Análise isogeométrica estendida acoplada à técnica global-local

Abstract

Isogeometric Analysis (IGA) has been shown to be a very efficient and effective method of solving problems of interest to engineering. When compared to the Finite Element Method (FEM), the IGA presents advantages in the exact representation of the problem geometry, the possibility of using the basis functions for the creation of the model geometry and analysis of the solution and the creation of refined meshes in an automated way to the solution analysis. The eXtended Isogeometric Analysis (XIGA) provides an expansion of the solution space of IGA, incorporating discontinuous resources into it, similar to what the Generalized/Extended Finite Element Method (G/XFEM) makes to the FEM methodology. The global-local technique aims to create a customized local enrichment function for the problem analyzed, making it more coherent with the phenomenon studied and less costly for the solution procedure. In this work, a new approach was developed, combining the global-local concepts with the characteristics of XIGA, named here XIGA GL (eXtended Isogeometric Analysis with global-local enrichment). The IGA can be used locally or globally, providing a better-conditioned stiffness matrix and improving the solution's accuracy and convergence rate. The implementation of this methodology was carried out on the computational platform INSANE (INteractive Structural ANalysis Environment) developed in the Department of Structural Engineering (DEES) UFMG. Several models were presented to validate the implementation carried out and also attest to the advantage of using XIGA GL in terms of the accuracy of the solution and conditioning of the stiffness matrix with savings in the models' degrees of freedom.