Isogeometric topology optimization of anisotropic metamaterials for controlling high‐frequency electromagnetic wave

Abstract

Summary This study presents a level set–based topology optimization with isogeometric analysis (IGA) for controlling high‐frequency electromagnetic wave propagation in a domain with periodic microstructures (unit cells). The high‐frequency homogenization method is applied to characterize the macroscopic high‐frequency waves in periodic heterogeneous media whose wavelength is comparative to or smaller than the representative length of a unit cell. B‐spline basis functions are employed for the IGA discretization procedure to improve the performance of electromagnetic wave analysis in a unit cell and topology optimization. Also, to keep the same order of continuity on the periodic boundaries as on other element edges in the domain, we propose the extended domain approach, while incorporating Floquet periodic boundary condition (FPBC). Two types of optimization problems are taken as examples to demonstrate the effectiveness of the proposed method in comparison with the standard finite element analysis (FEA). The optimization results provide optimized topologies of unit cells qualified as anisotropic metamaterials with hyperbolic and bidirectional dispersion properties at the macroscale.

Incorporation of gradient-enhanced microplane damage model into isogeometric analysis

“…For example, IGA is of advantage in dealing with frictional contact problems as demonstrated in Lu (2011De Lorenzis et al (2011), Temizer et al (2012; Nishi et al (2019a). Also, it is applied in other interesting areas such as damage/fracture (Verhoosel et al (2011), Borden (2012; , electromagnetics (Buffa et al, 2010), heat transfer (An et al (2018), , multiscale (Matsubara et al (2016) and structural optimization (Seo et al (2010); Dedè et al (2012); Nishi et al (2019b) problems. Nonetheless, IGA has never joined hands with the microplane damage model to the best of our knowledge.…”

A Comprehensive Review of Isogeometric Topology Optimization: Methods, Applications and Prospects

“…In Ref. [94], a level set-based ITO method was proposed for topology optimization to control the high-frequency electromagnetic wave propagation in a domain with periodic microstructures, where the high-frequency homogenization method is used to characterize the macroscopic highfrequency waves in periodic heterogeneous media. The corresponding numerical results are also given in Figure 7(c).…”

“…Xu et al [79] also utilized the density-based ITO method to discuss the rational design of ultra-lightweight architected materials with the extreme bulk modulus and extreme shear modulus, and a series of novel 3D ultra-lightweight architected material microstructures can be found. Nishi et al [94] utilized the LSM-based ITO method to discuss the design of periodic microstructures in anisotropic metamaterials to control high-frequency electromagnetic wave, in which anisotropic metamaterials with the hyperbolic and bidirectional dispersion properties at the macroscale can be obtained.…”

IgaTop: an implementation of topology optimization for structures using IGA in MATLAB

“…The T-splines-based ITO method was developed in (Zhao et al 2020a) to discuss the optimization of arbitrarily shaped design domains. The ITO for anisotropic metamaterials to control high-frequency electromagnetic wave was addressed in (Nishi et al 2020).…”