Isogeometric Analysis of Functionally Graded Plates using High-Order Theories

Functionally Graded Materials are composites, usually of ceramic and metal, in which the volume fraction of their constituents varies smoothly along an interest direction. These materials were initially proposed as a solution for thermal barriers development, but are currently used in different applications. The composition variation results in a gradual change in their properties, enhancing the performance of structures subjected to thermal and mechanical loads, but making structural analysis more complex. Plates, on the other hand, are three-dimensional flat structures in which the thickness is much smaller than their other two dimensions. Different theories have been proposed for structural analysis of plates. These theories can be grouped based on the considerations adopted for the behavior of transverse shear deformations. In this regard, there are the Kirchoff-Love Theory (also known as the Classical Plate Theory - CPT), which disregards the effect of these deformations, the Reissner-Mindlin Theory (also known as the First-Order Shear Deformation Theory - FSDT), which considers shear deformations constant throughout the plate thickness, and Higher-Order Shear Deformation Theories (HSDT’s), which consider a nonlinear variation of shear deformations through different approaches. Among these theories, the most robust and accurate ones are evidently the HSDT’s. However, it is important to clarify that they require the displacement field to have a C1 continuity, which is complex for isoparametric finite elements. Thus, Isogeometric Analysis emerges as a more viable alternative by employing high continuity elements based on Non-Uniform Rational B-Splines (NURBS) functions. Therefore, this paper presents a NURBS-based isogeometric formulation for buckling and free vibration analyses of functionally graded plates using a HSDTs. A series of tests were conducted to assess the accuracy of this formulation considering examples available in the literature with different geometries, boundary conditions, and materials. The obtained results present excellent agreement with the reference solutions for thin and thick plates.