Análise Isogeométrica de Placas com Gradação Funcional utilizando uma Teoria de Alta Ordem

Abstract

Functionally Graded Materials are composite materials with a gradual and continuously varying composition through a desired direction. Due to this characteristic, they present a mechanical advantage when compared to other composite materials, culminating in its utilization across several industries, such as ballistics and aerospace. Thereby, the structural analysis considering the Functionally Graded Materials is a high relevance topic within the academic research ambit throughout the world nowadays. This document proposes the static analysis process of one-dimensional and two-dimensional structures by using a NURBS based isogeometric formulation. The governing equations of the problems are dictated by the employment of the Third-Order Reddy Theory, which can exactly present the transverse shear effects along the thickness, disregarding the utilization of any correction factors, unlike the First-Order Shear Deformation Theory. The application of this theory is thoroughly discussed in this document, once it is not a trivial procedure. Besides that, it is valid to highlight the importance of an adequate modelling of the Functionally Graded Material. As it is a composite material with a varying composition, it is necessary to determine beforehand its components and the volume fraction equation along the thickness direction. However, one of the most important variables to be considered is the variation profile of the effective properties throughout the gradation, that is determined by a micromechanical model. To support this discussion, the Voigt, Mori-Tanaka and Self-consistent models will be used. The formulation used was previously validated by comparison with the literature, returning consistent results to the many situations brought by the examples, serving as basement to the necessary discussions. In the results, some highlighted topics of the Third-Order Reddy Theory are discussed, such as the shear locking, the differences between the displacements given by it and by the First-Order Theory and the shear stress variation profile along the cross-section, besides presenting an important deliberation about the right choice of the micromechanical model.