Análise não-linear de estruturas de concreto por meio do método Element Free Galerkin

Abstract

Softening behavior materials such as concrete, rocks and geomaterials, are initially modeled as a continuum, elastic, isotropic and homogeneous medium. However, this class of materials is inherently heterogeneous. Nonetheless, as the loads are applied, and the deformations thereof,such materials no longer exhibit the same initial behavior. The numerical simulation of such materials, in particular performing a physically nonlinear Finite Element Method (FEM) analysis, often leads to numerically induced localization problems. Furthermore, a reasonable accurate FEM discretization usually restricts the material's randomspatial characteristics to the geometry of the finite elements employed. Also, taking into account, for instance, material discontinuities, usually requires expensive remeshing operations to track the cracking path. In order to overcome such difficulties, much work has been devoted into the development of constitutive modelling, where some parameter associated to the finite element's geometric dimensions introduced into the formulation. This, however, renders an artificial modelling, which is physically inconsistent. One of the contributions of this Thesis was presenting a computational implementation of a meshless method while reusing the maximum possible legacy code INSANE, a software platform originally developed for the FEM. Another contribution was a novel form of calculating the predictor and corrector incremental loading factor used in the nonlinear solver, in which the nodal parameters associated to theMLS approximation are used instead of the nodal displacements. The numerical experiments performed throughtout this work suggest that when performing a physically nonlinear analysis using the EFG, one should take the same caution measures usually taken when using the FEM in the same circunstances. Also, it was detected that, from all of the possible parameters necessary to the EFG, the choices of the size of the domain of inuence, the numerical integration scheme and the polinomialbasis used, are fundamental to performing a physically nonlinear analysis.