The asymptotic concentration approach combined with isogeometric analysis for topology optimization of two-dimensional linear elasticity structures

Mingtao Cui; Wang Li; Guang Li; Xiaobo Wang; Mingtao Cui; Wang Li; Guang Li; Xiaobo Wang

doi:10.3934/era.2023196

Electronic Research Archive

2023, Volume 31, Issue 7: 3848-3878. doi: 10.3934/era.2023196

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The asymptotic concentration approach combined with isogeometric analysis for topology optimization of two-dimensional linear elasticity structures

1.
Research Center for Applied Mechanics, School of Mechano-electronic Engineering, Xidian University, Xi'an 710071, China
2.
Shaanxi Key Laboratory of Space Extreme Detection, Xi'an 710071, China
3.
Department of Mechanical Engineering, McGill University, Montreal H3A 2K6, QC, Canada

Received: 26 February 2023 Revised: 01 May 2023 Accepted: 06 May 2023 Published: 12 May 2023

We propose an asymptotic concentration approach combined with isogeometric analysis (IGA) for the topology optimization of two-dimensional (2D) linear elasticity structures under the commonly-used framework of the solid isotropic materials and penalty (SIMP) model. Based on the SIMP framework, the B-splines are used as basis functions to describe geometric model in structural finite element analysis, which closely combines geometric modeling with structural analysis. Isogeometric analysis is utilized to define the geometric characteristics of the 2D linear elasticity structures, which can greatly improve the calculation accuracy. In addition, to eliminate the gray-scale intervals usually caused by the intermediate density in the SIMP approach, we utilize the asymptotic concentration method to concentrate the intermediate density values on either 0 or 1 gradually. Consequently, the intermediate densities representing gray-scale intervals in topology optimization results are sufficiently eliminated by virtue of the asymptotic concentration method. The effectiveness and applicability of the proposed method are illustrated by several typical examples.
- structural topology optimization,
- asymptotic concentration method,
- isogeometric analysis,
- B-splines,
- gray-scale interval
Citation: Mingtao Cui, Wang Li, Guang Li, Xiaobo Wang. The asymptotic concentration approach combined with isogeometric analysis for topology optimization of two-dimensional linear elasticity structures[J]. Electronic Research Archive, 2023, 31(7): 3848-3878. doi: 10.3934/era.2023196

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Abstract

We propose an asymptotic concentration approach combined with isogeometric analysis (IGA) for the topology optimization of two-dimensional (2D) linear elasticity structures under the commonly-used framework of the solid isotropic materials and penalty (SIMP) model. Based on the SIMP framework, the B-splines are used as basis functions to describe geometric model in structural finite element analysis, which closely combines geometric modeling with structural analysis. Isogeometric analysis is utilized to define the geometric characteristics of the 2D linear elasticity structures, which can greatly improve the calculation accuracy. In addition, to eliminate the gray-scale intervals usually caused by the intermediate density in the SIMP approach, we utilize the asymptotic concentration method to concentrate the intermediate density values on either 0 or 1 gradually. Consequently, the intermediate densities representing gray-scale intervals in topology optimization results are sufficiently eliminated by virtue of the asymptotic concentration method. The effectiveness and applicability of the proposed method are illustrated by several typical examples.

References

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