An isogeometrical approach to structural level set topology optimization

Jahangiry, Hassan A.; Tavakkoli, S. M.

doi:10.1016/j.cma.2017.02.005

Cited by 59 publications

(23 citation statements)

References 24 publications

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“…Moreover, the point wise density mapping is directly used in the weak form of the governing equations and the adjoint sensitivity technique is applied to compute the derivative. Jahangiry et al [89] also discussed the application of IGA in the structural level set topology optimization to develop a new level set-based ITO framework, where the control mesh is gradually updated in the optimization iterations, and then the authors also discussed the application of the new level set-based ITO framework in the topology optimization of the concentrated heat flow and uniformly distributed heat generation systems [90]. Lee et al [91] also implemented the isogeometric topological shape optimization using dual evolution with boundary integral equation and level sets, where the implicit geometry using the level sets is transformed into the parametric NURBS curves by minimizing the difference of velocity fields in both representations.…”

Section: Level Set-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: Level Set-basedmentioning

confidence: 99%

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

Gao

Xiao

Zhang

et al. 2020

Chin. J. Mech. Eng.

View full text Add to dashboard Cite

show abstract

“…Model C shown in Figure 8 is selected as an initial configuration, and the third eigenmode at point M is targeted. In this case, as the components of T ij of the initial unit cell are evaluated as T 11 = −0.11 and T 22 = −1.48, F 2 = T 2 11 is employed for the objective function in Equation (52). Parameters for optimization, d, , dt, and AL , are set at 0.2, 0.0001, 0.01, and 0.01, respectively.…”

Section: Optimization For Metamaterials With Bidirectional Propagationmentioning

confidence: 99%

“…Also, Dedé et al incorporated the phase‐field model, which is based on the generalized Cahn‐Hilliard equation, with the IG topology optimization. Moreover, level‐set functions were employed for IG topology optimization by Wang and Benson, Jahangiry and Takvakkoli, and Ghasemi et al In these developments, the phase‐field variables or the level‐set functions defining material boundaries are discretized with spline functions to make the best use of the well‐known strong points of IGAs. Apart from this line, Hassani et al developed a density‐based method with IGA, which has been followed by Taheri and Suresh for multimaterial topology optimization.…”

Section: Introductionmentioning

confidence: 99%

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

Nishi

Yamada

Izui

et al. 2019

Numerical Meth Engineering

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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.

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“…The IGA was also introduced into the parametric LSM and developed a level‐set–based topology optimization method with IGA, where the level‐set function was interpolated by the NURBS basis functions, rather than using the compactly supported radial basis functions given in the works . In the work of Jahangiry and Tavakkoli, an isogeometric approach was also developed for the level‐set topology optimization, where three different problems were discussed, like the minimizing weight subject to the local stress constraints. Topology optimization with the global stress constraint was also studied in an IGA‐based SIMP framework .…”

Section: Introductionmentioning

confidence: 99%

Isogeometric topology optimization for continuum structures using density distribution function

Gao

Luo

et al. 2019

Numerical Meth Engineering

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Summary This paper will propose a more effective and efficient topology optimization method based on isogeometric analysis, termed as isogeometric topology optimization (ITO), for continuum structures using an enhanced density distribution function (DDF). The construction of the DDF involves two steps. (1) Smoothness: the Shepard function is firstly utilized to improve the overall smoothness of nodal densities. Each nodal density is assigned to a control point of the geometry. (2) Continuity: the high‐order NURBS basis functions are linearly combined with the smoothed nodal densities to construct the DDF for the design domain. The nonnegativity, partition of unity, and restricted bounds [0, 1] of both the Shepard function and NURBS basis functions can guarantee the physical meaning of material densities in the design. A topology optimization formulation to minimize the structural mean compliance is developed based on the DDF and isogeometric analysis to solve structural responses. An integration of the geometry parameterization and numerical analysis can offer the unique benefits for the optimization. Several 2D and 3D numerical examples are performed to demonstrate the effectiveness and efficiency of the proposed ITO method, and the optimized 3D designs are prototyped using the Selective Laser Sintering technique.

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An isogeometrical approach to structural level set topology optimization

Cited by 59 publications

References 24 publications

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

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

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

Isogeometric topology optimization for continuum structures using density distribution function

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