Finite Element Analysis and Fractal Remeshing in Geotechnics

Abstract

The purpose of this article is to show in a general way the mathematical basis of the fractal geometry and how this geometrical point of view is applied to problems which appear in the finite element analysis of complex civil engineering structures, where the definition of the size of the elements that compose the mesh is important, such that the discretization of the continuum medium be representative and consequently the obtained results be more reliable. To show the applicability of this technology, a fractal algorithm (developed by the authors) is presented, by means of which it is possible to do automatic efficient local remeshing of finite element meshes for twodimensional stress analyses. The results are compared with analytical solutions which are reproduced with excellent approximation.