Nitsche-based isogeometric approach for free vibration analysis of laminated plate with multiple stiffeners and cutouts

Abstract

On the basis of the first order shear deformation and Timoshenko beam theories, a general Nitsche-based isogeometric analysis (IGA) is developed for studying the free vibration behaviors of composite plates with/without stiffeners and cutouts. Firstly, the laminated plate with/without cutout is described by several non-overlapped NURBS patches. The stiffeners are placed on the common edges of adjacent patches and share the same control points with these sub-patch edges. Then, different patches are stuck together by the means of Nitsche method. Eventually, the proposed method is implemented for analyzing the free vibration of composite plates with/without stiffener and cutout. First of all, it avoids the discretization of the stiffener and the identification of plate elements where stiffener nodes are located at, that are required in finite element method and IGA. In addition, it can handle with laminated plate with multiple stiffeners and cutouts conveniently. At first, four meshing schemes with different element sizes are implemented to validate the good convergence and accuracy of the present method in case of laminated plate with stiffener. Then, rectangular, skew and elliptical plates without stiffener and cutout are considered and the obtained natural frequencies and mode shapes agree well with those reported in literature. Furthermore, results from composite plates with/without stiffener and cutout under different boundary conditions are analyzed by considering different lay-up numbers and orientations of fiber, shapes and numbers of cutout, orientation angles and numbers of stiffener.