Acta Mechanica Solida Sinica

, Volume 20, Issue 1, pp 87–94

# Stress intensity factors calculation in anti-plane fracture problem by orthogonal integral extraction method based on FEMOL

• Yongjun Xu
• Si Yuan
Article

## Abstract

For an anti-plane problem, the differential operator is self-adjoint and the corresponding eigenfunctions belong to the Hilbert space. The orthogonal property between eigenfunctions (or between the derivatives of eigenfunctions) of anti-plane problem is exploited. We developed for the first time two sets of radius-independent orthogonal integrals for extraction of stress intensity factors (SIFs), so any order SIF can be extracted based on a certain known solution of displacement (an analytic result or a numerical result). Many numerical examples based on the finite element method of lines (FEMOL) show that the present method is very powerful and efficient.

## Key words

anti-plane problem Hilbert space eigenvalue eigenfunction orthogonal relationship stress intensity factor finite element method of lines

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