Abordagem isogeométrica para o estudo da estabilidade de compósitos laminados considerando falha progressiva

Abstract

Buckling is very important to the design of laminated plates and shells, as these structures are usually very slender. The study of the post-critical behavior allows classifying the stability loss, evaluating the load capacity of the structure and quantifying its sensitivity to initial imperfections. There are many papers available in the literature studying the stability of laminated plates and shells, including in the determination of post-critical path. However, these studies generally do not include material failure considering that the loss of stability occur in the elastic range. In practice, even in the case of thin-walled structures, material failure can affect the post-buckling behavior. The interaction between the sources of nonlinearity may decrease the loading capacity of the laminate. The Isogeometric Analysis (IGA) is a recent numerical method similar to the Finite Element Method (FEM), but that uses for displacement interpolation the same functions used in geometric modeling and CAD (e.g. BSplines and NURBS). The use of these functions allows the representation of the exact geometry independent of the discretization level used to approximate the displacement field. This work presents an isogeometric formulation for geometric and material nonlinear analysis of laminated plates and shallow shells. Marguerre theory is adopted to represent shallow shells with moderate displacements and rotations. In material nonlinear analysis, instantaneous degradation models are used. Examples with focus on determination of buckling loads and post-critical behavior of laminated plates, with and without material nonlinear analysis, are presented. In sequence, a study of stability of shallow shells is shown. Also, it is observed that the use of first ply failure approach can lead to conservative designs for laminated shallow shells, since the onset of failure can occur at a level considerably lower than the critical load or the limit load of these structures.