Accurate analysis and thickness optimization of tailor rolled blanks based on isogeometric analysis

Ding, Chensen; Cui, Xiangyang; Li, G. Y.

doi:10.1007/s00158-016-1448-8

Cited by 27 publications

(10 citation statements)

References 39 publications

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“…Hughes et al (2005) and Cottrell et al (2009) firstly introduced the concept of IGA by using the spline basis functions [such as non-uniform rational B-splines (NURBSs)] constructing the exact geometric models as interpolation functions in CAE analysis. Up to now, this approach has also gained widespread reception from the scientific community and many applications have been verified, for example, structural optimization (Cho and Ha, 2009;Qian, 2010;Ding et al, 2016;Ding et al, 2018c;Lian et al, 2017;Lian et al, 2016;Hao et al, 2018a;Hao et al, 2019;Hao et al, 2018b), plate and composite structures (Thai et al, 2014;Yu et al, 2018;Thai et al, 2015;Nguyen-Xuan et al, 2014;Chang et al, 2016;Yin et al, 2015;Thanh et al, 2019b;Phung-Van et al, 2019;Thanh et al, 2019a;Thanh et al, 2018;Phung-Van et al, 2018;Thai et al, 2018b;Thai et al, 2018a;Tran et al, 2017;Thai et al, 2016), isogeometric boundary methods (Simpson et al, 2013;Simpson et al, 2012;Peng et al, 2017;Scott et al, 2013), stochastic analysis (Ding et al, 2019a;Ding et al, 2018b;Ding et al, 2019b;Ding et al, 2019c), other splines based methods (Atroshchenko et al, 2018;Nguyen-Thanh et al, 2011;Gu et al, 2018a;Gu et al, 2018b), and especially the severa...…”

Section: Cae Modelmentioning

confidence: 99%

Isogeometric independent coefficients method for fast reanalysis of structural modifications

Ding

2019

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Purpose This paper aims to provide designers/engineers, in engineering structural design and analysis, approaches to freely and accurately modify structures (geometric and/or material), and then quickly provide real-time capability to obtain the numerical solutions of the modified structures (designs). Design/methodology/approach The authors propose an isogeometric independent coefficients (IGA-IC) method for a fast reanalysis of structures with geometric and material modifications. Firstly, the authors seamlessly integrate computer-aided design (CAD) and computer-aided engineering (CAE) by capitalizing upon isogeometric analysis (IGA). Hence, the authors can easily modify the structural geometry only by changing the control point positions without tedious transformations between CAE and CAD models; and modify material characters simply based on knots vectors. Besides, more accurate solutions can be obtained because of the high order degree of the spline functions that are used as interpolation functions. Secondly, the authors advance the proposed independent coefficients method within IGA for fast numerical simulation of the modified designs, thereby significantly reducing the enormous time spent in repeatedly numerical evaluations. Findings This proposed scheme is efficient and accurate for modifying the structural geometry by simply changing the control point positions, and material characters by knots vectors. The enormous time spent in repeated full numerical simulations for reanalysis is significantly reduced. Hence, enabling quickly modifying structural geometry and material, and analyzing the modified model for practicality in design stages. Originality/value The authors herein advance and propose the IGA-IC scheme. Where, it provides designers to fasten and simple designs and modify structures (both geometric and material). It then can quickly in real-time obtain numerical solutions of the modified structures. It is a powerful tool in practical engineering design and analysis process for local modification. While this method is an approximation method designed for local modifications, it generally cannot provide an exact numerical solution and its effectiveness for large modification deserves further study.

