APPLICATION OF THE GFEM METHOD TO SOLVE STRUCTURAL MECHANICS PROBLEMS
Modeling of discontinuous fields with a standard finite element approximation presents challenges like restrictions on the finite element mesh to align with the discontinuity and the need for remeshing as the discontinuity evolves. The generalized finite element method (GFEM) was proposed as a numerical method to solve some of these challenges. It is based on the partition of unity framework. The GFEM method enriches the standard finite element shape functions locally with enrichment functions which are based on the physics associated with the problem. In this document, our aim is to utilize this method for modeling the nonlinear interface behavior of two surfaces in contact. The thesis is divided into two parts. In the first part, we explore the use of the generalized finite element method to solve a simple 1-D problem of a bar subjected to an axial body force. The force is applied in a highly localized location, and has high spatial derivatives and represents a significant challenge for traditional FEM approaches. We use the GFEM method to incorporate this local character in the underlying finite element mesh. This problem demonstrates the advantages of the GFEM method over the classical finite element method. The second part attempts to model a friction interface problem using the GFEM method. We consider a 1-D bar resting on a rigid support with friction at their interface. The bar is subjected to a uniform normal traction and a pull out point load. The analytical solution is described and the numerical framework for the GFEM method along with the solution algorithm is detailed. The GFEM method helps evaluate the stick-slip interface more efficiently (w.r.t number of degrees of freedom needed). The solution provides an insight into the selection of enrichment function and enrichment nodes.
School:University of Cincinnati
School Location:USA - Ohio
Source Type:Master's Thesis
Keywords:gfem friction enrichment
Date of Publication:01/01/2005