1D MATLAB XFEM Codes

Introduction

Here is a collection of MATLAB codes which are being offered for download in an attempt to help increase understanding of enriched finite element methods. Note that all codes were verified in MATLAB R2009a, thus older versions of MATLAB may have difficulties running parts of any of the following files.

All simulations in documentation or on the website were performed on a Pentium 4 3.0 GHz CPU with 4 GB of memory within MATLAB R2009a in x64 Windows XP.

1D Bi-Material Bar

The bi-material bar codes include symbolic derivations of the stiffness matrices for several enriched methods. In addition, codes are provided for bi-material bars modeled with single elements in four different enrichment schemes. Variables which can be modified include material properties (E1, E2), geometric properties (L, A, interface location) and applied loading (P).

EBE¹, Modified Absolute Value Enrichment (Stiffness Matrix) (Single Element)

XFEM², Modified Absolute Value Enrichment (Stiffness Matrix) (Single Element)

XFEM³, Shifted Absolute Value Enrichment (Stiffness Matrix) (Single Element)

XFEM³, Unshifted Absolute Value Enrichment (Stiffness Matrix) (Single Element)

Gallery

References

1. Pais, M., Kim, N.H., Peters, J. (2009) "Discussions on modeling weak discontinuities independent of the finite element mesh," 10th US National Congress on Computational Mechanics, Columbus, Ohio.

2. Moes, N., Cloirec, M., Cartraud, P., Remacle, J.F. (2003) "A computational approach to handle complex microstructure geometries," Computer Methods in Applied Mechanics and Engineering, 192, 3163-3177.

3. Sukumar, N., Chopp, D.L., Moes, N., Belytschko, T. (2001) "Modeling holes and inclusions by level sets in the extended finite-element method," Computer Methods in Applied Mechanics and Engineering, 190, 6183-6200.