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Section: Cae Modelmentioning

confidence: 99%

Isogeometric independent coefficients method for fast reanalysis of structural modifications

Ding

2019

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“…Finally, the use of solid-shell NURBS element offers the possibility to optimize through the thickness. The thickness optimization issue seems to be promising (Ding et al 2016), and it is investigated in the present work (see section 5).…”

Section: Imposing Shape Variationsmentioning

confidence: 99%

“…Indeed, the volume representation of the structure enables to optimize the thickness profile continuously by modifying the control point coordinates. In this respect, Ding et al (2016) highlight the benefits of making use of a NURBS solid element to accurately represent and analyze the thickness variations encountered in tailor rolled blanks. Thickness optimization becomes thus natural with the solid-shell approach and its inherent continuous transition between the thin and the thick case appears attractive in a large range of applications.…”

Section: Introductionmentioning

confidence: 99%

Isogeometric sizing and shape optimization of thin structures with a solid-shell approach

Hirschler

Bouclier

Duval

et al. 2018

Struct Multidisc Optim

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This work explores the use of solid-shell elements in the the framework of isogeometric shape optimization of shells. The main difference of these elements with respect to pure shell ones is their volumetric nature which can provide recognized benefits to analyze, for example, structures with non-linear behaviors. From the design point of view, we show that this geometric representation of the thickness is also of great interest since it offers new possibilities: continuous sizing variations can be imposed by modifying the distance between the control points of the outer surfaces. In other words, shape and sizing optimization can be performed in an identical manner. Firstly, we carry out a range of numerical experiments in order to carefully compare the results with the commonly adopted technique based on the Kirchhoff-Love formulation. These studies reveal that both solid-shell and Kirchhoff-Love strategies lead to very similar optimal shapes. Then we apply a bi-step strategy to integrate shape and sizing optimization. We highlight the potential of the proposed approach on a stiffened cylinder where the cross-section along the stiffener is optimized leading to a final design with smooth thickness variations. Finally, we combine the benefits of both Kirchhoff-Love and solid-shell formulations by setting up a multi-model optimization process to efficiently design a roof.

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“…Third, it is easier to refine the mesh than FEM and has greater accuracy in satisfaction of the essential boundary conditions. Due to these features, IGA has attracted many researchers to work in its theory and various engineering applications, such as shape and topology optimization [9][10][11][12][13][14], fluid mechanics [15][16][17] and fluid-structure interaction problems [18][19][20], contact mechanics [21][22][23], and damage and fracture mechanics [24][25][26] Yang proposed a matrix perturbation method for structural modal reanalysis [43,44].…”

Section: Introductionmentioning

confidence: 99%

“…T s y y y  y (14) the general solution of the balanced equations to satisfy the unbalanced equations. In order to use the SMW formula directly, the change in the stiffness matrix are converted to a low-rank form by using the Cholesky factorization of the initial stiffness matrix.…”

mentioning

confidence: 99%

Exact and efficient isogeometric reanalysis of accurate shape and boundary modifications

Ding

Cui

Huang

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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In the traditional design-through-analysis pipeline, geometric models and modifications are approximately represented and transformed with computational models. Besides, after each modification, the latest design often needs to be completely analyzed again leading to reanalysis. These procedures produce many errors and are extremely time-consuming. Therefore, in this paper, we propose a novel, and an exact and efficient isogeometric reanalysis methodology of accurate shape and boundary modifications that improves the totality of integration of design and analysis greatly. Geometric models and shape modifications are exactly represented and transformed. And, the corresponding computational models will change simultaneously when the geometric models are modified; thereby, reducing error and time in model representation and transformation. Furthermore, we extend and propose the isogeometric based exact reanalysis method termed Indirect Factorization Updating (IFU) with the combination of isogeometric based reanalysis. The method can efficiently obtain the exact solution of the modified structure, without solving the complete set of modified equations of the new structure. It is also applicable to all techniques for representing the CAD geometry model and complex problems. Several examples illustrate and verify the accuracy and efficiency of this proposed method; and furthermore, the larger the scale of the problem, the more advantageous the end result will be.

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Accurate analysis and thickness optimization of tailor rolled blanks based on isogeometric analysis

Cited by 27 publications

References 39 publications

Isogeometric independent coefficients method for fast reanalysis of structural modifications

Isogeometric independent coefficients method for fast reanalysis of structural modifications

Isogeometric sizing and shape optimization of thin structures with a solid-shell approach

Exact and efficient isogeometric reanalysis of accurate shape and boundary modifications

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