Análise isogeométrica de placas e cascas de material com gradação funcional utilizando elementos de Bézier

Abstract

This work deals with the stability and geometrically nonlinear analysis of functionally graded structures considering thermomechanical loads. Aspects such as the critical load and post-critical path of functionally graded plates and shallow shells were studied. The modeling of these structures was performed using Isogeometric Analysis (IGA), which is a numerical method of structural analysis that uses as approximation functions the same functions used by CAD programs for geometry representation (e.g. Bézier, B-Splines, NURBS). IGA presents advantages such as exact geometry representation, ease of model refinement and simpler integration between CAD programs and structural analysis programs. However, this method presents problems in the union of the problem geometry modeling steps and the numerical analysis, due to the boundary representation paradigm adopted in CAD systems, which does not provide the parameterization of the interior of the analyzed region. An alternative to this problem is the use of Bézier triangular elements, as they enable the automated connection between the CAD model and the analysis model. The presented formulation is based on Reissner-Mindlin plate theory considering the transverse shear and Marguerre nonlinear theory of shallow shells. Given the above, this work evaluates the performance of Bézier triangular elements in different examples. In all tests, the elements presented satisfactory results and showed that no special integration technique was needed to combat the locking problem inherent to the adopted formulation, being used the full integration by Gaussian quadrature. Formulations that consider the thermal effects of functionally graded structures were developed and implemented in the academic software FAST. Examples available in the literature were used in order to validate the implementations. The results obtained were excellent and confirmed the correct implementation of the thermal effects. In studies of thermal buckling of functionally graded materials (FGM) structures, it was found that boundary conditions, volume fraction variation, and the homogenization method for the determination of effective properties have a strong influence on the critical buckling temperature and post-critical behavior of functionally graded structures.