Acta Mechanica Solida Sinica

, Volume 20, Issue 2, pp 149–162

# Computation of stress intensity factors by the sub-region mixed finite element method of lines

• Si Yuan
• Yongjun Xu
• F. W. Williams
Article

## Abstract

Based on the sub-region generalized variational principle, a sub-region mixed version of the newly-developed semi-analytical ‘finite element method of lines’ (FEMOL) is proposed in this paper for accurate and efficient computation of stress intensity factors (SIFs) of two-dimensional notches/cracks. The circular regions surrounding notch/crack tips are taken as the complementary energy region in which a number of leading terms of singular solutions for stresses are used, with the sought SIFs being among the unknown coefficients. The rest of the arbitrary domain is taken as the potential energy region in which FEMOL is applied to obtain approximate displacements. A mixed system of ordinary differential equations (ODEs) and algebraic equations is derived via the sub-region generalized variational principle. A singularity removal technique that eliminates the stress parameters from the mixed equation system eventually yields a standard FEMOL ODE system, the solution of which is no longer singular and is simply and efficiently obtained using a standard general-purpose ODE solver. A number of numerical examples, including bi-material notches/cracks in anti-plane and plane elasticity, are given to show the generally excellent performance of the proposed method.

## Key words

stress intensity factors finite element method of lines sub-region generalized variational principle ordinary differential equation solver

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© The Chinese Society of Theoretical and Applied Mechanics and Technology 2007

## Authors and Affiliations

• Si Yuan
• 1
• Yongjun Xu
• 2
• F. W. Williams
• 3
1. 1.Department of Civil EngineeringTsinghua UniversityBeijingChina
2. 2.Chinese Academy of SciencesInstitute of MechanicsBeijingChina
3. 3.Structural Engineering DivisionCardiff UniversityCardiffUK