Adaptive isogeometric topology optimization using PHT splines

Gupta, Akhilesh; Mamindlapelly, Bhagath; Karuthedath, Philip Luke; Chowdhury, Rajib; Chakrabarti, Anupam

doi:10.1016/j.cma.2022.114993

Cited by 18 publications

(6 citation statements)

References 109 publications

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“…This advantage has been explored in [2] and will not be repeated in this paper. The focus of this paper is to provide a way to efficiently calculate weights for non-decay basis functions so that non-decay PHT splines can be used in specific applications, such as topology optimization [14].…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…PHT-splines possess a very efficient local refinement algorithm and inherit many good properties of T-splines such as adaptivity and locality. PHT-splines are now widely applied in adaptive geometric modeling [2][3][4], adaptive finite element [5], iso-geometric analysis [6][7][8][9][10][11][12][13] and topology optimization [14].…”

Section: Introductionmentioning

confidence: 99%

“…The partition of unity is a default ingredient in the construction of approximating functions in finite element methods [17][18][19]. Moreover, in the field of topology optimization [14], the density variable takes value in the range of [0,1]. The basis functions that form a partition of unity are more suitable for designing density variables that meet the range condition.…”

Section: Introductionmentioning

confidence: 99%

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The Weighted Basis for PHT-Splines

Yong,

Kang,

Chen

2024

Computer Modeling in Engineering &Amp; Sciences

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PHT-splines are defined as polynomial splines over hierarchical T-meshes with very efficient local refinement properties. The original PHT-spline basis functions constructed by the truncation mechanism have a decay phenomenon, resulting in numerical instability. The non-decay basis functions are constructed as the B-splines that are defined on the 2 × 2 tensor product meshes associated with basis vertices in Kang et al., but at the cost of losing the partition of unity. In the field of finite element analysis and topology optimization, forming the partition of unity is the default ingredient for constructing basis functions of approximate spaces. In this paper, we will show that the non-decay PHT-spline basis functions proposed by Kang et al. can be appropriately modified to form a partition of unity. Each non-decay basis function is multiplied by a positive weight to form the weighted basis. The weights are solved such that the sum of weighted bases is equal to 1 on the domain. We provide two methods for calculating weights, based on geometric information of basis functions and the subdivision of PHT-splines. Weights are given in the form of explicit formulas and can be efficiently calculated. We also prove that the weights on the admissible hierarchical T-meshes are positive.

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Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Weighted Basis for PHT-Splines

Yong,

Kang,

Chen

2024

Computer Modeling in Engineering &Amp; Sciences

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“…T-splines have received rapid development, given their excellent topological characteristics. Hierarchical T-splines, analysis-suitable T-splines (AST-splines), truncated T-splines, and various modified T-splines [ 18 , 19 , 20 , 21 , 22 , 23 ] have been developed from there. Recently, they have also been successfully applied to iso-geometrical analyses [ 23 , 24 ].…”

Section: Introductionmentioning

confidence: 99%

“…Hierarchical T-splines, analysis-suitable T-splines (AST-splines), truncated T-splines, and various modified T-splines [ 18 , 19 , 20 , 21 , 22 , 23 ] have been developed from there. Recently, they have also been successfully applied to iso-geometrical analyses [ 23 , 24 ]. For these large-scale complex geometry data, existing T-spline fitting algorithms suffer severe efficiency problems compared to NURBS, especially when high fitting accuracy is required.…”

Section: Introductionmentioning

confidence: 99%

Stitching Locally Fitted T-Splines for Fast Fitting of Large-Scale Freeform Point Clouds

Wang,

Bi,

Liu

et al. 2023

Sensors

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Parametric splines are popular tools for precision optical metrology of complex freeform surfaces. However, as a promising topologically unconstrained solution, existing T-spline fitting techniques, such as improved global fitting, local fitting, and split-connect algorithms, still suffer the problems of low computational efficiency, especially in the case of large data scales and high accuracy requirements. This paper proposes a speed-improved algorithm for fast, large-scale freeform point cloud fitting by stitching locally fitted T-splines through three steps of localized operations. Experiments show that the proposed algorithm produces a three-to-eightfold efficiency improvement from the global and local fitting algorithms, and a two-to-fourfold improvement from the latest split-connect algorithm, in high-accuracy and large-scale fitting scenarios. A classical Lena image study showed that the algorithm is at least twice as fast as the split-connect algorithm using fewer than 80% control points of the latter.

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