Advanced finite element and isogeometric modeling for homogeneous and composite shells involving plasticity, large deformations, and warping

Abstract

The aim of this work is to ll in some gaps in the non-linear Finite Element (FE) analysis of shell structures, both on the modeling and the numerical computation sides. Apart from the classic FE approach, also the Isogeometric analysis is brought into play, exploiting its high continuity properties. After introducing the numerical methods for the solution of the structural problem in Chapter one, attention is focused on the main topic. Shell FEs are usually adopted for modeling slender structures that are naturally prone to large displacement/rotation and buckling phenomena, owing to the ratios between their geometrical dimensions. Nevertheless, the versatility of these FEs makes it possible to use them for modeling other kinds of structures where material non-linearity takes on equal if not even greater importance. It is the case of reinforced concrete structures, that guide the discussion in the second Chapter of this thesis. The use of a mixed four-noded FE, known as MISS-4, is extended to a plasticity-based material behavior, with an elastic perfectly plastic model based on the con nement-sensitive plasticity yield surface for modeling the concrete behavior and a uni axial elastic perfectly plastic behavior for the reinforcement bars. Geometric non-linearity is addressed in Chapter three, where the models for laminated composites are the heart of the discussion, with particular focus on those made of alternating sti /soft stacking sequences. The peculiar behavior of this kind of structures during the deformation process is represented by warping. The cross section is no longer planar and assumes a piece-wise linear nal con guration (zig-zag shape). Starting from the phenomenological observation that the shear strains tend to concentrate in the soft layers, while the sti ones assume a classic Kirchho -Love-like behavior, a Total Lagrangian hierarchical approach is proposed to enrich the Isogeometric Kirchho -Love shell model with warping functions arbitrary chosen by the user. The nal discussion, in Chapter four, concerns the numerical solution of the non-linear equilibrium equation in case of both material and geometric non-linearities. When modeling geometrically non-linear problems with displacement-based FEs, the iterative cost grows considerably with axial-membrane/ exural sti ness ratio. What makes the di erence in the iterative process is the nature of the iteration itself, more than the interpolation/ approximation choices in the formulation of the FE. New mixed iteration schemes (i.e. where stress and/or strains are assumed as primary variables along with displacements at local level) are proposed for both displacement-based and mixed FE, identifying for each case the best approach when elasto-plasticity is coupled to geometric non-linearity