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

Abstract

Abstract 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.