Parametric mesh regularization for interpolatory shape design and isogeometric analysis over a mesh of arbitrary topology

Yuan, Xiaoyun; Ma, Weiyin

doi:10.1016/j.cma.2014.10.056

Cited by 7 publications

(3 citation statements)

References 57 publications

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“…In the framework of isogeometric shape optimization, although it is mentioned in Braibant et al Fleury (1984, 1985)] that a B-Spline parameterization automatically accounts for boundary irregularities, proper boundary and domain mesh regularizations are still required. This mainly because that (i) the boundary shape change may cause irregular mesh if the interior control points are not moved properly [Yuan and Ma (2015); Choi and Cho (2015)] and (ii) the non-uniform local supports of the control points can lead to unbalanced step-sizes for different design control points to give an irregular geometry [Nagy (2011); Wang, Abdalla and Turteltaub (2017)], as illustrated in Fig. 5.…”

Section: Shape and Mesh Updating Schemesmentioning

confidence: 99%

“…Both the shape change norm and the H1 gradient methods require to solve a system of equations. In Yuan et al [Yuan and Ma (2015)], a parametric mesh regularization based on a method of mapped basis functions is demonstrated with a iterative procedure. In Choi et al [Choi and Cho (2015)], a mesh regularization scheme is proposed by minimizing the Dirichlet energy functional and a dimensionless functional such that the uniform parametrization and the mesh orthogonality can be obtained.…”

Section: Shape and Mesh Updating Schemesmentioning

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: Shape and Mesh Updating Schemesmentioning

confidence: 99%

Section: Shape and Mesh Updating Schemesmentioning

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

“…Along with the wide application of IGA in various engineering problems Bui, 2015;Yuan and Ma, 2015;Temizer et al, 2014;Grossmann et al, 2012;Dedè et al, 2015), the relevant implementations of IGA have been introduced. Cottrell and Hughes (2009) wrote a book to elaborate on what IGA is and offered the key pseudo-code of IGA.…”

Section: Introductionmentioning

confidence: 99%

A Fortran implementation of isogeometric analysis for thin plate problems with the penalty method

Chang

Wang

Yan

et al. 2016

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Purpose As one of the earliest high-level programming languages, Fortran with easy accessibility and computational efficiency is widely used in the engineering field. The purpose of this paper is to present a Fortran implementation of isogeometric analysis (IGA) for thin plate problems. Design/methodology/approach IGA based on non-uniform rational B-splines (NURBS) offers exact geometries and is more accurate than finite element analysis (FEA). Unlike the basis functions in FEA, NURBS basis functions are non-interpolated. Hence, the penalty method is used to enforce boundary conditions. Findings Several thin plate examples based on the Kirchhoff-Love theory were illustrated to demonstrate the accuracy of the implementation in contrast with analytical solutions, and the efficiency was validated in comparison with another open method. Originality/value A Fortran implementation of NURBS-based IGA was developed to solve Kirchhoff-Love plate problems. It easily obtained high-continuity basis functions, which are necessary for Kirchhoff formulation. In comparison with theoretical solutions, the numerical examples demonstrated higher accuracy and faster convergence of the Fortran implementation. The Fortran implementation can well solve the time-consuming problem, and it was validated by the time-consumption comparison with the Matlab implementation. Due to the non-interpolation of NURBS, the penalty method was used to impose boundary conditions. A suggestion of the selection of penalty coefficients was given.

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A class of blending functions with $C^{\infty }$ smoothness

Zhu

2021

Numer Algor

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Parametric mesh regularization for interpolatory shape design and isogeometric analysis over a mesh of arbitrary topology

Cited by 7 publications

References 57 publications

Structural Design Optimization Using Isogeometric Analysis: A Comprehensive Review

Structural Design Optimization Using Isogeometric Analysis: A Comprehensive Review

A Fortran implementation of isogeometric analysis for thin plate problems with the penalty method

A class of blending functions with $C^{\infty }$ smoothness

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