Análise e otimização de cascas laminadas considerando não linearidade geométrica e falha progressiva

Abstract

Composite materials are being extensively studied, as their use allows the design of structures that are lighter and stronger than their metal counterparts and feature good thermal insulation and fatigue resistance. Fiber Reinforced Composites (FRC), the focus of the present work, consist in stacking multiple laminae, each one consisting of unidirectional fibers embedded in a polymeric matrix. Laminated shells are used in many industrial applications, such as modern aircraft fuselages and wing systems, offshore structures, among others. Due to the many variables involved in the design of such structures, such as the number of layers (plies) and the mate- rial, thickness and fiber orientation of each layer, the traditional trial-and-error design procedure becomes arduous, which leads to the use of optimization techniques. In the structural analysis of laminated shells, numerical methods are commonly used, particularly the Finite Element Method (FEM), which is capable of modeling complex geometries, loads and boundary conditions. In order to determine the final load-carrying capacity of such shells, it is necessary to take into account not only the presence of large displacements (geometric non-linearity) but also its failure behavior (material non-linearity). In the present work, the geometric non-linearity was introduced by using the Total Lagrangian approach in a shallow shell finite element based on Marguerre’s Shell Theory. The element was implemented in an academic finite element software and multiple benchmark numerical examples were treated. The obtained results showed that the element is efficient when dealing with shells with small initial curvatures and moderately large displacements and rotations. The material non-linearity was considered by using progressive failure models, with the instantaneous degradation of the mechanical properties of layers that fail during the analysis. Three distinct progressive failure methods were formulated and implemented and the numerical examples yielded promissing results, with the correct determination of the ultimate failure load of laminates subjected to in-plane and bending loads, which were in good agreement with experimental and numerical results from the literature. The structural performance evaluated through the analysis procedure was then used in an optimization model in order to find the optimum stacking sequence for a given applied load. Here, a novel Genetic Algorithm with a hybrid computational parallelization scheme was proposed. The algorithm is based on the island model and can be executed in both clusters and personal computers alike. The algorithm was implemented and combined with the analysis procedures in the optimization of laminated shells considering both linear and non-linear analysis. In the linear examples, the algorithm was verified and the efficiency and execution time gains due to the parallel implementation were measured. The results show that the parallel algorithm not only runs faster than a sequential one, but also provides better results. In the non-linear examples, significant lighter and more efficient designs were obtained due to the consideration of the two types of non-linearities.