A Cut NURBS Element Method for the Isogeometric Analysis of Arbitrary Complex-Cutouts Laminate Reissner-Mindlin Plates

Abstract

The modeling of complex geometries with cutouts in NUBRS-based isogeometric analysis usually needs a multiple-patches strategy. It is still an obstacle because of the requirement of very specialized knowledge of computer-aided design (CAD) to generate a NURBS mesh. In this paper, a cut NURBS element method is proposed for the free vibration and buckling analysis of the complex-shaped laminate Reissner-Mindlin plate. Here, three major issues including the shearing locking, the representation of the cut objects, and the localized eigenmodes must be addressed. Firstly, in order to address these issues, an artificial shear correction factor is introduced to avoid shearing locking. Secondly, a level set approach on a structured NURBS mesh is used to produce the cut NURBS element as well as describe the arbitrary and crisp interface between the cut objects and the initial simple geometry through the thresholding of the level set value. Then, a segmented density method is adopted to represent the contribution of the solid, void, and cut NURBS elements. Finally, the different density interpolation formulas for element stiffness, mass, and geometrical matrices are introduced to overcome localized eigenmodes. The numerical results show the proposed method can effectively avoid the existence of shear locking and localized eigenmodes. By comparing with the results from other methods, the proposed method is proven to obtain highly accurate numerical results and effectively reduce computational cost.