The Research On Isogeometric Analysis Of Plate Models With Non-conforming Multi-patch

Based on the Isogeometric method and finite element method, a new high-efficiency method is proposed to solve bending and free vibration problems for conforming and non-conforming plates. Nitsche method is employed to solve non-conforming problems and applied to the Mindlin and Kirchhoff theories. The validity, robustness and convergence of the presented method are verified by numerous numerical examples.The basis functions of exact geometrical model concurrently serve as the shape functions of analytical model in isogeometric analysis which realizes the seamless integration of Computer Aided Design (CAD) and Finite Element Analysis (FEA). As a significant research field in finite element analysis, plate and shell structures have been applied to the areas of vehicle, airplane, vessel, home furniture and so on. So far, isogeometric method has been successfully employed to the analysis of various plate structures generated with single patch and conforming multi-patch. However, it is still a cutting edge area to the application on non-conforming structures. The plate structures in engineering practice are usually built with non-conforming multi-patch. Extending the isogeometric analysis to these plate models, thus, becomes more important.With Nitsche method gluing non-conforming multiple Non-uniform Rational B-spline (NURBS) patches, isogemetric method is employed to solve static bending and free vibration problems in Mindlin moderately plate and Kirchhoff thin plate. The isogeometric stiffness equations are deduced from two types of plate theory and Nitsche's weak method, and abundant successful numerical cases are presented. The presented method can be directly used to analyze non-conforming models and save much time in the process of tedious mesh generation. It also offers effective idea and method to analyze complicated models in enginerring practice.