NURBS-based modeling and analysis for free vibration and buckling problems of in-plane bi-directional functionally graded plates

In this article, a novel idea of utilizing a non-uniform rational B-spline (NURBS)-based material mesh independently defined with the analysis mesh to represent the material distribution is introduced to free vibration and buckling problems of in-plane bi-directional functionally graded (IBFG) plates. Two power-law material models with the symmetrical and asymmetrical volume fraction distribution are proposed as the first experiment. By applying the k-refinement scheme, the C0-continuous condition at symmetrical interfaces of material profiles can be easily achieved, while material gradations are still guaranteed elsewhere due to the outstanding advantage of material NURBS basis functions in controlling continuity. Either the rule of mixture or the Mori–Tanaka scheme is then used to estimate effective material properties. The analysis mesh is constructed by generalized shear deformation theory (GSDT)-based isogeometric analysis (IGA) for exactly modeling geometrical domains and approximately solving unknown solutions in finite element analysis (FEA). Accordingly, the C1-continuous requirement of the Galerkin isogeometric finite element model is simply met owing to the possibility of flexibly fulfilling high-order derivatives and continuity of analysis NUBRS functions. Additionally, the present formulation is also completely free from shear correction factors, yet still considering shear deformation influences. Several numerical examples are presented to demonstrate the performance and effectiveness of the proposed method. The effects of material gradations, aspect ratios, and different boundary conditions on IBFG plate responses are examined in detail as well.