Análise e otimização de estruturas laminadas utilizando a formulação isogeométrica

Abstract

The laminate structures are made using a set of layers of a composite material stacked in a particular sequence in order to obtain a good structural performance. Currently, the analysis of laminated structures is mainly performed using the Finite Element Method (FEM). However, this method is not able to accurately represent complex geometries. An alternative to the FEM is the Isogeometric Analysis (IGA). IGA uses in the numerical analysis the same functions used by Geometric Modeling in CAD systems, as B-splines and NURBS, allowing an exact representation of the geometry regardless of model discretization level. This study used the isogeometric formulation based on NURBS for performing geometric nonlinear analysis of laminated structures. This formulation was implemented in an academic finite element software. Using an appropriate formulation of the method and the Object Oriented Programming (OOP), it was possible to minimize the changes made in the structure of the program for implementing the Isogeometric Analysis, including in laminated structures problems. The verification of the implementation is carried out based on available examples in literature. Several examples of linear and non-linear analyzes of structures with isotropic and laminated composite material were performed and they obtained excellent results. In laminated structures project, it is necessary to determine the number of layers of composite material and the characteristics of each layer (material, thickness, and fiber orientation). Because there are numerous possible combinations, the standard procedure based on trial and error is not appropriate, requiring the use of optimization techniques. Bio-inspired optimization algorithms, such as Genetic Algorithms and Particle Swarm Optimization, perform well in combinatorial optimization problems. Considering these aspects, the present study was developed a hybrid algorithm, based on the Particle Swarm Optimization and Genetic Algorithm methods for optimization of laminated structures. Some variants of the proposed algorithm were compared considering several optimization examples. A calibration process of the algorithm parameters was conducted in order to avoid biased results. These variants were used in the optimization of laminated plates and shells. In the case of shells, the isogeometric analysis was used as a structural analysis tool. The results showed that the proposed optimization method presents comparable performance with the genetic algorithms in traditional laminates optimization, where the orientation of the fibers is limited to a few angles. Moreover, the proposed method outperforms genetic algorithm in the optimization of dispersed laminates.