Computation of Stress Intensity Factors Using Wavelet-Based Element

Xiang, Jiawei; Liang, Ming; Zhong, Yongteng

doi:10.1017/jmech.2016.2

Cited by 7 publications

(1 citation statement)

References 24 publications

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“…Later, the 1D and 2D nonsingular transformation matrix introduced by Xiang et al (2006) maps the wavelet expansion coefficient into the physical space, which greatly promotes the development of BSWI FEM (Xiang et al2007;Xiang et al2008). Xiang et al (2016) computed SIFs of 2D plane plate using based on the wavelet FEM. After that, Wei et al (2021) employed a wavelet-based BEM to calculate the band structures of two-dimensional phononic crystals and photonic crystals.…”

Section: Introductionmentioning

confidence: 99%

Construction of wavelet boundary element method for solving SIFs of two-dimensional plates

Yuan

Xiang

2022

Preprint

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Using one-dimensional (1D) scaling functions of B-spline wavelet on the interval (BSWI) as the interpolation functions, a wavelet boundary element method (WBEM) is presented to solve stress intensity factors (SIFs) for two-dimensional (2D) plates with singular stress fields. Firstly, to discrete the geometrical boundary, 1D wavelet-based elements are employed through the non-singular transformation matrices to transfer coefficients of wavelets expansions in the wavelet space to the physical space. The crack plate with symmetry is simplified according to symmetric conditions, and the asymmetric crack plate is divided into several subdomains to be solved according to the conditions of displacements continuity and traction equilibrium. Secondly, for the singular integrals in the WBEM, the gaussian integral and logarithmic gaussian integral are used to solve its by coordinate transformation matrices. Meanwhile, BSWI elements with good approximation characteristics and multi-resolution contain local asymptotic behavior of the stress fields at the tip of a crack, and can thus appropriately describe the singular near-tip stress fields for cracked plates. Finally, SIFs of crack tip are obtained by fitting the crack opening displacement. The performance of the method is investigated through the comparison of the results with six numerical cases of the plane stress elastic and bi-material plates.

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Section: Introductionmentioning

confidence: 99%