18SC003 - Enriched Finite Element Methods


C. Armando Duarte, University of Illinois at Urbana-Champaign

Angelo Simone, Delft University

Alejandro M. Aragon, Delft University

Course description and objectives:

The finite element method (FEM) is undoubtedly the established procedure for solving problems to solid mechanics.  Yet, the application of FEM to many problems involving complex/evolving geometries rapidly exposes the main pitfall of the procedure: creating matching meshes is a tedious and error-prone process that can take most of the time in practical applications of the method.

Enriched FE methods such as the eXtended/Generalized Finite Element Method (X/GFEM) have received increased attention and undergone substantial development during the last decade.  Enriched methods ofer unprecedented flexibility in the construction of shape functions and corresponding approximation spaces.  With the propoer selection of enrichment functions, these methods are able to address many shortcoming and limitations of the classical FEM while retaining its attractive features.

In this short course we will delve into enriched finite eement formulations, presenting a survey on state-of-the-art methodologies for solving, in an elegant manner, problems that challenge the classical FEM.  Participants will be introduced to the approximation theory of these methods and its application to model discontinuities (material interfaces, cracks, voids).  Recent developments such as the Stable Generalized FEM (SGFEM) is also presented.  The newly introduced Discontinuity-Enriched Finite Element Method (DE-FEM) will also be discussed.  We discuss the implementation details of tehse methods in existing displacement-based FEm software.  A 3D implementation of X/GFEM will also be given to participants and thoroughly discussed.

By the end of this course, participants will:

  1. Understand state-of-the-art enriched finite element formulations and identify problems where such formulations could be used;
  2. Understand the computational challenges associated with the implementation of enriched method in standard displacement-based finite element packages

Who will benefit from this course?

Doctoral and post-doctoral students, researchers, academics as well as developers from industry.