Geometrically nonlinear analysis of Reissner–Mindlin plates using multi-patch isogeometric analysis based on Nitsche’s method

Abstract

Within the isogeometric analysis framework, industrial products or complex shapes are represented using multiple NURBS patches, resulting in non-matching interfaces and introducing additional numerical challenges, particularly in scenarios involving nonlinear behavior. This paper introduces the application of Nitsche’s method to address interface coupling challenges presented in non-matching multi-patch configurations. A detailed formulation addressing geometric non-linearity in multiple Reissner–Mindlin plates is developed, and the resulting nonlinear equations are solved using the Newton–Raphson approach. The proposed formulation’s effectiveness is demonstrated by a series of numerical examples involving complex geometries represented by multi-patches with non-matching interfaces. These examples are validated against the analytical solutions and results obtained using the commercial finite element package, Abaqus.