Isogeometric shape optimization on triangulations

Wang, Cunfu; Xia, Songtao; Wang, Xilu; Qian, Xiaoping

doi:10.1016/j.cma.2017.11.032

Cited by 40 publications

(15 citation statements)

References 50 publications

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“…A more general and complex approach is to perform a secondary correction in the in-plane direction after the normal surface update to maintain surface validity. Such in-plane updates can be explicit corrections [20] or involve the solution of a sub-problem minimising a mesh quality criteria [34] or physical analogy such as plane stress equilibrium [35] akin to variational surface fairing. However, performing normal perturbations followed by a non-linear in-plane correction requires limiting the normal perturbation step size [20] and also introduces dependency on the initial shape from which the normal directions are defined.…”

Section: Shape Parameterisationmentioning

confidence: 99%

Gradient-Limiting Shape Optimisation Applied to AIAA ADODG Test Cases

Kedward

Allen

Rendall

2019

AIAA Scitech 2019 Forum

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Without addressing shape smoothness, gradient-based optimisation methods naturally amplify high-frequency shape components which can lead to poor convergence of the optimisation problem and a convergence rate exhibiting dependency on the fidelity of shape-control. Recent work by the authors demonstrated that this problem arises due to the discrete shape problem being ill-posed by naturally including geometries that are invalid both in physicality (shape) and discretisation (mesh), and a new shape control methodology has been developed which addresses this explicitly. The new approach uses two-dimensional control to recover shaperelevant displacements and surface gradient constraints to ensure smooth and valid iterates. The shape gradient constraints, approximating a C 2 continuity condition, are derived for two local shape control methods: discrete grid point control and cubic B-Splines. The local control methods provide high-fidelity control whereas the surface constraints exclude non-physical shapes from the design space making the shape problem well-posed. As a result, high-fidelity shape optimisation is possible at a reasonable computational cost. In this paper, further results are presented for the aerodynamic optimisation of two standard test cases defined by the AIAA aerodynamic design optimisation discussion group. A value of 7 drag counts is achieved on the inviscid case and 66 drag counts on the viscous case; to the authors' knowledge these are the lowest results published for either case.

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Section: Shape Parameterisationmentioning

confidence: 99%

Gradient-Limiting Shape Optimisation Applied to AIAA ADODG Test Cases

Kedward

Allen

Rendall

2019

AIAA Scitech 2019 Forum

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“…Representative parameterization methods include analysis suitable T-splines in Scott et al [Scott, Li, Sederberg et al (2012); da Veiga, Buffa, Cho et al 2012], an analysis-suitable parameterization framework using harmonic method in Xu et al [Xu, Mourrain, Duvigneau et al (2013)], a method of using mapped B-spline basis functions in [Yuan and Ma (2014)] and an optimized trivariate B-spline solids parameterization approach in Wang et al [Wang and Qian (2014)]. Representative analysis techniques for shape design optimization problems in-clude the T-Spline based IGA in Ha et al [Ha, Choi and Cho (2010) [Speleers and Manni (2015)], isogeometric B-Rep analysis for trimmed surfaces in Philipp et al [Philipp, Breitenberger, D'Auria et al (2016)], an immersed method termed immersogeometric methods in Wu et al [Wu, Kamensky, Wang et al (2017)], an combination of immersed method and bound-ary method in Marco et al [Marco, Ródenas, Fuenmayor et al (2018)], and triangulations based IGA in Wang et al [Wang, Xia, Wang et al (2018)]. It should be noted that among these methods, the boundary element method is popular for its certain advantages over the domain-based methods, e.g.…”

Section: Isogeometric Shape Optimization With Different Parameterizatmentioning

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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“…[38,39]) and general curved structures (e.g., in Refs. [40][41][42][43][44][45]). 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.…”

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 shape optimization on triangulations

Cited by 40 publications

References 50 publications

Gradient-Limiting Shape Optimisation Applied to AIAA ADODG Test Cases

Gradient-Limiting Shape Optimisation Applied to AIAA ADODG Test Cases

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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