The Generalized or eXtended Finite Element Method (G/XFEM) has received increased attention and undergone substantial development during the last decade. This method offers unprecedented flexibility in the construction of shape functions and corresponding approximation spaces. With the proper selection of enrichment functions, the G/XFEM is able to address many shortcoming and limitations of the classical FEM while retaining its attractive features.

This short course will introduce participants to the approximation theory of G/XFEM and its formulation for three-dimensional fractures, polycrystalline and fiber-reinforced materials. The implementation of the G/XFEM in an existing FEM software is discussed. Recent developments such as the Stable Generalized FEM (SGFEM) and GFEMs for problems with multiple spatial scales of interest (GFEMgl) are also presented. Representative implementations of the G/XFEM in MATLAB illustrating the performance and practical aspects of the method will be discussed.

Bayesian Model Updating and Uncertainty Quantification: Theory, Computational Tools, and Applications

THIS IS A FULL DAY COURSE, 6 HOURS

Sunday, May 22, 2016
9:00am – 4:00pm, Featheringill-Jacobs Hall 313

Instructors:

Babak Moaveni, Associate Professor, Tufts University

Costas Papadimitriou, Professor, University of Thessaly, Greece

Course Abstract:

In simulations of complex physical systems, uncertainties arise from imperfections in the mathematical models introduced to represent the systems and their interactions with the environment. Such uncertainties lead to significant uncertainties in the predictions using simulations. Since such predictions form the basis for making decisions, the knowledge of these uncertainties is very important. The course will present the Bayesian model updating framework, the associated computational tools, and selected applications, along with the main challenges for quantifying and propagating uncertainties in complex structural dynamic simulations.