FSDT-Based Isogeometric Analysis for Free Vibration Behavior of Functionally Graded Skew Folded Plates

Abstract

In this paper, an isogeometric analysis (IGA) approach for free vibration analysis of functionally graded skew folded (FGSF) plates is presented for the first time. This method uses non-uniform rational B-splines (NURBS) as basis functions to provide a flexibility in refinement process. Furthermore, the IGA is able to exactly regenerate the geometry in comparison with the finite-element method (FEM), even at a coarse level of discretization. It is assumed that the mechanical properties of the FG metal–ceramic plates vary continuously through the thickness according to a power-law distribution. Also, the effective mechanical properties are captured by conventional rule of mixture. Regardless of the commonly used plates, the skew folded plates need to be modeled using two NURBS patches. The simple first-order shear deformation theory (S-FSDT) is employed to derive the equations of motion for each patch. After assemblage of the element matrices within each patch, the mass and stiffness matrices are modified and transformed to the global coordinates by employing an appropriate coordinate transformation. Subsequently, the bending strip method is utilized to accomplish the continuity conditions along the interface of the patches. The accuracy and reliability of the proposed IGA model are checked through comparison of the computed results with the available solutions in the open literature. The comparative study exhibits that the presented S-FSDT-based isogeometric formulation is promising to precisely predict the natural frequencies of FGSF plates with a low computational time. Eventually, a parametric study is performed and the variations of the natural frequencies with respect to the effective parameters such as crank angle, skew angle, length-to-thickness ratio, volume fraction and boundary conditions are examined.