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

Javier Videla; Felipe Contreras; Hoang Nguyen; Elena Atroshchenko

doi:10.1016/j.cma.2019.112754

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

Javier Videla, Felipe Contreras, Hoang Nguyen, Elena Atroshchenko^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

23 Citations (Scopus)

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Abstract

In this work, we present an eXtended Geometry Independent Field approximaTion (X–GIFT) formulation for cracked Kirchhoff–Love plates. The plate geometry is modeled 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.

Original language	English
Article number	112754
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	361
Early online date	29 Nov 2019
DOIs	https://doi.org/10.1016/j.cma.2019.112754
Publication status	Published - 1 Apr 2020

Keywords

Adaptive refinement
Extended isogeometric analysis
Fracture mechanics
Kirchhoff–Love plate theory
PHT-splines
Recovery-based error estimates

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10.1016/j.cma.2019.112754

NRL_44480Accepted author manuscript, 9.6 MBLicence: CC BY-NC-ND

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title = "Application of PHT-splines in bending and vibration analysis of cracked Kirchhoff–Love plates",

abstract = "In this work, we present an eXtended Geometry Independent Field approximaTion (X–GIFT) formulation for cracked Kirchhoff–Love plates. The plate geometry is modeled 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.",

keywords = "Adaptive refinement, Extended isogeometric analysis, Fracture mechanics, Kirchhoff–Love plate theory, PHT-splines, Recovery-based error estimates",

author = "Javier Videla and Felipe Contreras and Hoang Nguyen and Elena Atroshchenko",

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doi = "10.1016/j.cma.2019.112754",

language = "English",

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T1 - Application of PHT-splines in bending and vibration analysis of cracked Kirchhoff–Love plates

AU - Videla, Javier

AU - Contreras, Felipe

AU - Nguyen, Hoang

AU - Atroshchenko, Elena

PY - 2020/4/1

Y1 - 2020/4/1

N2 - In this work, we present an eXtended Geometry Independent Field approximaTion (X–GIFT) formulation for cracked Kirchhoff–Love plates. The plate geometry is modeled 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.

AB - In this work, we present an eXtended Geometry Independent Field approximaTion (X–GIFT) formulation for cracked Kirchhoff–Love plates. The plate geometry is modeled 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.

KW - Adaptive refinement

KW - Extended isogeometric analysis

KW - Fracture mechanics

KW - Kirchhoff–Love plate theory

KW - PHT-splines

KW - Recovery-based error estimates

UR - https://www.scopus.com/pages/publications/85075887777

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DO - 10.1016/j.cma.2019.112754

M3 - Article

AN - SCOPUS:85075887777

SN - 0045-7825

VL - 361

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

M1 - 112754

ER -

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

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Keywords

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