Adaptive Isogeometric analysis for plate vibrations: An efficient approach of local refinement based on hierarchical a posteriori error estimation

Yu, Peng; Anitescu, Cosmin; Tomar, Satyendra; Bordas, Stéphane P.A.; Kerfriden, Pierre

doi:10.1016/j.cma.2018.08.010

Cited by 47 publications

(9 citation statements)

References 30 publications

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“…Recently, Anitescu et al [12] employed the GIFT idea in a high-order PHTsplines formulation for problems of 2D and 3D elasticity and adaptive refinement. Peng et al [16] employed the GIFT formulation to study adaptive refinement for frequency analysis in vibration of Reissner-Mindlin plates. Note, that the formulation, developed in [16], is not locking-free.…”

Section: Geometry Independent Field Approximation (Gift)mentioning

confidence: 99%

“…Peng et al [16] employed the GIFT formulation to study adaptive refinement for frequency analysis in vibration of Reissner-Mindlin plates. Note, that the formulation, developed in [16], is not locking-free. Shearlocking phenomena can be addressed by developing approximation spaces for the displacements and rotations, that satisfy the Kirchhoff constrain at the limit of thickness tending to zero [17].…”

Section: Geometry Independent Field Approximation (Gift)mentioning

confidence: 99%

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Application of PHT-splines in bending and vibration analysis of cracked Kirchhoff–Love plates

Videla

Contreras

Nguyễn

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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In this work, we present an eXtended Geometry Independent Field approximaTion (X-GIFT) formulation for cracked Kirchhoff-Love plates. The plate geometry is modelled by Non-Uniform Rational B-Splines (NURBS) while the solution is approximated by Polynomial Splines over Hierarchical T-meshes (PHT-splines) and enriched by the Heaviside function and crack tip asymptotic expansions. The adaptive refinement is driven by a recovery-based error estimator. The formulation is employed for bending and vibration analysis. We compare different strategies for refinement, enrichment and evaluation of fracture parameters. The obtained results are shown to be in a good agreement with the reference solutions.

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Section: Geometry Independent Field Approximation (Gift)mentioning

confidence: 99%

Section: Geometry Independent Field Approximation (Gift)mentioning

confidence: 99%

Application of PHT-splines in bending and vibration analysis of cracked Kirchhoff–Love plates

Videla

Contreras

Nguyễn

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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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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“…The physical fields are exactly expressed and integrated without additional process of mesh generation. Up to now, IGA has been applied widely for vibration [39], buckling [40] and optimization of structures [41]. Here, the axisymmetric isogeometric analysis is presented to consider wave propagation in the inhomogeneous media.…”

Section: Introductionmentioning

confidence: 99%

Guided waves propagation in sandwich cylindrical structures with functionally graded graphene-epoxy core and piezoelectric surface layers

Han

2020

Jnl of Sandwich Structures & Materials

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As an ideal reinforcing nanofiller, graphene platelets (GPLs) can significantly improve physical properties of nanocomposites, which have attracted considerable attention for design and development of advanced lightweight nanocomposite structures in engineering. In this paper, a sandwich cylindrical structure is considered for dispersion properties of wave propagation by axisymmetric isogeometric analysis (IGA). The sandwich structure is composed of a functionally graded (FG) nanocomposite core and piezoelectric surface layers. Graphene platelets are dispersed in the interlayer by three typical distribution patterns through the thickness. In virtue of the symmetry and the advantages of isogeometric analysis, the sandwich cylindrical structure can be described by one-dimensional representation along the radial direction. Based on Hamilton’s principle, parameterized governing equation for wave propagation is obtained with the non-uniform rational B-splines (NURBS), which leads to an second-order eigenvalue problem. The modified wave finite element (WFE) method and the Chebyshev spectral element (SE) method are utilized to verify the reliability and accuracy of this approach. Then, the effects of several significant parameters of GPLs and geometric sizes of the sandwich structure on wave propagation characteristics are discussed in details. The results of this study are beneficial to deeply understanding and control of wave propagation in advanced piezoelectric composites for the applications in structural health monitoring and nondestructive evaluation.

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Adaptive Isogeometric analysis for plate vibrations: An efficient approach of local refinement based on hierarchical a posteriori error estimation

Cited by 47 publications

References 30 publications

Application of PHT-splines in bending and vibration analysis of cracked Kirchhoff–Love plates

Application of PHT-splines in bending and vibration analysis of cracked Kirchhoff–Love plates

Isogeometric independent coefficients method for fast reanalysis of structural modifications

Guided waves propagation in sandwich cylindrical structures with functionally graded graphene-epoxy core and piezoelectric surface layers

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