Isogeometric shape optimization of photonic crystals via Coons patches

Qian, Xiaoping; Sigmund, Ole

doi:10.1016/j.cma.2011.03.007

Cited by 69 publications

(36 citation statements)

References 25 publications

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“…Another area where IGA has shown advantages over traditional approaches is optimisation problems Manh et al (2011);Qian (2010); Qian and Sigmund (2011);Wall et al (2008). IGA is particularly suited to such problems due to the tight coupling with CAD models and offers an extremely attractive approach for industrial applications.…”

Section: Introductionmentioning

confidence: 99%

Extended Isogeometric Analysis for Strong and Weak Discontinuities

Nguyen

Bordas

2015

Isogeometric Methods for Numerical Simulation

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Isogeometric analysis (IGA) is a fundamental step forward in computational mechanics that offers the possibility of integrating methods for analysis into Computer Aided Design (CAD) tools and vice versa. The benefits of such an approach are evident, since the time taken from design to analysis is greatly reduced leading to large savings in cost and time for industry. The tight coupling of CAD and analysis within IGA requires knowledge from both fields and it is one of the goals of the present paper to outline much of the commonly used notation. In this manuscript, through a clear and simple Matlab R implementation, we present an introduction to IGA applied to the Finite Element (FE) method and related computer implementation aspects. Furthermore, implementation of the extended IGA which incorporates enrichment functions through the partition of unity method (PUM) is also presented, where several fracture examples in both two-dimensions and three-dimensions are given as illustration. The open source Matlab R code which accompanies the present paper can be applied to one, two and threedimensional problems for linear elasticity, linear elastic fracture mechanics, structural mechanics (beams/plates/shells including large displacements and rotations) and Poisson problems with or without enrichment. It also implements the Bézier extraction concept that allows FE analysis to be performed on T-spline geometries. An attempt was also made to include a review of recent developments of IGA.G. Beer, S.Bordas (Eds.), Isogeometric Methods for Numerical Simulation,

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Section: Introductionmentioning

confidence: 99%

Extended Isogeometric Analysis for Strong and Weak Discontinuities

Nguyen

Bordas

2015

Isogeometric Methods for Numerical Simulation

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“…For example, the swept volume [3], harmonic functions [4], multi-block [5], and Coons patch [6] techniques have recently been developed to construct NURBS representations of volumetric domains. To extend NURBS representation to complex topologies while also allowing for adaptive refinement, T -splines [7] have been used in isogeometric analysis [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Isogeometric analysis on triangulations

Jaxon

Qian

2014

Computer-Aided Design

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“…This allows certain geometries to be represented exactly that can only be approximated by polynomial functions, such as conic and circular sections. Another area where IGA has shown advantages over traditional approaches is optimisation problems Manh et al (2011);Qian (2010); Qian and Sigmund (2011);. Piegl and Tiller (1996); Rogers (2001)) and as a result of several decades of research, many efficient computer algorithms exist for their fast evaluation and refinement.…”

Section: Introductionmentioning

confidence: 99%

Isogeometric Methods for Numerical Simulation

Beer¹,

Bordas²

2015

CISM International Centre for Mechanical Sciences

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Isogeometric shape optimization of photonic crystals via Coons patches

Cited by 69 publications

References 25 publications

Extended Isogeometric Analysis for Strong and Weak Discontinuities

Extended Isogeometric Analysis for Strong and Weak Discontinuities

Isogeometric analysis on triangulations

Isogeometric Methods for Numerical Simulation

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