Errors Estimation of Different Numerical Integration Techniques on Stiffness Matrix and Stress Intensity Factor in XFEM

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Errors Estimation of Different Numerical Integration Techniques on Stiffness Matrix and Stress Intensity Factor in XFEM

Original Article, C42
Ghohani Arab H, Ghasemi M.R.
Journal. Civil Eng. Urban. 3(5):265-278. 2013
 

ABSTRACT:One of the new methods in the analysis of cracked structures is extended Finite Element Method (XFEM). In this method, unlike the conventional finite element method to calculate the integral of stiffness matrix using Gauss quadrature rule, accuracy of stiffness matrix of cracked elements is reduced. This article builds on the relationship between errors in the calculations if one uses different methods to calculate the stiffness matrix integral. The three methods of integration used and presented here are trapezoidal rule integration, Gauss quadrature integration and sub element rule integration. The average stiffness matrix error and maximum stiffness matrix errors were considered as the assessing criteria. L2-norm and energy norm criteria were also used. Finally accuracy of stress intensity factor (SIF) determined by XFEM were compared with different integration rules conventionally used in the literature.
Keywords:Gauss Quadrature Integration, SIF ,Stiffness Matrix, Sub Element Rule Integration, Trapezoidal Rule Integration, XFEM

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