7. Conclusion
In this work, we have adopted the Nitsche method to develop the NURBS-based isogeometric analysis of multi-patch plates, which are discretized into non-conforming mesh along the interfaces. The presented method relieves us from the complicated coupling operation that often occurs in isogeometric method in order to obtain conforming mesh, which is time-saving and straightforward. The Reissner–Mindlin plate theory has been employed to analyze some classical plate models and a complex cantilever plate model. Analytical solutions in Kirchhoff hypothesis, numerical solutions of singlepatch models in Mindlin theory and results from the ABAQUS hexahedral element have been used to make comparison. In the comparison with different variables in classical thin plate, we find that solutions in Mindlin theory are slightly different with that in Kirchhoff theory because of the augmentation of shear deformation terms to the total potential energy functional. Meanwhile, for the same model, the results obtained from non-conforming situations coincide with that from single patch in Mindlin theory under the framework of isogeometric analysis. Optimal convergence rate can be achieved with Nitsche method. The results in different examples show the robustness, accuracy and high-efficiency convergence of Nitsche method in conjunction with isogeometric method. We investigated the numerical examples with single-patch, two-patch and four-patch plates, and limited the contributions to the linear elastic problems. More complex geometries with non-conforming multi-patches and trimming patches are frequently designed in practical use. Thus, future studies will focus on the complex geometries built with non-conforming and trimming multi-patches, and the extension of this method to non-linear problems.
