Free vibration analysis of stiffened rectangular plate with cutouts using Nitsche based IGA method

摘要

The Nitsche based non-uniform rational B-splines (NURBS) isogeometric analysis (IGA) method is employed to study the free vibration of stiffened plate with holes. The plate with stiffeners is modeled by the Reissner- Mindlin theory and Timoshenko beam theory. Along the intersection lines between middle surface of plate and stiffeners, the plate is artificially divided into several non-overlapping NURBS patches, and stiffeners are located at the intersection lines. The holes are also constructed using several different non-overlapping NURBS patches along the common boundaries. Nitsche method is employed to glue different patches. Then, the free vibration analysis of stiffened plate with holes are conducted. One of the advantages of the presented method is that it is not necessary to identify the plate elements within which stiffener nodes located while the plate and stiffener need to be remeshed. The other advantage is that the presented method can be conveniently used to analyze the vibration of stiffened plate with multiple holes. Numerical examples are given to validate the correctness of presented method. The dimensionless frequencies and mode shapes of stiffened plate with holes or without holes are obtained by the present method and compared with the results that are available in the literature or those obtained using the ANSYS software. The results show that the effectiveness of the present method.