دانلود رایگان مقاله روش Nitsche برای تحلیل ایزوهندسی صفحه رایسنر-Mindlin با چند تکه غیر منطبق

Abstract

Nitsche method application in non-conforming plate is presented in the context of isogeometric analysis. Reissner–Mindlin plate theory is employed to build governing equation and stiffness matrix. We use this theory to solve the elasticity problems of various classical plate models, and compare the obtained results to those from single-patch models and the exact solutions in Kirchhoff theory. The solutions of problem involving the use of complex model are as well obtained using the same Reissner–Mindlin theory and compared to the results from finite element method. All models are built with NURBS (non-uniform rational B-spline) patches with non-conforming mesh along the common boundaries. The algorithms of knot insertion and order elevation are applied to enrich the basis functions of NURBS patches. The results of numerical examples show the accuracy, robustness and high convergence rate of this method.

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.