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Abstract <p>This paper develops an adaptive extended isogeometric analysis (XIGA) based on locally refined Non-Uniform Rational B-Splines (LR NURBS) for static, free vibration, and buckling analyses of cracked Kirchhoff-Love thin plates. The Kirchhoff-Love theory offers the advantage of requiring only deflection unknowns instead of rotation unknowns, thus reducing the number of degrees of freedom. By leveraging the high-order continuity properties of XIGA, this approach satisfies the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11964_2025_9052_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\mathcal{C}}^{1}}\)</EquationSource> <!--MechSol2460628Yuan-m1--> </InlineEquation>‑continuity required by the Kirchhoff-Love theory and addresses the third-order derivative problem encountered when calculating stress intensity factors (SIF) using the interaction integral method. By introducing enrichment functions, XIGA achieves mesh independence from crack configurations, thereby enhancing the efficiency of fracture problem computations. This method utilizes the local refinement capabilities of LR NURBS and implements Zienkiewicz and Zhu’s recovery technique to guide the generation of adaptive meshes within the computational domain. To validate the accuracy and effectiveness of the proposed method, several benchmark problems related to Kirchhoff-Love plates are presented.</p>

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Statics, Free Vibration, and Buckling Analyses of Cracked Kirchhoff-Love Thin Plates Using Adaptive XIGA

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • H. Yuan,
  • K. Bao,
  • T. Bao,
  • W. Wang

摘要

Abstract

This paper develops an adaptive extended isogeometric analysis (XIGA) based on locally refined Non-Uniform Rational B-Splines (LR NURBS) for static, free vibration, and buckling analyses of cracked Kirchhoff-Love thin plates. The Kirchhoff-Love theory offers the advantage of requiring only deflection unknowns instead of rotation unknowns, thus reducing the number of degrees of freedom. By leveraging the high-order continuity properties of XIGA, this approach satisfies the \({{\mathcal{C}}^{1}}\) ‑continuity required by the Kirchhoff-Love theory and addresses the third-order derivative problem encountered when calculating stress intensity factors (SIF) using the interaction integral method. By introducing enrichment functions, XIGA achieves mesh independence from crack configurations, thereby enhancing the efficiency of fracture problem computations. This method utilizes the local refinement capabilities of LR NURBS and implements Zienkiewicz and Zhu’s recovery technique to guide the generation of adaptive meshes within the computational domain. To validate the accuracy and effectiveness of the proposed method, several benchmark problems related to Kirchhoff-Love plates are presented.