Integrating multiplicative Nitsche's method with HIGA platform: Isogeometric analysis of hydraulic tunnels lining thickness

Isogeometric Analysis (IGA) is a novel numerical analysis method that can occupy the gap between geometrical and analytical models. IGA, when integrated with splicing algorithms, enables the splicing and coupling of multiple computational domains. This approach offers a novel solution for simulating complex hydraulic tunnels and similar practical engineering applications involving complex computational models. In this paper, a multiplicative Nitsche's method is proposed. The method determines the stabilization parameter $\alpha$ for contact models through a precise control coefficient computation equation, based on a chosen weighting parameter $\gamma$, and is integrated into the Hydraulic IsoGeometric Analysis (HIGA) platform. This method addresses the instability issues typically associated with the traditional Nitsche's method, which arise from empirically selected control parameters. Compared with the conventional Nitsche's method, multiplicative Nitsche's method significantly enhances the accuracy and stability of IGA while maintaining computational efficiency, according to the results of several 2D and 3D numerical examples. To demonstrate the engineering application prospects of multiplicative Nitsche's method, the proven applicability of IGA with the multiplicative Nitsche's method is showcased through a static analysis of a hydraulic tunnel model with complex geological features. The results demonstrate the method's capability to handle large-scale, multi-patch engineering problems, underscoring its potential for simulating and analyzing hydraulic tunnels under complex topographical and geological conditions.