An isogeometric formulation for material and geometric nonlinear analysis of functionally graded plates

Abstract

Composite materials recent spotlight is due to presenting a wide range of applications throughout many industries. Functionally Graded Materials (FGM) are a specific class of composites, presenting a smooth and continuous volume fraction gradation of their constituents. Due to the modernization of both machinery and methodologies associated to their fabrication, the FGM are receiving a growing attention in academic research. Functionally Graded Materials effective elastic properties vary along with the volume fractions, being evaluated by the employment of adequate micromechanical models. Due to the associated complexity, the development of analytical solutions for FGM problems is usually impossible. Thus, it is necessary to employ computational methods in order to obtain approximated solutions, such as the Finite Element Method (FEM) and the Isogeometric Analysis (IGA). This work employs both geometric nonlinearity, to include the structural effect of large displacements, and material nonlinearity, to allow the consideration of elastoplastic behavior. Regarding FG structures, the Tamura-TomotaOzawa model is used to estimate the effective plastic properties. Therefore, a 3D formulation that enables the consideration of tridirectional gradation for solids of any geometry is presented. Regarding plate problems, kinematic structural theories are used to enhance the model analysis efficiency. In this work, a novel NURBS-based Quasi-3D isogeometric formulation using a degenerated solid approach is developed. By presenting an integration over the volume, the same material nonlinearity algorithms for 3D models can be adopted. The presented formulations are employed in multiple types of analyses, considering multiple geometries, boundary conditions, FGM constituents and volume fraction profiles. Numerical examples present a close agreement with the literature for every formulation. Results show that the novel Quasi-3D approach is able to accurately represent both material and geometric nonlinear behavior in FG plates.