The development of mortar method for the non-conforming multi-patch elastic problems in isogeometric analysis

Abstract Isogeometric Analysis (IGA) leverages Non-Uniform Rational B-Splines (NURBS) for complex geometries, offering an attractive alternative to traditional Finite Element Analysis (FEA). However, connecting NURBS patches in IGA often requires non-conforming interfaces. The Mortar method addresses this challenge by efficiently coupling such interfaces in solving Partial Differential Equations (PDEs). This work presents a novel development of the Mortar method tailored explicitly for non-conforming multi-patch elastic problems in IGA. We introduce a novel formulation for the coupling coefficient within the Mortar method, ensuring accurate solution transfer across non-matching interfaces. The efficient implementation of this method in the IGA framework is also presented. The effectiveness of the proposed method is demonstrated through numerical examples, showcasing its ability to handle complex geometries with significant computational speedup compared to conforming patches. Validation is performed using established benchmark problems in linear elasticity. Finally, we discuss the advantages and limitations of the proposed Mortar method, highlighting its potential for practical engineering applications. We also identify promising avenues for future research in this area. This work contributes significantly to developing robust IGA techniques for complex engineering problems involving multi-patch domains. It provides a valuable resource for researchers and practitioners seeking efficient solutions for elastic analysis using IGA.