Studies on knot placement techniques for the geometry construction and the accurate simulation of isogeometric spatial curved beams

Hosseini, Seyed Farhad; Hashemian, Ali; Reali, Alessandro

doi:10.1016/j.cma.2019.112705

Cited by 15 publications

(10 citation statements)

References 49 publications

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“…The optimization of knot distribution has primarily been dealt with in curve interpolation/approximation research, where the methods applied include particle swarm optimization [54], gaussian-mixture models [55] and multi-objective genetic algorithms [56] (see also commentaries in Section 2.2 for additional references on knot construction techniques). Besides approximation/interpolation, the issue of optimal knot distribution has also been recently studied in the context of isogeometric analysis [42,43]. It seems that not much attention has been given to the topic of knot vector optimization in feedrate optimization related literature so far, however, in [21] the problematic of optimal knot placement was considered in the context of generation of jerk-minimizing toolpaths via reparametrization (see also [20] for additional details).…”

Section: Discussion and Limitationsmentioning

confidence: 99%

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Linear programming feedrate optimization

Petráček

Vlk

Sveda

2022

Int J Adv Manuf Technol

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This paper focuses on two aspects of feedrate optimization via linear programming methods. Namely, the effect of curve sampling on time optimality of the resultant feedrate profile and a method of feedrate profile adaptation in response to a feedrate override command. A comparison of three distinct curve sampling approaches (uniform in parameter, uniform in arc length and curvature adaptive) is performed on a series of standard tool path curves. Results show that the curvature-adaptive sampling approach leads to substantial machining time reduction for tool path curves displaying high degree of curvature variation. Secondly, a method by which a new feedrate profile can be calculated in response to a feedrate override command is developed. The method formulates a new set of boundary conditions on the control point sequence of the feedrate curve in such a way that the resulting profile is guaranteed to coincide with the currently active profile up to the moment of override command, while minimizing the arc length necessary for transition to the newly commanded feedrate.

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Section: Discussion and Limitationsmentioning

confidence: 99%

“…The applications of knot vector construction method are not exclusively limited to curve interpolation or approximation, see e.g. [42,43].…”

Section: Linear Programming -Evaluation Points and Knot Vector Constr...mentioning

confidence: 99%

Linear programming feedrate optimization

Petráček

Vlk

Sveda

2022

Int J Adv Manuf Technol

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“…IGA addresses many scientific and engineering problems (c.f., [2][3][4][5]). Some of its specific applications are in, e.g., structural analysis [6][7][8], fluid mechanics [9][10][11][12], fluid-structure interactions [13,14], chemical physics [15][16][17], and electromagnetics [18,19]. IGA uses spline basis functions, which are standard in computer-aided design (CAD), as shape functions of finite element analysis (FEA).…”

Section: Introductionmentioning

confidence: 99%

Refined isogeometric analysis for generalized Hermitian eigenproblems

Hashemian

Pardo

Calo

2021

Computer Methods in Applied Mechanics and Engineering

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We use refined isogeometric analysis (rIGA) to solve generalized Hermitian eigenproblems (Ku = λMu). rIGA conserves the desirable properties of maximum-continuity isogeometric analysis (IGA) while it reduces the solution cost by adding zero-continuity basis functions, which decrease the matrix connectivity. As a result, rIGA enriches the approximation space and reduces the interconnection between degrees of freedom. We compare computational costs of rIGA versus those of IGA when employing a Lanczos eigensolver with a shift-and-invert spectral transformation. When all eigenpairs within a given interval [λ s , λ e ] are of interest, we select several shifts σ k ∈ [λ s , λ e ] using a spectrum slicing technique. For each shift σ k , the factorization cost of the spectral transformation matrix K − σ k M controls the total computational cost of the eigensolution. Several multiplications of the operator matrix (K − σ k M) −1 M by vectors follow this factorization. Let p be the polynomial degree of the basis functions and assume that IGA has maximum continuity of p − 1. When using rIGA, we introduce C 0 separators at certain element interfaces to minimize the factorization cost. For this setup, our theoretical estimates predict computational savings to compute a fixed number of eigenpairs of up to O(p 2 ) in the asymptotic regime, that is, large problem sizes. Yet, our numerical tests show that for moderate-size eigenproblems, the total observed computational cost reduction is O(p). In addition, rIGA improves the accuracy of every eigenpair of the first N 0 eigenvalues and eigenfunctions, where N 0 is the total number of modes of the original maximum-continuity IGA discretization.

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“…Since the number and distribution of the knots are both unknown in advance, the issue becomes a multivariate and multimodal nonlinear optimization problem [9]. In practical applications, three uniform placement methods are commonly used: uniform knot placement (UKP) [10,11], the knot placement technique (KTP) [10,11], and the new KTP [12]. These methods uniformly place knots among the given points through instant computation, which can provide stable and appropriate curve fitting.…”

Section: Introductionmentioning

confidence: 99%

An approximation method combined with conformal transformation for the fast measurement of blade section curves

Lu¹,

Zhao²,

Yang³

et al. 2021

Meas. Sci. Technol.

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To realize high-precision machining of free-form blade surfaces, it is necessary to measure and reconstruct the blade morphology several times. Sampling measurements and data compression through free-curve approximation technology are of great benefit in shortening the processing time. A novel B-spline approximation method is proposed in this paper, which can determine a few dominant points based on curvature characteristics to approximate dense and noisy measured points with high precision. We adopt a unique adaptive knot placement strategy combined with a curvature dependent evaluation parameter and a conformal transformation method. This strategy is error-bounded in the initial knot placement, which greatly reduces the time consumed by subsequent iterative insertions. The proposed method shows advantages in approximation accuracy, compression rate, and especially in computational efficiency, in comparison with four traditional knot placement methods. Experiments were carried out and the results show that the dominant point selected by this method can replace the fine measurement results, and the compression rate of the measurement points can reach more than 90%. This method is suitable for the sampling measurement and compression of the data of blades, aircraft wings, and other similar free-form surfaces, and is especially suitable for solving the inefficiency problem caused by repeated measurements made in the process of iterative machining of aero-engine blades.

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Studies on knot placement techniques for the geometry construction and the accurate simulation of isogeometric spatial curved beams

Cited by 15 publications

References 49 publications

Linear programming feedrate optimization

Linear programming feedrate optimization

Refined isogeometric analysis for generalized Hermitian eigenproblems

An approximation method combined with conformal transformation for the fast measurement of blade section curves

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