem of conformal lattice materials (CLMs). Full-scale analyses are not needed during optimization process, so this method is much more efficient compared with other optimization methods for CLMs, especially when the number of microbars is considerably large. On microscope, inherent heterogeneity of CLM makes it hard to introduce homogenization method to scale down the problem. For substitute, a new method derived from extended multiscale finite element method (EMsFEM) is used to calculate the effective stiffness of the microlattice structures, and two improvements are given to increase the accuracy and extend its application to CLM. On macroscope, based on gradient-based topology optimization method, a multiscale optimization algorithm is raised for a minimum compliance design under volume constraint. The diameters of microbars are set to be design variables. Sensitive analyses based on EMsFEM are carried out, so the effective calculating process can be seamlessly integrated in the optimization algorithm. Furthermore, considering the discontinuity of bars laid on elements’ edges, a post-processing method is proposed to determine the diameters of these bars. This optimization method is validated by two mechanical experiments on specimens fabricated by 3D printing, and its efficiency is tested by comparing with the optimization method with full-scale FE analyses. The results of both mechanical experiments and finite element simulations show that the optimized structures do have better mechanical properties, exposing the material redistribution tendency during optimizing process. Keywords Conformal lattice material · Extended multiscale finite element method · Multiscale analysis · Topology optimization
1 Introduction Lattice materials, also known as prismatic materials or truss materials, are lightweight materials with excellent mechanical properties and designability. Like other cellular materials, such as mental foams and honeycombs, lattice materials have high specific stiffness (Wallach and Gibson 2001) and the ability of absorbing energy, so they are widely used in aerospace and civil engineering, as Responsible Editor: Xu Guo Shu Li
[email protected] Tongyu Wu tony [email protected] 1
School of Aeronautic Science and Engineering, Beihang University, Beijing, China
efficient bearing structures or bumpers. In some cases, lattice materials perform better than mental foams and honeycombs. Lattice materials outperform foams, whose cells are arranged stochastically, with higher strength, because the deformation of lattice is governed by stretch and compress, whereas foams’ major deformation mode is cell wall bending (Rosen 2007). Besides, lattice structures can be designed
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