Parameterized level set method for structural topology optimization based on the Cosserat elasticity

Chen, Lianxiong; Wan, Ji; Chu, Xihua; Liu, Hui

doi:10.1007/s10409-020-01045-z

Cited by 9 publications

(4 citation statements)

References 33 publications

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“…Only a few non-classical continuum models have been investigated within the context of topology optimisation since the pioneering work reported by Rovati and Veber [33]. To date, the reported works deal with Cosserat (micropolar) medium [34–37], classical couple stress [38], and strain gradient [39] elasticity models. Recent contributions include Tuna and Trovalusci’s [37] extension of topology optimisation from the classical Cosserat medium to the strongly non-local Eringen [8, 40] description, Ortigosa et al’s [41] investigation of optimal design of flexoelectric energy harvesters using micromorphic continuum, and Li et al’s [39] proposed isogeometric topology optimisation based on strain gradient theory.…”

Section: Introductionmentioning

confidence: 99%

Topology optimisation for vibration bandgaps of periodic composite plates using the modified couple stress continuum

Cong,

Xia,

et al. 2024

Mathematics and Mechanics of Solids

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We propose a topology optimisation approach that can effectively account for the size effect of periodic composite plates to determine the optimal material distribution for achieving the largest bandgap width. The approach is based on the modified couple stress continuum and uses the relative bandgap width as the objective function, with volume constraints defined as the constraint function. The material properties are represented by the solid isotropic material with penalisation (SIMP) interpolation model, and the optimality criteria (OC) algorithm is employed to update the design variables. To address the significant size effect of the microplate structure, we use the modified couple stress continuum to model the dynamic behaviour of the unit cell. The Melosh–Zienkiewicz–Cheung (MZC) finite element is employed to ensure nodal [Formula: see text] continuity and achieve high-order elasticity with respect to inter-element continuity. Our results demonstrate that the proposed topology optimisation methodology is capable of effectively designing optimal unit cell configurations that account for size effect and significantly improve the bandgap width. We also investigate the impact of thickness and volume limitations on the optimised unit cell configuration. The obtained results suggest that the proposed topology optimisation framework is a promising approach for designing unit cell geometries with the account for size effect.

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Section: Introductionmentioning

confidence: 99%

Topology optimisation for vibration bandgaps of periodic composite plates using the modified couple stress continuum

Cong,

Xia,

et al. 2024

Mathematics and Mechanics of Solids

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“…Parameter studies have been conducted to investigate the effect of the intrinsic length [27,52,41,5,38], the fundamental eigenfrequencies [13,60,61], the Cosserat shear modulus [17], and even 3D non-centrosymmetricity [64]. A majority of the investigations were based on the use of the SIMP and the level set methods to obtain the results.…”

Section: Introductionmentioning

confidence: 99%

Topology optimization of periodic beam lattices using Cosserat elasticity

Molnár

Blal

2023

Computers & Structures

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“…In the available literature, only a few work addresses the topology optimization problem of structures modelled by non-classical continuum theories; such as micropolar, couple stress, and strain gradient elasticity (Rovati and Veber 2007;Liu and Su 2009;Arimitsu et al 2011;Veber and Taliercio 2012;Bruggi and Taliercio 2012;Li and Khandelwal 2015;Li et al 2017;Da et al 2018;Su and Liu 2020;Chen et al 2021), while even less deals with optimal design of systems that are related to other interesting fields of applied mathematics (e.g. conduction, diffusion) governed by non-local type equations Muñoz 2015, 2017;Bellido 2019b, 2020).…”

Section: Introductionmentioning

confidence: 99%

Topology optimization of scale-dependent non-local plates

Tuna

Trovalusci

2022

Struct Multidisc Optim

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The main objective of this work is to extend finite element-based topology optimization problem to the two-dimensional, size-dependent structures described using weakly non-local Cosserat (micropolar) and strongly non-local Eringen’s theories, the latter of which finds an application for the first time, to the best of Authors’ knowledge. The optimum material layouts that minimize the structural compliance are attained by means of Solid Isotropic Material with Penalization approach, while the desired smooth, mesh-independent, binary solutions are obtained using density filter accompanied by volume preserving Heaviside projection method. The algorithms are enhanced by including an element removal and reintroduction strategy to reduce the computational cost, and to prevent spurious excessive distortion of elements with very low density. Example problems of practical importance are investigated under the assumption of linear elasticity to validate the code and to clearly demonstrate the influence of internal length scales and different non-locality mechanisms on final configurations. Obtained macro-scale optimum topologies admit the characteristics of corresponding continuum theories, and appear to be in agreement with the mechanical response governed by particle interactions in micro/nanoscale.

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Parameterized level set method for structural topology optimization based on the Cosserat elasticity

Cited by 9 publications

References 33 publications

Topology optimisation for vibration bandgaps of periodic composite plates using the modified couple stress continuum

Topology optimisation for vibration bandgaps of periodic composite plates using the modified couple stress continuum

Topology optimization of periodic beam lattices using Cosserat elasticity

Topology optimization of scale-dependent non-local plates

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