Análise da estabilidade de estruturas laminadas e de materiais com gradação funcional utilizando uma formulação isogeométrica

Abstract

The stability study of slender structures is of fundamental importance to guarantee the safety of the plates and shells, especially when high structural performances, like fiber-reinforced composite and functionally graded materials (FGM), are used. Isogeometric Analysis (IGA) is a recent technique that approximates the displacement field using the same functions used by CAD programs to geometry modeling (e. g. B-Splines and NURBS). IGA presents advantages such as the exact representation of the geometry and the model refinement simplicity. This work discusses isogeometric analysis plates and shallow shells of composite materials, focusing on fiber-reinforced composite laminates and functionally graded materials composed of metal and ceramic. The presented formulation is based on Reissner-Mindlin plate theory considering the transversal shear and Marguerre theory nonlinear analysis of shallow shells. It was verified that low-order approximation elements suffer from shear locking when full integration by Gaussian quadrature is applied. The use of higher order basis functions decreases, but do not eliminate, the locking problem. On the order hand, reduced integration techniques were applied with success to solve the locking problem for any approximation order. Excellent results were obtained from all analyzed examples. In the stability of laminated plates, it was observed that convergence and post-critical behavior depend on the composite layup. It was verified that angle-ply plates need to be more refined than cross-ply and isotropic plates. Furthermore, the critical loads of angle-ply laminates can be higher than the buckling loads of cross-ply laminates. However, angle-ply laminates present a smaller post-critical strength reserve. Laminated plates showed stable-symmetric bifurcation with small sensitivity to initial imperfections in all cases. The results showed the critical load of FGM plates increase with the ceramic volume fraction and that the boundary conditions have a strong influence on the stability of these plates. The presented IGA formulation also allowed to successfully study with the influence of thickness, layup and volume fraction variation on the nonlinear behavior and the stability of shallow shells.