Linear elastic fracture simulation directly from CAD: 2D NURBS-based implementation and role of tip enrichment

Peng, Xuan; Atroshchenko, Elena; Kerfriden, Pierre; Bordas, Stéphane Pierre Alain

doi:10.1007/s10704-016-0153-3

Cited by 83 publications

(34 citation statements)

References 94 publications

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“…The third difficulty associated to the domain parametrization can be naturally overcome by the isogeometric boundary element methods (IGABEM) [62,1,63,64,2,3,65,66,67]. The idea of IGABEM is to employ the basis/blending functions in CAD to discretize the boundary integral equation (BIE).…”

Section: Introductionmentioning

confidence: 99%

Shape optimization directly from CAD: An isogeometric boundary element approach using T-splines

Lian

Kerfriden

Bordas

2017

Computer Methods in Applied Mechanics and Engineering

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127

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We develop a T-spline isogeometric boundary element method (IGABEM) [1, 2, 3] to shape sensitivity analysis and gradient-based shape optimization in three dimensional linear elasticity. Contrary to finite element based isogeometric analysis (IGA) approaches, no parametrization of the volume is required. Hence, the iterative optimization algorithm can be implemented directly from CAD without any mesh generation nor postprocessing step for returning the resulting structure to CAD designers. T-splines also guarantee a watertight geometry without the manual geometrical-repair work as with non-uniform rational B-splines (NURBS). We demonstrate the worth of the method by analysing problems with and without analytical solutions, including engineering examples involving complex shapes. Additionally, we provide all the derivations of the required sensitivities and the details pertaining to the geometries examined in the benchmarking, to provide helpful reference problems for 3D shape optimization.

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Section: Introductionmentioning

confidence: 99%

Shape optimization directly from CAD: An isogeometric boundary element approach using T-splines

Lian

Kerfriden

Bordas

2017

Computer Methods in Applied Mechanics and Engineering

Self Cite

127

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“…The method exhibits superior accuracy per degree of freedom and is naturally able to simulate complex geometries. The application of IGABEM in fracture mechanics [46,45] further demonstrated its potential in dealing with moving boundaries and singularities. So far, IGABEM has been applied successfully in wave-resistance [23], elasto-plastic inclusions [6,5], structural-acoustic coupling [36], electromagnetics [56], etc.…”

Section: Introductionmentioning

confidence: 99%

Structural shape optimization of three dimensional acoustic problems with isogeometric boundary element methods

Chen

Lian

Liu

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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133

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The boundary element method (BEM) is a powerful tool in computational acoustics, because the analysis is conducted only on structural surfaces, compared to the finite element method (FEM) which resorts to special techniques to truncate infinite domains. The isogeometric boundary element method (IGABEM) is a recent progress in the category of boundary element approaches, which is inspired by the concept of isogeometric analysis (IGA) and employs the spline functions of CAD as basis functions to discretize unknown physical fields. As a boundary representation approach, IGABEM is naturally compatible with CAD and thus can directly perform numerical analysis on CAD models, avoiding the cumbersome meshing procedure in conventional FEM/BEM and eliminating the difficulty of volume parameterization in isogeometric finite element methods. The advantage of tight integration of CAD and numerical analysis in IGABEM renders it particularly attractive in the application of structural shape optimization because (1) the geometry and the analysis can be interacted, (2) remeshing with shape morphing can be avoided, and (3) an optimized solution returns a CAD

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“…Methods of parameterization of the interior domain while retaining the geometry exactness from the CAD model have been devised [39,40], and isogeometric collocation method is one of the most important among these methods [39]. With regard to interior discretization obstacles, the isogeometric boundary element method is a suitable candidate [41] because only boundary data are required for analysis, and it enables stress analysis [42], fracture analysis [43,44], acoustic analysis [45], and shape optimization [46,47]. Considering that the integral efficiency of IGA is limited by the tensor product structure of NURBS, an efficient quadrature rule, which is more suitable for NURBS-based IGA compared with the Gaussian quadrature rule, has been proposed in Ref.…”

Section: Introductionmentioning

confidence: 99%

Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency

Wang

Xie

2019

Front. Mech. Eng.

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Maximizing the fundamental eigenfrequency is an efficient means for vibrating structures to avoid resonance and noises. In this study, we develop an isogeometric analysis (IGA)-based level set model for the formulation and solution of topology optimization in cases with maximum eigenfrequency. The proposed method is based on a combination of level set method and IGA technique, which uses the non-uniform rational B-spline (NURBS), description of geometry, to perform analysis. The same NURBS is used for geometry representation, but also for IGA-based dynamic analysis and parameterization of the level set surface, that is, the level set function. The method is applied to topology optimization problems of maximizing the fundamental eigenfrequency for a given amount of material. A modal track method, that monitors a single target eigenmode is employed to prevent the exchange of eigenmode order number in eigenfrequency optimization. The validity and efficiency of the proposed method are illustrated by benchmark examples.

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Linear elastic fracture simulation directly from CAD: 2D NURBS-based implementation and role of tip enrichment

Cited by 83 publications

References 94 publications

Shape optimization directly from CAD: An isogeometric boundary element approach using T-splines

Shape optimization directly from CAD: An isogeometric boundary element approach using T-splines

Structural shape optimization of three dimensional acoustic problems with isogeometric boundary element methods

Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency

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