X‐FEM in isogeometric analysis for linear fracture mechanics

TLDR

The extended finite element method (X‑FEM) is an accurate, robust technique for fracture mechanics, traditionally applied with linear basis functions but also explored with quadratics. This study incorporates X‑FEM into isogeometric analysis to achieve higher‑order convergence in linear fracture mechanics. The authors implement the X‑FEM formulation using NURBS‑based isogeometric elements, enabling higher‑order basis functions. Compared to conventional finite elements of the same degree, NURBS‑based isogeometric X‑FEM attains equal asymptotic convergence and accuracy while reducing degrees of freedom, with results presented for linear to quartic NURBS basis functions. © 2011 John Wiley & Sons, Ltd.

Abstract

Abstract The extended finite element method (X‐FEM) has proven to be an accurate, robust method for solving problems in fracture mechanics. X‐FEM has typically been used with elements using linear basis functions, although some work has been performed using quadratics. In the current work, the X‐FEM formulation is incorporated into isogeometric analysis to obtain solutions with higher order convergence rates for problems in linear fracture mechanics. In comparison with X‐FEM with conventional finite elements of equal degree, the NURBS‐based isogeometric analysis gives equal asymptotic convergence rates and equal accuracy with fewer degrees of freedom (DOF). Results for linear through quartic NURBS basis functions are presented for a multiplicity of one or a multiplicity equal the degree. Copyright © 2011 John Wiley & Sons, Ltd.