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A new variational approach for coupling of non-conforming patches in Isogeometric Analysis
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DOI：10.1016/j.compstruc.2025.108067.png)
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Abstract
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Isogeometric Analysis is known to be a powerful numerical method in bridging between Computer-Aided Design and Computational Mechanics by utilizing special spline basis functions for both geometric and field discretization, resulting in reduction of errors corresponding to geometric approximations in traditional Finite Elements Method. Moreover, it can satisfy higher-order continuity to ensure stability and accuracy. However, there are several challenges in dealing with multi-patch domains, especially in the case of non-conforming patches in establishing continuity across the patch interfaces. Existing methods such as the penalty method, Lagrange multipliers and Nitsche’s method often encounter several numerical issues such as ill-conditioned systems, saddle point problem and computational overhead. This study presents a novel variational formulation for coupling of non-conforming patches while preserving higher-order continuity without introducing new degrees of freedom. In addition, the proposed method ensures a symmetric system, guaranteeing stable and efficient implementation. The constraints are applied through the variational formulation and therefore, no other approach is utilized within the procedure. Some benchmark numerical examples are provided to demonstrate the performance, accuracy and effectiveness of the proposed method.
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