Isogeometric configuration design sensitivity analysis of finite deformation curved beam structures using Jaumann strain formulation

Choi, Myung-Jin; Yoon, Mi Young; Cho, Seonho

doi:10.1016/j.cma.2016.05.040

Cited by 12 publications

(11 citation statements)

References 32 publications

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“…In Wang et al [Wang and Turteltaub (2015)], the shape sensitivity analysis considering discontinuities in the objective functions is derived using continuum adjoint method. In Choi et al [Choi, Yoon and Cho (2016)], the continuum adjoint method is derived for finite deformations of curved beams. It is also notable that with the development of isogeometric analysis, shape optimization has been applied to structures with increasingly complicated geometries, e.g.…”

Section: Some Remarks and Discussion In Isogeometric Shape Optimizationmentioning

confidence: 99%

“…In the context of isogeometric shape optimization, the exact geometric representation enables the computation of the boundary geometric parameters easily and seamlessly, hence, providing a natural platform to implement the continuum adjoint method. This has been intensively studied by Seonho Cho and his co-authors in Cho et al [Cho and Ha (2009)] for general discussions, in Ha et al [Ha, Choi and Cho (2010)] using T-spline based isogeometric method, in Ahn et al [Ahn and Cho (2010)] for level-set-based topology optimization of heat conduction problems, in Koo et al [Koo, Yoon and Cho (2013)] coping with Kronecker delta property, in Yoon et al [Yoon, Ha and Cho (2013); Yoon, Choi and Cho (2015)] for shape design optimization of heat conduction problems, in Choi et al [Choi and Cho (2014)] for stress intensity factors of curved crack problems, in Lee et al [Lee and Cho (2015)] for optimizing built-up structures, in Lee et al [Lee, Lee and Cho (2016)] for ferromagnetic materials in magnetic actuators, in Yoon et al [Yoon and Cho (2016)] for boundary integral equations, in Choi et al [Choi, Yoon and Cho (2016)] for designing curved Kirchhoff beams with finite deformations, in Lee et al [Lee, Yoon and Cho (2017)] for topological shape optimization using dual evolution with boundary integral equation and level sets, in Choi et al [Choi and Cho (2018a)] for designing lattice structures embedded on curve surfaces, in Choi et al [Choi and Cho (2018b)] for using curved beams to design auxetic structures and in Ahn et al [Ahn, Choi and Cho (2018); Ahn, Koo, Kim et al (2018)] for designing nanoscale structures. Wang and his co-authors implemented the continuum adjoint method in Wang et al [Wang and Turteltaub (2015)] for quasi-static problems considering discontinuities in the objective functions, in Wang et al ; Wang and Kumar (2017)] for transient heat conduction problems and in Wang et al [Wang, Poh, Dirrenberger et al (2017)] to design auxetic structures using numerical homogenization method.…”

Section: Ddimentioning

confidence: 99%

See 1 more Smart Citation

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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Section: Some Remarks and Discussion In Isogeometric Shape Optimizationmentioning

confidence: 99%

Section: Ddimentioning

confidence: 99%

Structural Design Optimization Using Isogeometric Analysis: A Comprehensive Review

Wang¹,

Wang²,

Xia³

et al. 2018

CMES

View full text Add to dashboard Cite

show abstract

“…It is noted that, hereafter, the argument is often omitted for brevity. The linearized translational and rotational strains are discretized aswhere W N,S defines the differentiation of NURBS basis function with respect to the arc-length coordinate, calculated by using a chain rule of differentiation 31 . From the governing equations of Eq.…”

Section: Methodsmentioning

confidence: 99%

Optimal design of lattice structures for controllable extremal band gaps

Choi

Koo

et al. 2019

Sci Rep

Self Cite

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This paper presents very large complete band gaps at low audible frequency ranges tailored by gradient-based design optimizations of periodic two- and three-dimensional lattices. From the given various lattice topologies, we proceed to create and enlarge band gap properties through controlling neutral axis configuration and cross-section thickness of beam structures, while retaining the periodicity and size of the unit cell. Beam neutral axis configuration and cross-section thickness are parameterized by higher order B-spline basis functions within the isogeometric analysis framework, and controlled by an optimization algorithm using adjoint sensitivity. Our optimal curved designs show much more enhanced wave attenuation properties at audible low frequency region than previously reported straight or simple undulated geometries. Results of harmonic response analyses of beam structures consisting of a number of unit cells demonstrate the validity of the optimal designs. A plane wave propagation in infinite periodic lattice is analyzed within a unit cell using the Bloch periodic boundary condition.

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“…( 5). We define an arc-length parameter s ∈ Ω ≡ [0, L] that parameterizes the beam neutral axis with the initial (undeformed) length L in a way that [6] s(ϕ 0 (ξ)) =…”

Section: Linear Kinematics and Equilibrium Equationsmentioning

confidence: 99%

Isogeometric configuration design optimization of three-dimensional curved beam structures for maximal fundamental frequency

Choi

Kim

Koo

et al. 2021

Struct Multidisc Optim

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This paper presents a configuration design optimization method for three-dimensional curved beam built-up structures having maximized fundamental eigenfrequency. We develop the method of computation of design velocity field and optimal design of beam structures constrained on a curved surface, where both designs of the embedded beams and the curved surface are simultaneously varied during the optimal design process. A shear-deformable beam model is used in the response analyses of structural vibrations within an isogeometric framework using the NURBS basis functions. An analytical design sensitivity expression of repeated eigenvalues is derived. The developed method is demonstrated through several illustrative examples.

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Isogeometric configuration design sensitivity analysis of finite deformation curved beam structures using Jaumann strain formulation

Cited by 12 publications

References 32 publications

Structural Design Optimization Using Isogeometric Analysis: A Comprehensive Review

Structural Design Optimization Using Isogeometric Analysis: A Comprehensive Review

Optimal design of lattice structures for controllable extremal band gaps

Isogeometric configuration design optimization of three-dimensional curved beam structures for maximal fundamental frequency

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