Isogeometric analysis based topology optimization design with global stress constraint

Liu, Hongliang; Yang, Dan; Hao, Peng; Zhu, Xuefeng

doi:10.1016/j.cma.2018.08.013

Cited by 70 publications

(23 citation statements)

References 53 publications

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“…Taheri et al [74] also studied the application of the ITO to the multimaterial topology optimization problem and the design of functionally graded structures, where the multi-material interpolation scheme proposed by Stegmann and Lund [75] to realize the discrete material optimization is directly used. Liu et al [76] also addressed the stressconstrained topology optimization problem of plane stress and bending of thin plates using the ITO framework, where two stability transformation methods are developed to stabilize the optimization using the P-norm function for global stress constraint. Later, Gao et al [77] proposed a NURBS-based Multi-Material Interpolation (N-MMI) model in the ITO method [69] to develop a Multi-material ITO (M-ITO) method.…”

Section: Density-basedmentioning

confidence: 99%

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

Gao

Xiao

Zhang

et al. 2020

Chin. J. Mech. Eng.

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Topology Optimization (TO) is a powerful numerical technique to determine the optimal material layout in a design domain, which has accepted considerable developments in recent years. The classic Finite Element Method (FEM) is applied to compute the unknown structural responses in TO. However, several numerical deficiencies of the FEM significantly influence the effectiveness and efficiency of TO. In order to eliminate the negative influence of the FEM on TO, IsoGeometric Analysis (IGA) has become a promising alternative due to its unique feature that the Computer-Aided Design (CAD) model and Computer-Aided Engineering (CAE) model can be unified into a same mathematical model. In the paper, the main intention is to provide a comprehensive overview for the developments of Isogeometric Topology Optimization (ITO) in methods and applications. Finally, some prospects for the developments of ITO in the future are also presented.

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Section: Density-basedmentioning

confidence: 99%

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

Gao

Xiao

Zhang

et al. 2020

Chin. J. Mech. Eng.

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show abstract

“…Therefore, the IGA is especially suitable for topology optimization with stress constraint, since the stress is discontinuous between elements in FEM. Liu et al [Liu, Yang, Hao et al (2018)] presented a stress-constrained ITO of thin bending plates, where two stability transformation methods (STMs) were proposed to achieve the stable iterations. Due to the high continuity of IGA, the ITO can meet the requirement of C1 continuity for the Kirchhoff plate formulations, and the example results indicate that the ITO shows superior performance for both accuracy and efficiency.…”

Section: Density-based Isogeometric Topology Optimizationmentioning

confidence: 99%

Structural Design Optimization Using Isogeometric Analysis: A Comprehensive Review

Wang¹,

Wang²,

Xia³

et al. 2018

CMES

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Isogeometric analysis (IGA), an approach that integrates CAE into conventional CAD design tools, has been used in structural optimization for 10 years, with plenty of excellent research results. This paper provides a comprehensive review on isogeometric shape and topology optimization, with a brief coverage of size optimization. For isogeometric shape optimization, attention is focused on the parametrization methods, mesh updating schemes and shape sensitivity analyses. Some interesting observations, e.g. the popularity of using direct (differential) method for shape sensitivity analysis and the possibility of developing a large scale, seamlessly integrated analysis-design platform, are discussed in the framework of isogeometric shape optimization. For isogeometric topology optimization (ITO), we discuss different types of ITOs, e.g. ITO using SIMP (Solid Isotropic Material with Penalization) method, ITO using level set method, ITO using moving morphable components (MMC), ITO with phase field model, etc., their technical details and applications such as the spline filter, multi-resolution approach, multi-material problems and stress constrained problems. In addition to the review in the last 10 years, the current developmental trend of isogeometric structural optimization is discussed.

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“…The ease of achieving multiple resolutions, and the high order shape functions of IGA, also promote the development of topology optimization, e.g., in Refs. [46][47][48][49][50][51][52]. A generalized shape optimization method combining level set method and finite cell method [53] for structural designs using IGA can be found in Refs.…”

Section: Introductionmentioning

confidence: 99%

An isogeometric numerical study of partially and fully implicit schemes for transient adjoint shape sensitivity analysis

2020

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In structural design optimization involving transient responses, time integration scheme plays a crucial role in sensitivity analysis because it affects the accuracy and stability of transient analysis. In this work, the influence of time integration scheme is studied numerically for the adjoint shape sensitivity analysis of two benchmark transient heat conduction problems within the framework of isogeometric analysis. It is found that (i) the explicit approach (β = 0) and semi-implicit approach with β < 0.5 impose a strict stability condition of the transient analysis;(ii) the implicit approach (β = 1) and semi-implicit approach with β > 0.5 are generally preferred for their unconditional stability; and (iii) Crank-Nicolson type approach (β = 0.5) may induce a large error for large time-step sizes due to the oscillatory solutions. The numerical results also show that the time-step size does not have to be chosen to satisfy the critical conditions for all of the eigen-frequencies. It is recommended to use β % 0:75 for unconditional stability, such that the oscillation condition is much less critical than the Crank-Nicolson scheme, and the accuracy is higher than a fully implicit approach.

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Isogeometric analysis based topology optimization design with global stress constraint

Cited by 70 publications

References 53 publications

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

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

Structural Design Optimization Using Isogeometric Analysis: A Comprehensive Review

An isogeometric numerical study of partially and fully implicit schemes for transient adjoint shape sensitivity analysis

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