This paper proposes a unified hybrid discretization and analysis framework that intrinsically enforces interfacial coupling at the element level through explicit corner-to-corner connectivity and the construction of hybrid basis functions. The framework is well suited for models with complex boundaries and fine geometric features. Directional connection rules are prescribed via a set of assumptions, under which linear and higher-order Lagrange curves as well as NURBS curves are employed to connect element corners, leading to three types of hybrid elements. By relaxing these assumptions, three orientation-independent hybrid element clusters are obtained, improving the versatility of the proposed discretization. Leveraging tensor-product construction and projective transformation, the general form of the hybrid-element displacement approximation is derived and discretized to obtain the associated basis functions. Additionally, the linear independence, partition of unity, continuity, and completeness requirements were verified, with all passing the standard patch test. Several 2D and 3D cases with complex interfaces demonstrate that the proposed hybrid method reduces discretization errors and yields accurate displacement and stress fields. In terms of convergence rate, the Type-RpL1L1 hybrid model exhibits a rate close to that of the linear FEA model, whereas the Type-<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$R_{p} L_{p} L_{p}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mi>p</mi> </msub> <msub> <mi>L</mi> <mi>p</mi> </msub> <msub> <mi>L</mi> <mi>p</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> and Type-<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$R_{p} R_{p} L_{p}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mi>p</mi> </msub> <msub> <mi>R</mi> <mi>p</mi> </msub> <msub> <mi>L</mi> <mi>p</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> hybrid models converge at rates comparable to the corresponding IGA model with the same basis degree. Moreover, for a fixed element count, the proposed hybrid models provide higher analysis accuracy than the corresponding FEA and IGA models of the same polynomial degree.

Mechanism study of hybrid discrete analysis with different curve connections between NURBS and Lagrange subdomain elements

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发表日期：

2026年4月27日

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Yanpeng Shang,
Ming Wei,
Long Chen

摘要

This paper proposes a unified hybrid discretization and analysis framework that intrinsically enforces interfacial coupling at the element level through explicit corner-to-corner connectivity and the construction of hybrid basis functions. The framework is well suited for models with complex boundaries and fine geometric features. Directional connection rules are prescribed via a set of assumptions, under which linear and higher-order Lagrange curves as well as NURBS curves are employed to connect element corners, leading to three types of hybrid elements. By relaxing these assumptions, three orientation-independent hybrid element clusters are obtained, improving the versatility of the proposed discretization. Leveraging tensor-product construction and projective transformation, the general form of the hybrid-element displacement approximation is derived and discretized to obtain the associated basis functions. Additionally, the linear independence, partition of unity, continuity, and completeness requirements were verified, with all passing the standard patch test. Several 2D and 3D cases with complex interfaces demonstrate that the proposed hybrid method reduces discretization errors and yields accurate displacement and stress fields. In terms of convergence rate, the Type-R_pL₁L₁ hybrid model exhibits a rate close to that of the linear FEA model, whereas the Type- $R_{p} L_{p} L_{p}$ $R_{p} L_{p} L_{p}$ and Type- $R_{p} R_{p} L_{p}$ $R_{p} R_{p} L_{p}$ hybrid models converge at rates comparable to the corresponding IGA model with the same basis degree. Moreover, for a fixed element count, the proposed hybrid models provide higher analysis accuracy than the corresponding FEA and IGA models of the same polynomial degree.